Approaches to Coercion and Polysemy Oslo Studies in Language

Oslo Studies in Language 10 (2) / 2018

Alexandra Anna Spalek & Matthew Gotham (eds.)

General editors: Atle Grønn and Dag Haug

Issue editors:

Alexandra Anna Spalek University of Oslo Matthew Gotham University of Oslo Oslo Studies in Language 10 (2) / 2018

Alexandra Anna Spalek & Matthew Gotham (eds.)

Approaches to Coercion and Polysemy Oslo Studies in Language, 10(2), 2018. Alexandra Anna Spalek and Matthew Gotham (eds.): Approaches to Coercion and Polysemy Oslo, University of Oslo

Set in LATEX fonts Gentium Book Basic and Linux Libertine by Gotham and Spalek. Cover design by UniPub publishing house. Printed by Print House AS from camera-ready copy supplied by the editors. http://www.journals.uio.no/osla Contents

Introduction 1 Alexandra Anna Spalek & Matthew Gotham Polysemous posture in English: A case study of non-literal meaning 9 Katherine Fraser I’m done my homework: Complement Coercion and Aspectual Adjectives in Canadian English 29 Patrick Murphy Dispensing with Unwanted Polysemy: Verbal Idioms and the Lex- icon 47 Jan Wiślicki

Semelfactives 65 Markus Egg

Coercion in Languages in Flux 83 Robin Cooper Counting Constructions and Coercion: Container, Portion and Measure Interpretations 97 Peter R. Sutton & Hana Filip

Identity Criteria of CNs: Quantification and Copredication 121 Stergios Chatzikyriakidis & Zhaohui Luo

Coercion as Proof Search in Dependent Type Semantics 143 Eriko Kinoshita, Koji Mineshima & Daisuke Bekki

v vi CONTENTS Alexandra Anna Spalek and Matthew Gotham (eds.) Approaches to Coercion and Polysemy, Oslo Studies in Language 10(2), 2018. 1–7. (ISSN 1890-9639 / ISBN 978-82-91398-12-9) http://www.journals.uio.no/index.php/osla

introduction

ALEXANDRAANNASPALEK&MATTHEWGOTHAM University of Oslo

[1] background to this issue: the copo 2017 workshop Coercion is the term used for a variety of phenomena whereby the interpretation of an expression seems to vary depending on another expression that it stands in a predication or modification relationship with. Some examples of coercion that are prominently discussed in the literature are given in the following sentences and contrasts, along with possible interpretations.

(1) a. Fred began a book. began reading? b. Fred began an essay. began writing? (2) a. Fred is a good boy. morally good? b. Fred is a good pianist. good at playing? (3) a. Fred froze the water. b. Fred froze the bottle. the contents of the bottle? (4) a. Fred drinks coffee. b. Fred drank two coffees. two cups of coffee? (5) a. Fred played the sonata for 1 min. a complete sonata? b. Fred played the piano for 10 years. without pause?

Coercion is widespread and has often been remarked on within formal semantics, pragmatics and computational linguistics (Pustejovsky 1995; Egg 2003; de Swart 2011; Asher 2011; Dölling 2014; Piñango & Deo 2016; Lukassek & Spalek 2018; Nunberg 1979; Recanati 2004). However, the nature of coercion remains not well-understood in various respects and its theoretical account is still much discussed. Thus the workshop Approaches to Coercion and Polysemy (CoPo 2017), held at the University of Oslo on 20–21 November 2017, was organized so as to particularly focus on the following questions:

• To what extent do examples like (1)–(5) represent a unified phenomenon, and what constrains the availability of these kinds of enriched interpretations?

• What do these examples tell us about the nature of the lexicon, and the nature of predication? [2] spalek & gotham

– To what extent do we need lexical meaning to be context-dependent? – To what extent do we need a more sophisticated compositional system than is commonly assumed in formal semantics?

• How can the coerced interpretation be formally implemented?

It was our intention in organizing the workshop to create a forum to enable comparison of lexical, compositional and pragmatic approaches to these questions, and interaction between people coming from formal semantics, pragmatics and computational linguistics backgrounds. We were particularly interested in the interaction between coercion and the wider issue of polysemy, where a word may have more than one closely-related meaning. In the event, we had contributions looking at coercion and polysemy from the perspectives, and using the techniques, of psycholinguistics, corpus linguistics, syntax, distributional semantics and logical semantics. We had semantic analyses couched in simple type theory (Church 1940) but also in various extended type theories: Generative Lexicon (Pustejovsky 1995), Type Theory with Records (Cooper 2005), Type Composition Logic (Asher 2011), and variations on Martin- Löf’s intuitionistic type theory (Martin-Löf 1975, 1984). The programme of the workshop was as follows:

(i) Katherine Fraser: Polysemy of an English Posture Verb: A Case Study of Non- Literal Meaning

(ii) Patrick Murphy: ‘I’m done my homework’: Complement Coercion and Aspectual Adjectives in Canadian English

(iii) Jan Wiślicki: Dispensing with Unwanted Polysemy: Deriving Verbal Idioms by Co- ercive Typing

(iv) Nicholas Asher: Type Presuppositions and Fine Grained Types: From Coercion to Co-composition and a Finer Grained Look at Determiners

(v) Julia Lukassek: Coercion and Underspecification Integrated: The State-Event- Ambiguity of Aspectual Verbs

(vi) Markus Egg: Semelfactives

(vii) Bryan Leferman: The Aspectual Uniformity of Evaluative Adjectives

(viii) Emmanuele Chersoni, Alessandro Lenci & Philippe Blache: Modeling the Com- positional Cost of Logical Metonymies with Distributional Semantics

(ix) Robin Cooper: Coercion in Languages in Flux

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(x) Peter Sutton & Hana Filip: Coercion: Container, Contents and Measure Readings

(xi) Stergios Chatzikyriakidis & Zhaohui Luo: Identity Criteria of CNs: Quantifica- tion and Copredication

(xii) Eriko Kinoshita, Koji Mineshima & Daisuke Bekki: Coercion as Proof Search in Dependent Type Semantics

(xiii) Alexandra Anna Spalek & Matthew Gotham: Closing Comments and Discussion

Abstracts of the talks are available online at www.tinyurl.com/CoPo2017/.

[2] this special issue of oslo studies in language (osla) This special issue of OSLa contains eight of the contributions from the CoPo 2017 workshop. The first four articles in this volume present diverse rich empirical data, both documenting novel contexts where we find coercion (see Fraser and Murphy) and providing new theoretical accounts of well-known phenomena (see Wiślicki and Egg). The article that opens the volume provides a rich description of English posture verbs with a special focus on sit. Based on an in-depth exploration of English corpus data, Katherine Fraser illustrates that posture verbs are regularly ambiguous between their literal and non-literal readings, but that sit stands out in that its non-literal meaning does not merely encode a posture orientation in a metaphorical extension. Rather, it is regularly ambiguous between its primary meaning that describes a sitting posture and its secondary meaning that denotes an idle state, frequently with a negative connotation. In its secondary reading, sit puts no constraints on the position, but requires a location argument and restricts the state to be transitory, expressed either by means of progressive aspect or a secondary predicate. Fraser’s case study of English posture verbs thus points to the need for coercion as a regular reinterpretation mechanism. The second article reports on an eye-tracking experiment that examines an English dialectal construction, where coercion is at play. After testing processing times for the Canadian English I’m done/finished + noun phrase, Patrick Murphy reports increased processing times for the construction, when the noun phrase denotes an entity (e.g. comic), but not when it denotes an event (e.g. audition). These experimental results are reminiscent of what is known about aspectual verbs like finish, which trigger complement coercion with entity denoting nouns. Murphy interprets the additional processing cost of I’m done/finished the comic in line with a previous proposal by Fruehwald & Myler (2015), who argued that done and finished are adjectival versions of aspectual verbs that semantically select for event descriptions and trigger complement coercion in case of entity-denoting nouns. This psycholinguistic paper thus reports clear coercion effects for the Canadian

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English construction in support of Fruehwald & Myler (2015), and although it favors a type-shifting account, it leaves room for further theoretical discussion about the exact nature of the underlying semantic adjustments. The third article in the collection, by Jan Wiślicki, turns to idioms as a potential empirical challenge, likely to represent a disruption in the compositional system. It points out that, traditionally, idioms have been understood as non- compositional units that are stored in the lexicon as variants of polysemous lexical items. In opposition to this view, the author develops a novel way of analysing idioms, which fits with general linguistic processes. Based on a couple of well-known examples, Wiślicki shows that idioms can be understood as emerging from cyclic derivation and a kind of structural coercion, where syntactic derivation marks the proper points for lexicalization of the strictly idiomatic parts. Co- ercion in this paper is thus redefined in a novel way as a pre-semantic operation that occurs at the derivation level and serves in storing complex conceptual information that can become a lexicalized item. Combining these two mechanisms allows Wiślicki to give an explanation for the puzzling property of idioms which exhibit atomic behaviour alongside varying degrees of morphosyntactic accessibility and flexibility. The fourth article, by Markus Egg, discusses the class of semelfactive verbs and their variable aspectual properties in English and contrasts them with Rus- sian and Hungarian, which use richer verb morphology to indicate aspectual differences. After reviewing previous analyses of semelfactives, the author defends an account that treats semelfactives as denoting singleton eventualities, whereas the iterative use of semelfactives in English is derived as a result of aspectual coercion. In line with his previous works on other meaning adjustment phenomena (Egg 2003, for example), Egg models coercion in terms of a suitable operator (here: an iterative coercion operator), which avoids an impending aspectual mismatch for semelfactives that are the complement of durative verbs such as keep on or are modified by durative adverbials. By postulating a coercion operator for the iterative readings of semelfactives the author turns to a well-known semantic resource that helps to avoid compositional conflicts and dispenses with unnecessary polysemy. The final four articles in this volume explore various linguistic phenomena involving coercion and polysemy using extended type theories which, to a greater or lesser degree, make meaning adjustments something to be expected. The fifth article, by Robin Cooper, is a programmatic paper in which he outlines and motivates a view of linguistic semantics according to which it is a somewhat chaotic system subject to communicative constraints. On this view, coercion does not represent a disturbance in a highly formal and precise linguistic system, but rather a regularization of a highly flexible one. Cooper illustrates this perspective on language by means of two case studies, which he analyzes using Type Theory with Records

OSLa volume 10(2), 2018 introduction [5]

(TTR). The first is the phenomenon of what Krifka (1990) called ‘event-related readings’; for example, the interpretation of four thousand ships passed through the lock involving quantification not over ships, but over lock traversals. The second is the development of dynamic generalized quantifier theory, which is argued to be an example of where property coercions are part of the basic compositional semantic system, rather than something used only to generate additional interpretations for expressions. In the sixth article, Peter R. Sutton and Hana Filip provide an analysis in TTR of the various coercion interpretations that are available when a numerical quantifier combines with a mass noun, as in e.g. two beers. They note that the container interpretation (‘two glasses filled with beer’) and the portion interpretation (‘two portions of beer, each equivalent to the contents of one glass’) are easier to arrive at than the measure interpretation (‘beer to the amount of two glassfuls’)—which is some ways is surprising, since this discrepancy is not evident for the equivalent full pseudo-partitive two glasses of beer. They argue that the explanation is that the measure interpretation is derived by an additional coercion from the portion interpretation which, along with the container interpretation, is lexically encoded in a dot-type in the sense of Pustejovsky (1995). They motivate this analysis with data from copredication. The seventh article also deals with copredication data. Building on previous work that interprets common nouns as types and addresses copredication by means of dot-types in a subtype hierarchy, e.g. in which book is a subtype of phys • info which is a subtype of phys, Stergios Chatzikyriakidis and Zhaohui Luo expand their analysis to account for entailment data in copredication sentences that rely on e.g. books-as-physical-objects having different individuation criteria to books-as-informational-objects. The crucial element is to interpret common nouns as setoids, i.e. pairs consisting of a type and an equivalence relation. This then opens up the possibility that these equivalence relations are not necessarily preserved when moving from a type to any of its supertypes, which turns out to be exactly what is required to account for the entailment data in copredication. In the eighth and final article, Eriko Kinoshita, Koji Mineshima and Daisuke Bekki give an account of coercion behaviour that isn’t triggered by a type mismatch; an example would be an interpretation of the lion escaped in which the lion is interpreted as referring to an actor playing the part of a lion. Building on previous work in Dependent Type Semantics (DTS) that treats selectional restrictions as presuppositions, and presupposition satisfaction as resolved by type checking, they present an account according to which each predicate encodes a ‘transfer frame’, which expresses the presupposition that there is a contextually salient relation between the argument to the predicate and something satisfying the selectional restrictions of the predicate (where identity is always contextuallly salient).

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[3] reflections The contributions to the CoPo 2017 workshop, and this volume, show natural language to be a highly flexible and adaptable system. Whether or not we take this flexibility and adaptability to be evidence, as Cooper puts it in this volume, that ‘speakers of a natural language are constantly in the process of creating new language to meet the needs of novel situations in which they find themselves’, they indicate that meaning adjustments described as coercion and polysemy are too widespread and multifaceted to be viewed simply as the exception that proves the rule. This is the reason why more and more research in formal semantics, pragmatics and computational linguistics is making an effort to meet the needs of natural language and incorporate adjustment mechanisms, such as coercion, as a part of their regular inventory of tools. What the diversity of empirical data and theoretical approaches united in this volume however also illustrate, is that enriched interpretations and the nature of coercion are still a very rich area of ongoing research, on which diverse researchers differ in the way they understand, constrain and formalise coercion.

acknowledgments The CoPo 2017 workshop was funded jointly by the Department of Literature, Area Studies and European Languages, and the Department of Philosophy, Classics, His- tory of Art and Ideas, at the University of Oslo. It would not have been possible without the help of our session chairs and others who helped with practicalities: Elena Callegari, Atle Grønn, Nick Allott, Pritty Patel-Grosz, Kjell Johan Sæbø, Dag Haug and Cathrine Fabricius Hansen. We are also greatly indebted to our review- ers for both the workshop and this volume. The intellectual energy behind the workshop came from interactions in the SynSem research programme in the Fac- ulty of Humanities at the University of Oslo, which we will remember very fondly.

references Asher, Nicholas. 2011. Lexical meaning in context. Cambridge: Cambridge Univer- sity Press.

Church, Alonzo. 1940. A formulation of the simple theory of types. The Journal of Symbolic Logic 5(2). 56–68.

Cooper, Robin. 2005. Records and record types in semantic theory. Journal of Logic and Computation 15(2). 99–112.

Dölling, Johannes. 2014. Aspectual coercion and eventuality structure. In Klaus Robering (ed.), Events, arguments, and aspects: Topics in the semantics of verbs, 189– 226. Amsterdam: John Benjamins.

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Egg, Markus. 2003. Beginning novels and finishing hamburgers: Remarks on the semantics of to begin. Journal of Semantics 20(2). 163–191. doi:10.1093/jos/20.2. 163.

Fruehwald, Josef & Neil Myler. 2015. I’m done my homework – case assignment in a stative passive. Linguistic Variation 15(2). 141–168.

Krifka, Manfred. 1990. Four thousand ships passed through the lock. Linguistics and Philosophy 13. 487–520.

Lukassek, Julia & Alexandra Anna Spalek. 2018. Distinguishing coercion and underspecification in Type Composition Logic. In Uli Sauerland & Stephanie Solt (eds.), Proceedings of Sinn und Bedeutung 22, 71–87. ZAS.

Martin-Löf, Per. 1975. An intuitionistic theory of types: Predicative part. In H.E. Rose & J.C. Shepherdson (eds.), Logic colloquium ‘73 (Studies in Logic and the Foundations of Mathematics 80), 73–118. Amsterdam: North-Holland.

Martin-Löf, Per. 1984. Intuitionistic type theory. Naples: Bibliopolis.

Nunberg, Geoffrey. 1979. The non-uniqueness of semantic solutions: Polysemy. Linguistics and Philosophy 3(2). 143–184. doi:10.1007/BF00126509.

Piñango, Maria Mercedes & Ashwini Deo. 2016. Reanalyzing the complement coercion effect through a generalized lexical semantics for aspectual verbs. Journal of Semantics 33(2). 359–408.

Pustejovsky, James. 1995. The generative lexicon. Cambridge, MA: MIT Press.

Recanati, François. 2004. Literal meaning. Cambridge: Cambridge University Press. de Swart, Henriëtte. 2011. Mismatches and coercion. In Claudia Maienborn, Paul Portner & Klaus von Heusinger (eds.), Semantics: An international handbook of natural language meaning, 574–597. Berlin: de Gruyter. author contact information Alexandra Anna Spalek University of Oslo [email protected]

Matthew Gotham University of Oslo [email protected]

OSLa volume 10(2), 2018

Alexandra Anna Spalek and Matthew Gotham (eds.) Approaches to Coercion and Polysemy, Oslo Studies in Language 10(2), 2018. 9–28. (ISSN 1890-9639 / ISBN 978-82-91398-12-9) https://www.journals.uio.no/index.php/osla

polysemous posture in english: a case study of non-literal meaning

KATHERINEFRASER University of the Basque Country (UPV/EHU) abstract It has been observed that cross-linguistically the core posture verbs ‘sit’/ ‘stand’/lie can extend their meaning beyond the literal sense encoding posture or spatial orientation (see Newman 2002 for an overview). In the cognitive literature, the conceptual background of these extensions has been discussed, but up to now, there has been no discussion of the non-literal senses in the theoretical linguistic literature, including how the different senses are disambiguated. This paper supplements the cognitive descriptions of posture verbs, presenting data from an independent corpus study and proposing a formal analysis. The in-depth investigation of one English posture verb, ‘sit’, yields an empirical generalization that contributes to the discussion surrounding non-literal meaning.

[1] introduction The focus of this paper is the English verb ‘to sit’. This verb belongs to a group of verbs known as posture verbs, which canonically describe animate subjects in “at-rest” positions (Newman 2002). The stative meaning of ‘sit’ in its literal sense is ‘to be in a sitting position (at location z)’, like the human subject in (1-a). The meaning in the non-literal sense is ‘to be at z’, like the inanimate subject in (1-b).1

(1) a. Sam is sitting on the bench. literal b. The book is sitting on the bench. non-literal

For the literal use in (1-a) to be felicitous, the human subject must be at-rest, in a “relatively compact position” (Newman 2002: 2; cp. “elongated position”, either vertical or horizontal, for ‘stand’ or ‘lie’), her upper body must be vertical, and her buttocks must be located on the flat part of the bench (cp., e.g., ‘stand’, where the subject’s feet would have to be the body part on top of the bench). For the non-literal use in (1-b) to be felicitous, the inanimate subject must be not in

[1] The brackets following the example indicate whether the examples are from a web search [web], a Google Books result [books], or from Corpus of Contemporary American English (Davies 2008-) [COCA]; any em- phasis or indices in these examples are my own markings; examples without marked sources are my own [KF]. [10] katherine fraser

use, or “idle”, and physically located on the bench; there are no requirements for position when ‘sit’ is used in the non-literal sense. Utterances like (1-b) are not the same as, e.g., This house is sitting on a fortune., because the subject is not physically located on the fortune. This paper’s object of study is the locative, non-literal ‘sit’, particularly in English. Although posture verbs have been observed to be polysemous, non-literal uses have been largely ignored in the theoretical linguistic literature. Investigations of these verbs in the cognitive literature have focused on conceptual ideas behind their meaning (see Newman 2002 for a cross-linguistic overview; Lemmens 2002 for Dutch), frequencies of their literal meaning in English (Newman 2009; New- man & Rice 2004, inter alia) or a description of the various non-literal uses of one posture verb, i.e., Gibbs et al. (1994) on English stand. The current study builds upon these findings, and examines the complex lexical semantics of one English posture verb, ‘sit’. (2) is a naturally-occurring example of the use of ‘sit’ under investigation; the relevant predicate is boldfaced.

(2) It’s sort of ironic that the scotch is sitting there unopened after two experiments, and we don’t know whether it would be a good idea to toast these results or not. [COCA]

In the example, the boldfaced phrase contains a subject and the verb ‘sit’. This sentence is interesting because in the real, non-comic book, world, bottles cannot be in a sitting position. There is also an additional layer of meaning, contrib- uted by sitting itself. Namely, with the inclusion of this lexical item, an evaluative meaning is added to the descriptive one. In (2), the phrases it’s sort of ironic and we don’t know whether it’s a good idea are indicative of anxiety or uncertainty, normally negatively-valued emotions, regarding the unopened, unused, state of the scotch bottle. Without sitting, a sentence like (3-a) is odd with the ironic evaluation; a sentence like (3-b) is felicitous, with the addition of the aspectual adverb still.

(3) a. #It’s sort of ironic that the scotch is there unopened. b. It’s sort of ironic that the scotch is still there unopened.

One goal of this investigation is to examine the possible interaction of aspect and evaluation in non-literal ‘sit’. States are typically not felicitous in the progressive aspect. However, as observed by Comrie (1976), English states can sometimes appear with the progressive to encode a contingent, temporary state. The corpus study presented here will take a look at the differences in frequency of evaluation between when ‘sit’ is used with the progressive or simple past. This non-literal use of ‘sit’ is also interesting, as it is not restricted to idioms like in the closely-related German (4). In both of the utterances of (4), the subject is not located in or at the argument of the prepositional phrase; the interpretation

OSLa volume 10(2), 2018 polysemous posture in english: a case study of non-literal meaning [11] is idiomatic and not compositional. This paper will concern only non-idiomatic, non-literal uses of the posture verb, such as in (1-b) and (2).

(4) german a. Lovis saß zwischen Baum und Borke. Lovis sat between tree and bark ‘Lovis was faced with a difficult/unpleasant decision.’ b. Mattis saß auf einem Pulverfass. Mattis sat on a powder-keg ‘Mattis was in a precarious situation.’

The primary goal of this paper is to describe just what the non-literal sitting encompasses. Observations from the literature about non-literal sitting are presented, and then empirically looked at with a qualitative corpus search. The main finding of the exploratory study is that, in addition to an obligatory location argument, aspect influences when non-literal ‘sit’ can be used: a temporary interpretation is a condition on felicity; progressive morphology or a secondary predicate can fulfill this requirement. Secondarily, this paper is interested in the source of the evaluation. One hypothesis is that the source comes from aspectual coercion, but I will show how the evaluative component’s source is, in fact, not due to the sitting-state being coerced in the progressive. Within the goal of probing the lexical semantics, I am interested in what mechanism(s) are involved in disambiguating the different senses of ‘sit’. I will argue that the lexical entry for ‘sit’ comprises an animate subject, a posture predicate, an at-rest predicate, and an optional location slot. Following Asher (2011); Lukassek & Spalek (2018), I assume that there is one lexical entry for the possible senses. When the selectional restrictions of literal ‘sit’ aren’t met, i.e., when there is an inanimate subject, the meaning of ‘sit’ is reinterpreted, from the literal meaning of ‘an animate subject at-rest in a sitting position (at location z)’ to the non-literal meaning of ‘inanimate subject idle at location z’. In other words, coercion is at play here, and the literal meaning of at-rest in a sitting posture is reinterpreted as not in use (idle), in no particular posture. The structure of the paper is as follows. Section [2] presents an overview of posture verbs, both in their literal and non-literal senses. Section [3] describes the exploratory corpus study that was undertaken to better understand the construction. Section [4] discusses the findings, including the transiency constraint, and Section [5] concludes.

[2] posture verbs The cardinal posture verbs are ‘sit’, ‘lie’, and ‘stand’—not, e.g., ‘crouch’ or ‘lean’— because the former are the only posture verbs to exhibit cross-linguistic gram-

OSLa volume 10(2), 2018 [12] katherine fraser

maticalisation patterns (Kuteva 1999; Newman 2002). ‘Sit’, ‘lie’,or ‘stand’ are the core posture verbs used as locational or existential predicates and often as tense or aspect markers (see Newman 2002 for an overview). Kuteva (1999) proposes a path of grammaticalisation as in (5).

(5) posture > locative/existential > aspect

The literal use of an English posture verb represents the first stage of (5), which concerns the spatial configuration of animate subjects, and the non-literal use is in the second, where spatial configuration sometimes constrains the lexical choice but not always (more below). Dutch and Norwegian are examples of languages where posture verbs have been grammaticalised, becoming a functional word (see, e.g., Lemmens 2005; Fraser & Pots 2018 for Dutch and Lødrup 2002 for Norwegian). As is often the case for partially grammaticalised locational predicates (Comrie 1976), posture verbs are used as a progressive aspect marker, in addition to the posture and locative/existential uses; cf. (6).2

(6) Omdat ik achter een trein aan zit te hollen, heb ik de trein waar ik because I after a train at sit to run, have I the train where I eigenlijk in hoor te zitten gemist. actually in have to sit missed ‘Because I was running for a train, I missed the one that I actually had to be [sitting] in.’ [dutch, Lemmens 2005, p. 205]

This example includes two instances of zitten: the first, boldfaced, is in the periphrastic progressive construction, and the second, underlined is a simple locative use. The local linguistic context disambiguates the aspectual marker from the locative predicate: te ‘to’ is after the boldfaced auxiliary zit and before the underlined full verb zitten. The boldfaced ‘sit’ of the first clause is missing in the English translation because would contradict the main predicate’s semantics— sitting and running simultaneously is impossible; this first instance of ‘to sit’ in (6) is an example of a semantically-bleached, grammaticalised posture verb. In fact, Lemmens (2005, 189) reports that the posture verb is “essentially obligatory” in locational expressions; using zijn ‘to be’ in such utterances is very marked or even ungrammatical for some speakers. In English, the simple copula is preferred in locational expressions (Newman 2002), indicating that Dutch is further along than English on the path of grammaticalisation. This paper concerns the instances of ‘sit’ in locative, non-literal posture uses. Henceforth, the discussion will be centered on English. The locative use of ‘sit’ can be lexically ambiguous with the posture use. This can be seen in (7). The utterance in (7) is infelicitous because it forces the inter-

[2] All Dutch examples from Lemmens have been double-checked with a native speaker: Cora Pots (p.c.).

OSLa volume 10(2), 2018 polysemous posture in english: a case study of non-literal meaning [13] pretation that the second clause’s subject, book, is in a sitting position. As books are non-pliable, this is pragmatically odd.

(7) John was sitting on the floor #…and the book was, too.

The following subsections discuss the linguistic differences between non-literal and literal senses of core posture verbs. We will begin more broadly, looking at all three core verbs, before narrowing in on ‘sit’.

[2.1] Non-literal posture and its constraints

Before beginning the discussion on differences between non-literal and literal ‘sit’, let us define what it means to be literally sitting. As mentioned in the introduction, literal ‘sit’ describes an animate subject at-rest, in a posture of sitting. The relevant posture is to in a compact position, with a vertical upper body and the buttocks on/at a contextually-specified location. The position of the legs is not important; it is only important that the legs are positioned relatively perpendicular to the upper body. For an inanimate object to be described as in a sitting position, this object would also have to be compact in the sense that the upper and lower parts are perpendicular. This is in contrast to ‘stand’ or ‘lie’, both of which concern only an elongated posture.

For non-literal, non-idiomatic uses of core posture verbs, both the theme and location arguments are obligatory. Compare the literal uses, where the location can be felicitously omitted; cp. (8-a)/(8-b).

(8) (Non-)omissibility of location a. The woman is sitting (on the couch). literal b. My toothbrush is sitting #(in the sink). non-literal

Maienborn (1996) observed that when the locational PP is omitted in a posture verb construction, the posture of the subject becomes salient. As the woman denotes an animate subject, and can be in a sitting position, it is possible to omit the location in (a). In contrast, my toothbrush denotes an inanimate subject and not capable of sitting, so it is infelicitous for the posture meaning to be salient in (b). This shows us that, unlike the literal use, the non-literal use of sitting does not actually encode the meaning ‘to sit’. I propose location-omission as a diagnostic

OSLa volume 10(2), 2018 [14] katherine fraser

for disambiguating literal and non-literal posture.3 A second difference between the literal and non-literal senses is that the literal sense requires an animate subject. As we saw in (7) above, it is difficult to combine an inanimate subject with literal ‘sit’. Even with a more flexible subject, like a pillow in a pillow is sitting, there is a funny, forced, animate interpretation— and the utterance is marked. The other two core posture verbs, ‘lie’ and ‘stand’, also require an animate subject in their literal senses, although in the non-literal use (able to be disambiguated with the above location-omission test), the subject’s spatial orientation is still strongly encoded. I claim here that the literal sense of a posture verb encodes the body position of animate subjects, not inanimates, and propose the argument structure in (9) for literal posture verbs. This entry builds on Levin & Rappaport-Hovav (1995)’s entry, and includes an at-rest predicate, animate subject, posture predicate, and the optional location insights from above. The at-rest predicate is representat- ive of that state the subject is in. Namely, when in a sitting state, the subject is not moving around with their legs or whole body. Of course, it is possible to be involved in working or eating/drinking while sitting, but in those cases the legs are still at-rest.

(9) Literal posture = [ xanim [ idle-be & posture ([ at z ]) ]]

Posture is salient for the subjects of ‘lie’ and ‘stand’, even in the metaphorical extension (regardless of the subject’s animacy). According to Lemmens (2002), these are the maximal orientations for humans, being maximally elongated along the vertical or horizontal axis, and this maximality restricts variation in the spatial configurations they encode. Lemmens’ work is on Dutch, but English data supporting this can be seen in the sentences below.

(10) a. The papers are on the floor. b. The papers lay on the floor. c. #The papers stood on the floor.

[3] Relevant here is the event-external location, not the event-internal location. According to Maienborn (2003), event-internal locations modify the manner of the event, rather than describing the location. For example, in (i) the underlined event-internal location describes how the standing eventuality occurred (using the back flippers to prop itself up); whereas the boldfaced event-external location describes where it occurred (near the swimming pool).

(i) The sea lion stood on its back flippers next to the pool.

As the event-internal location adds additional information about the posture of the subject in the eventuality, it is odd to combine such a phrase with non-literal sit; cf. (ii).

(ii) #The bottle was sitting on its underside.

OSLa volume 10(2), 2018 polysemous posture in english: a case study of non-literal meaning [15] The pieces of paper in (10) are felicitous with lay, but not stood. This makes sense when one thinks about a sheet of paper: it is thin, having virtually no vertical dimension, so that the horizontal dimension is the salient one. In this way, something without a vertical dimension is not capable of standing, and instead is used with the appropriate horizontally-oriented verb, lying. These simple examples indicate that orientation can still be strongly encoded in some English posture verbs, even when used in a metaphorical extension. Interestingly, in contrast to ‘lie’ and ‘stand’, it is possible to felicitously combine ‘sit’ with an additional posture predicate. In the examples of (11), the second predicate, underlined, describes the orientation, and ‘sit’, the location.

(11) a. I am just glad I am seeing Sarah McLachlan Friday before the season starts, if I didn’t [sic] have something to do, I would be sitting at home pacing all weekend lol. I hope everyone has something to oc- cupy themselves for the weekend, I sure as hell gonna need it.[web] b. […] we passed markets full of colourful fruit; pineapples, bananas, and papayas sat stacked high on wooden tables. [web]

In (a) the predicate sitting at home is not actually interpreted as being in a seated position at one’s home. If that were the case, the addition of the second posture verb would be odd. However, it is this second verb pacing, which describe the relevant posture, while ‘sit’ is locative . Similarly, in (b), the underlined stacked high describes a vertically-oriented configuration, while ‘sit’ locates the fruits on tables. As such, these non-literal uses of ‘sit’ represent the second step in the grammaticalisation path (5), location/existence. Interestingly, there is another difference between non-literal ‘sit’ and ‘stand’/ ‘lie’ constructions: those with ‘sit’ carry an additional expectation about the idleness, in the sense that the sitting state is expected or wished to change at one point. The three sentences in (12) illustrate.

(12) a. The shark is sitting in its tank, waiting for the next feeding. b. The shark is lying in its tank (#waiting for the next feeding). dead c. #The shark is standing in its tank.

The first variant (12-a), with sitting, does not concern posture at all: the shark is not in a seated position but is idle, it is possible to append a continuation with content indicating a more active state is expected in the future. The situation changes with ‘lie’ in (12-b): the animal is at-rest, yes, but a future expectation is less plausible, as native speakers4 interpret the shark as being dead or asleep. In (12-c), the use of the posture verb is infelicitous for the simple reason that ‘stand’

[4] By informal survey.

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requires a vertical orientation and sharks, in the real world, do not stand, nor do they swim in a vertical orientation. These shark examples, as well as those in (11) above, demonstrate that (i) non-literal, locative ‘sit’ lacks a posture entailment and (ii) is accompanied by an evaluation. Considering the above, I propose the argument structures in (13) for the non- literal posture senses. Both entries allow animate or inanimate subjects, encode an “at-rest” state (idle), and require a location. The difference is that ‘stand’/‘lie’ (a) also encode the posture, while ‘sit’ (b) does not.

(13) Argument structure of non-literal, locative posture

a. ‘stand’/‘lie’ = [ x±anim [ idle-be & posture [ at z ] ] ] b. ‘sit’ = [ x±anim [ idle-be [ at z ] ] ]

The next subsection will look more closely at only non-literal ‘sit’, as it behaves differently from the other two core verbs. More specifically, this subsection will be concerned with the additional aspectual interaction.

[2.2] A closer look at non-literal ‘sit’ In addition to its core meaning of ‘idleness’ and locating its subject somewhere, the locative use of non-literal ‘sit’ has an inference concerning speaker evaluation of the sitting state, which seems to be related to the state’s temporal interval. This subsection will explore this further, first by comparing minimal pairs (with and without ‘sit’), then by adding aspectual particles such as still, and finally with a comparison to lexical aspect. To begin, the scotch example from the introduction is repeated here as (14); (a) is the original sentence from COCA and (b) is the modified sentence, without sitting. Underlined in these two sentences is an evaluative phrase, it’s sort of ironic. The adapted example (b) is intended to see whether an overt evaluation is felicitous with non-literal ‘sit’.

(14) a. It’s sort of ironic that the scotch is sitting there unopened after two experiments, and we don’t know whether it would be a good idea to toast these results or not. [COCA] b. #It’s sort of ironic that the scotch is there unopened …

Sentence (14-b) has an evaluation, but no sitting, and is marked; in informal terms, it feels like something is missing from the sentence. To get a better idea of what is going on, let us try this with another example; see (15)/(16).

(15) a. Alistairi hovered in mid water and started shaking the chum bag at the end of hisi flasher, with the sharkj sitting over hisi shoulder. Hei still hadn’t seen itj. I was a little worried with the sharkj so close […] Itj was stationary about a meter and a half off on hisi right, watching

OSLa volume 10(2), 2018 polysemous posture in english: a case study of non-literal meaning [17]

himi intently. [web; indices by me, KF] b. Alistair hovered in mid-water […] with the sharkj over hisi shoulder. Hei still hadn’t seen itj. I was a little worried with the shark so close.

(i) …Itj was stationary about a meter and a half off on hisi right, watching himi intently. (ii) …Itj was swimming slowly towards himi.

In (15-a), the writer describes an uneasy situation where his fishing companion, Alistair, was in close proximity to a shark. The writer explicitly says that they were worried about the shark being so close (underlined), and that it was in an stationary state (stationary) with the implication that the creature was waiting for its next move (watching him intently). When sitting is deleted, like in (15-b), the utterance is felicitous—even with the underlined evaluative content—but the inference about waiting or expecting a change is no longer so salient. For (15-b), it is possible to continue with either a sentence describing a stationary shark (i) or a moving one (ii); for (15-a), the swimming continuation would be marked. As it is possible that the evaluation’s source was the predatory nature of sharks, rather than the predicate ‘sit’, I tried this deletion test with a different context and a non-descript fish (16).

(16) {There are many varieties of fish, big/small, benign/dangerous : } a. The fish was sitting over his shoulder. I was worried what would happen next. b. The fish was over his shoulder. #I was worried what would happen next.

The continuation containing evaluative content is felicitous in (a), but not (b). In- terestingly, utterances like (14-b) and (16-b), without ‘sit’ but with an evaluation, can be “saved” with an aspectual particle like still. This is seen in (17).

(17) a. It’s sort of ironic that the scotch is still there unopened. b. The fish was still over his shoulder. I was worried what would happen next.

The particle still describes an eventuality that is asserted to have begun before the reference time and is inferred to end sometime after the reference time (see Löb- ner (1989); Krifka (2000) for a formal discussion of aspectual particles). That still improves the felicity of these two utterances which had had ‘sit’ deleted, suggests that non-literal, locative ‘sit’ has a similar inference. In other words, this use of ‘sit’ carries a meaning of transiency. As still is an aspectual particle, I was curious as to whether lexical aspect also

OSLa volume 10(2), 2018 [18] katherine fraser

interacts with the meaning. The progressive is notorious for its inability to have a non-temporary subject like cities or buildings (Dowty 1979). Additionally, it has been noted that the progressive is compatible with an evaluation, particularly in combination with states (Comrie 1976). The minimal pair in (18) shows how an evaluation is needed to combine a building as a subject with progressive ‘sit’.

(18) a. {Sam is describing where different institutions are located : } The library is (#sitting) on the corner of 45th street. b. {The local library was recently repainted neon orange. Sam, who hates orange, is telling a friend where it is : } The library is (sitting) on the corner of 45th street.

I propose that the differences seen above arise from the meaning that non-literal, locative ‘sit’ encodes: a temporary state, like waiting, which the speaker can eval- uate.5 In order to support this claim, I decided to look at the difference between progressive and simple past forms of non-literal, locative ‘sit.’ The next section will present this study.

[3] exploratory corpus study

For this corpus study, the two main research questions were (i.) what sort of context dependencies are there for non-literal ‘sit’? and (ii.) does it always co- occur with an evaluation? For the first, based on the descriptive generalisations above, at least a location is necessary. There is also an interaction with aspect, so it is possible that the sitting state must be temporally bounded. For the second question, my prediction was that it often occurred with a negative evaluation but I did not know if there was a pattern to the distribution. The following subsections will describe the methodology and answers to these two questions.

[3.1] Methodology The methodology for the qualitative corpus study was created after Spalek (2014, 2015), whose work also examined the non-literal use of polysemous verbs. Namely, I extracted sentences from the magazine and news categories in the Corpus of Contemporary American English (COCA). In the last update (December 2015), this corpus had “more than 520 million words in 220,225 texts”,6 as well as a user-

[5] I am being purposely vague in characterising the “evaluation”, mostly because I think it is more complex than a simple bad. For space reasons, I will leave this topic aside in this paper. [6] 533,788,932 words total; 110,110,637 words in the magazine category and 105,963,844 words in the news category [http://corpus.byu.edu/coca; last accessed May 2016].

OSLa volume 10(2), 2018 polysemous posture in english: a case study of non-literal meaning [19] friendly interface.7 While Spalek’s study explicitly included various argument structures, my investigation of sitting targeted only the ontology. This is mainly because it was already known that the relevant, non-literal, use has an inanimate subject argument; whether there the locative PP is necessary was a question for the study. Additional syntagmatic features like a lone preposition indicate irrelevant, overtly dynamic (i.e., encoding the actual spatial orientation) meanings of the posture verb. For this reason, the syntactic categorisation of Spalek’s approach is omitted here. The specific search query was as in (19), incorporating both forms of simple past and -ing. The first curly brackets contain the subject, with the part-of-speech (POS) tag nn*, for all nouns (excluding proper names). This tag prevents irrelevant results; in this case, of all results without a noun directly preceding the verb. The second curly bracket is the verb (phrase). When a word is enclosed in square brackets, like with [be] sitting, the command means that it should search for any form of that verb. Finally, in the third curly bracket, there is a minus sign followed by three prepositions separated by a vertical line, which is an or operator. The minus sign indicates that these prepositions were not included in the search.

(19) a. { nn* } { [be] sitting } { –around|down|up } b. { nn* } { sitting } { –around|down|up } c. { nn* } { [sit] } { –around|down|up }

The reason for having both [be] sitting and sitting was to reduce the possibility of extra factors. Namely, the intention was to eliminate the chance that a full verb phrase versus a participle affected the answers to the research question. Addi- tionally, the choice of a simple verb form was limited to the past tense, because an eventuality in the past can be analysed with respect to the temporal interval, while in the future or present, the endpoint of the interval is unknown. Also, the present encompasses also generic or habitual readings, an unneeded further complication for this exploratory study. The final bracketed part of the search query regards the avoidance of prepositions after sit. As noted in Newman & Rice (2004), around contributes an expressive meaning, which would have affected the analysis of expressive meaning and non-literal sit. The deliberate omission of down and up was to avoid any dynamic eventualities of assuming/exiting a seated position, which are different than the non-literal posture use being investigated here.

[7] The British National Corpus (BNC) was also considered, but due to its smaller size (96,263,399 words total; 7,261,990 words in the magazine category and 10,466,422 in the news category), and therefore less frequent instances of metaphorical ‘sit’, it was rejected as a source. Future work would ideally compare different dialects of English, instead of focussing solely on American English; since the investigation of ‘sit’ originally took place (Spring/Summer 2016), a new corpus with different dialects of English, Global Web-based English (GloWBE) is available.

OSLa volume 10(2), 2018 [20] katherine fraser

The sentences to be analysed were randomly extracted from the search results. From these extracted sentences, I manually looked at each, omitting any irrelevant uses. Specifically, any literal posture uses were thrown out. This means that the majority of the subjects are inanimates, but if it was determined from the context that an animate was not in a specific posture, the sentence was kept in the database; unclear cases were not included. Also, sentences such as (20) were thrown out, as this metaphorical extension is idiomatic, and therefore different— even while still referring to inactivity.

(20) For one thing, the wolf isn’t at the door. Apple is sitting on $1.7 billion in cash and short-term notes. [COCA]

The subject of (20)’s main clause, the company Apple, is not actually located on the money. Rather the company is in possession of it. This sense of ‘sit’ is often used in collocation with on plus money or things of value. The final number of analysed sentences was 275. All of these utterances had been extracted from the COCA search described above, and all were instances of non-literal ‘sit’.

Annotation Once the corpus was chosen and the sample set was extracted, the next delibera- tion was annotation. Two main categorizations were relevant for this study: eval- uating the (evaluative) valence of the utterance and annotating the arguments of “sit”. The valence of the sentence refers to whether it was a neutral locative construction, concerning the existence of the subject at a certain location (“locative”), or whether the utterance was accompanied by an evaluation (“expressive”). This difference was determined from the context provided by COCA, namely the KWIC (“keyword in context”); of course, there were a few unclear cases due to the brevity of the context, which were omitted from the final numbers. In addition to the valence of the utterance, I annotated the semantic type of the arguments. This annotation was completed based on linguistic intuitions; intuitions are verified by sources such as FrameNet8 for clues, then standard English dictionaries like Merriam-Webster (2003). These two subsections have outlined how I approached the corpus. With that in mind, let us move on to what was discovered.

[3.2] Corpus data This subsection concerns answers to the two research questions (context dependency of the construction and distribution of evaluation). For more detailed information on the corpus data, see Fraser (2016). Considering the goals of the

[8] https://framenet.icsi.berkeley.edu/fndrupal/ [Last access on 30 May 2016.]

OSLa volume 10(2), 2018 polysemous posture in english: a case study of non-literal meaning [21] study (fine-grained semantic examination), the findings were analysed with only a simple statistics. As to the overall numbers: of the 275 collected examples, about two-thirds were the -ing form and the last third as the simple past, as can be seen in Table 1.

table 1: Number of examples for each form of sit.

Form N [be] sitting 83 sitting 92 sat 100

275

Answering the research questions: Context dependency and evaluativity The question of whether the construction is dependent on its linguistic context will be addressed here. More specifically, the data reported is the semantics of the possible subject arguments and whether a locative argument is required. First: beyond inanimate, a specific semantic type of the subject is not a requirement of non-literal, locative ‘sit’. The most common subjects sitting were concrete concepts, of the semantic types vehicle, device, document; most common locations were also concrete, of the types furniture and area, such as drive- ways or garages. Less common were buildings—which were never in neutrally- labelled utterances. That is to say, examples like (21) were rare.

(21) A ROCKY START. The house had been constructed by a mill worker from redwood hand-milled at the Mill Valley Lumber Co. There was no foundation – the house was sitting on rocks. The redwood was sound (redwood naturally repels predators) but the floors and stairs were creaky and the kitchen was primitive. [COCA]

There were a handful of sentences without a locative prepositional phrase: 34 examples, (12% of 275). Note that the location was lacking only in evaluative uses and only with a secondary predicate,9 regardless of verb form. Examples of secondary predicates are as in (22), where the boldfaced expressions are depictive predicates (a), and the underlined ones temporal expressions (b).

(22) a. “…In Pine Bluff, Arkansas, trailers sat rusting alongside tiny Depres- sion -era houses.” The picture Jargowski paints in his research is not

[9] Predicates that describe a “state or condition, or a role, function or life stage” holding at the same time as main predicate’s eventuality (Schultze-Berndt & Himmelmann 2004, p. 64).

OSLa volume 10(2), 2018 [22] katherine fraser

pretty. [COCA] b. His attorney filed a motion to revise the sentence {of 15 years in prison for manslaughter} but the request sat for nearly eight years until the sentencing judge acted upon it. [COCA]

In these examples, the subject’s location is not explicitly expressed in the clause containing ‘sit’. Instead, a depictive predicate (rusting) follows the verb in (a), and a temporal for-phrase in (b); both of these are secondary predicates. Both sentences also include an extra layer of evaluative meaning, in that the subject’s idleness is considered undesired by somebody within the context: in (a), the state of the trailers is undesirable, and in (b) the speaker implies that the request being idle for so long is considered undesirable These, and the 32 other sentences of the without-location subset were categorised as evaluative. Looking at secondary predicates in the entire data set: 60% of the simple past forms included a secondary predicate, whereas only 17% of the -ing forms did. This suggests that the meaning encoded by the progressive (e.g., ‘transiency’) is a requirement of non-literal, locative ‘sit’, and that the secondary predicate can provide the necessary transiency meaning when there is no progressive morphology. The sentences in (23) are examples of the simple past form with secondary predicates and a location argument.

(23) a. On the bridge […] a truck sat jammed nose-down through a huge hole in the middle of the concrete, its rear-end jutting out like the monster of the blue lagoon. [COCA] b. Instead, their plane sat for six hours on the tarmac, and the two slept on the floor Wednesday night. [COCA]

Looking at the evaluative utterances in the entire data set: 60% of all examples were accompanied by an evaluation; 63% of the -ing examples were evaluative and 51% of the simple past. As such, the answer to the second research question is that non-literal, locative ‘sit’ is often but not exclusively evaluative. Interestingly, 94% of the subset simple past plus secondary predicate(regardless of whether it has a location argument) were evaluative. This is in contrast to only 26% of the -ing plus secondary predicate subset. This information, plus the without-location subset again suggest that the secondary predicate takes over when there is no progressive morphology. To summarise the corpus study: the subset included various types of subjects, only permanent-type buildings were less frequent; the location argument can be omitted, but only when a secondary predicate is present; secondary predicates also overwhelmingly lead to evaluation in simple past forms. The next section will explore the role of a secondary predicate and how it relates to the progressive. In addition, the next section will discuss whether either might be the source of the

OSLa volume 10(2), 2018 polysemous posture in english: a case study of non-literal meaning [23] evaluative component often accompanying non-literal, locative ‘sit’.

[4] discussion This final section will look at the theory behind secondary predicates and the progressive and will consider and then reject the notion that aspectual coercion is the source of an evaluation.

[4.1] Secondary predicates and the progressive Following Schultze-Berndt & Himmelmann (2004) and Rothstein (2000), I assume that secondary predicates contextualise the aspect of the main event. In the corpus examples in (24), the subjects’ current state is expressed by the depictive predicates, unattended (a) and rusting (b). This describes an eventuality holding true at the same time as the main predicate, sat.

(24) a. …the neighborhood is teeming with kids. […] But over the weekend, the street was strangely silent. A tricycle sat unattended, across the street from a colourful chalk drawing of a young girl. [COCA] b. “…In Pine Bluff, Arkansas, trailers sat rusting alongside tiny Depres- sion era houses.” The picture Jargowski paints in his research is not pretty. [COCA]

We know that (i) secondary predicates spatially bind the main verb and (ii) the 34 corpus examples without a location included a secondary predicate. Based on this, I propose that non-literal ‘sit’ requires spatial contextualisation. Additionally, 60% of the simple past forms included a secondary predicate, a big difference from the 17% of the progressive ones. Following, e.g., Comrie (1976), I assume that the progressive aspect reports an event as being within a larger temporal frame. Also considering that secondary predicates temporally contextualise the main event’s time—in addition to the uncontroversial idea that a temporal for-expression explicitly constrains the main event’s time—I propose that non-literal ‘sit’ requires both spatial and temporal contextualisation.

[4.2] The source of the evaluative component Although not all of the corpus examples were judged to be evaluative by the native speaker annotator, more than half were. The cognitive literature (Newman 2002; Lemmens 2002, e.g.) often ascribes negative associations to a posture verb like ‘lie’ and positive ones to ‘stand’. Sometimes, ‘sit’ is associated with concepts like being stuck or precarious, but it is only a tendency. Because of this ambivalence, I hesitate to pinpoint the social-cultural associations of ‘sit’ as being the source of the evaluation. Another possibility is aspectual coercion (to be distinguished from the coercion from literal to non-literal meaning).

OSLa volume 10(2), 2018 [24] katherine fraser

Cross-linguistically, the progressive is often known to carry an evaluative meaning. In English it can be used to describe a a contingent state (Comrie 1976). In Breton the interpretation is that an agent is intentionally doing something eval- uated as bad (Hewitt 1986). In languages such as Dutch and Afrikaans (Lemmens 2005; Breed 2017; Fraser & Pots 2018, a.o.) the posture verb in a verb cluster can carry an evaluation. The examples below illustrate.

(25) I’ve only had six whiskies and already I’m seeing pink elephants. (Comrie 1976, p.37) (26) Me a= gav din ’mañ ar maer o lared gewier Me temp find to.me is the mayor prog say lies I think the mayor is deliberately telling lies (and I think this is bad). (breton; Hewitt 1986, 67) (27) Het enige nadeel met ziggo digitaal is live voetbal, de hele The only downside with Ziggo Digitaal is live football, the entire buurt loopt te juichen en hier valt de goal 30 seconde later neighbourhood walks to cheer and here falls the goal 30 seconds later ‘The only downside about Ziggo Digitaal10 is watching live football; the entire neighbourhood is cheering, only at home the goal is made 30 seconds later.’ (lit. ‘the entire neighbourhood walks to cheer’)

[Dutch, twitter.com; example from Fraser & Pots 2018]

Also, the English progressive is often considered to involve a hidden coercion operator (de Swart 1998; Michealis 2004). That is, when the input is a state, the operator “adapts” it to be compatible, i.e., the state is transformed into a dynamic entity; according to de Swart (2008: 20), the output is still a state, but “more dynamic than the underlying state”. However, ‘sit’ can be used in a neutral, locative way, so this is not a good enough motivation to say that the evaluation’s source is solely the state-dynamic coercion. Additionally, the secondary predicates ar- guably do not coerce anything in this construction. It is possible to say that the lexical semantics of a depictive predicate like forlornly in (28) carries an evaluative meaning; the temporal for-expressions only delineate a temporal interval.

(28) [She] pauses just long enough to admire her latest pet project: an enorm- ous electronic sign that blares STEER CLEAR OF SHELL-BOYCOTT NOW at a Shell service station sitting forlornly across the road. [COCA]

If it is not aspectual coercion, what might be triggering an evaluation? Data from a corpus study of Dutch and Afrikaans suggest that degree of grammaticalisation

[10] Ziggo Digitaal is a type of TV contract in the Netherlands.

OSLa volume 10(2), 2018 polysemous posture in english: a case study of non-literal meaning [25] is connected to evaluative content (Fraser & Pots 2018). That is, in Dutch and Afrikaans, the three core posture verbs and the motion verb ‘walk’ can be used as progressive markers. The more grammaticalised the progressive marker is (determined by factors such as frequency of appearance with an animate subject and degree of semantic bleaching of the marker), the more often the utterance is likely to be considered as evaluative. In the English construction of the present paper, the posture verb ‘sit’ is semantically bleached to the extent that posture is not encoded at all, only location. While this parallel does not provide a clear answer to the question of an evaluation trigger, it shows that ‘sit’ belongs to a class of verbs which are capable of grammaticalising to the point of losing their original posture meaning, and when this happens, an evaluation is likely to accompany the utterance. Future work will have to be dedicated to pinpointing why it is these verbs that are participating and whether there is any more specific trigger for the evaluation.

[5] conclusion

This paper looked in detail at the lexically ambiguous English posture verb ‘sit’. It described how this verb describes, in its literal sense, an animate subject at rest in a compact position with a vertical upper half. When the subject is inanimate, the meaning is reinterpreted and posture is no longer encoded. Instead, the location of the subject in an idle state is described. As such, the non-literal sense requires a location argument, whereas the literal sense does not. A qualitative corpus study also found that the location argument can be fulfilled by a spatially-contextualising secondary predicate. Additionally, non-literal ‘sit’ must be temporally bounded, either by the progressive aspect or a secondary predicate. Unlike two other core posture verbs, non-literal ‘sit’ does not encode a posture orientation in its metaphorical extension; it is therefore more productive than ‘stand’/‘lie’. Finally, the corpus study showed that an evaluative component is often, but not always, present in the non-literal ‘sit’ utterances. Being a case study, this paper had a narrow focus, concentrating on just one verb of just one class. That being said, this study still has implications for other polysemous verbs, even outside of the posture verb class.

Next steps will be looking more closely at the transient meaning and the evaluation. More specifically, it will be interesting to see whether the transiency is entailed or a presupposition (cp. aspectual particles). The evaluation’s meaning will also be investigated and finally accounted for in a multi-dimensional model (e.g., Gutzmann 2015).

OSLa volume 10(2), 2018 [26] katherine fraser

acknowledgments Thanks to editor Alexandra Spalek and the anonymous reviewer, Elena Castro- viejo, Berit Gehrke, Agustín Vicente, and the audience at CoPo2017 for helpful comments. The author gratefully acknowledges the predoctoral grant BES-2016- 076783 (Spanish Ministry of Economy, Industry, and Competitiveness, MINECO), project FFI2015-66732-P, (MINECO and FEDER), the IT769-13 Research Group (Basque Government), and UFI11/14 (UPV/EHU).

references Asher, Nicholas. 2011. Lexical meaning in context. a web of words. Cambridge: Cam- bridge University Press.

Breed, Adri. 2017. The subjective use of postural verbs in afrikaans (i): development from progressive to modal. Stellenbosch Papers in Linguistics 1–21.

Comrie, Bernard. 1976. Aspect: an introduction to the study of verbal aspect and related problems. Cambridge: Cambridge University Press.

Davies, Mark. 2008-. The corpus of contemporary american english: 560 million words, 1990-present. http://corpus.byu.edu/coca/.

Dowty, David. 1979. Word meaning and montague grammar. Reitel: Dordrecht.

Fraser, Katherine. 2016. Sitting and waiting: Idle meanings of an English posture verb. MA Thesis, Universität Stuttgart.

Fraser, Katherine & Cora Pots. 2018. Evaluation in the periphrastic progressive: An empirical comparison of Dutch and Afrikaans. Unpublished ms. U. of the Basque Country & KU Leuven.

Gibbs, Raymond, Dinara Beitel, Michael Harrington & Paul Sanders. 1994. Taking a stand on the meanings of Stand: Bodily experience as motivation for polysemy. Journal of Semantics 11. 231–251.

Gutzmann, Daniel. 2015. Use-conditional meaning. studies in multidimensional semantics Oxford Studies in Semantics and Pragmatics 6. Oxford: Oxford Uni- versity Press.

Hewitt, Steve. 1986. Le progressif en breton à la lumière du progressif anglais. La Bretagne Linguistique 1 49–70.

Krifka, Manfred. 2000. Alternatives for aspectual particles: Semantics of still and already. In Proceedings of the twenty-sixth annual meeting of the berkeley linguistics society: General session and parasession on aspect, 401–412.

OSLa volume 10(2), 2018 polysemous posture in english: a case study of non-literal meaning [27] Kuteva, Tania. 1999. On ‘sit’/‘stand’/‘lie’ auxiliation. Linguistics 37(2). 191–213.

Lemmens, Maarten. 2002. The semantic network of Dutch posture verbs. In John Newman (ed.), The linguistics of sitting, standing, and lying, 103–139. John Ben- jamins Publishing Company.

Lemmens, Maarten. 2005. Aspectual posture verb constructions in Dutch. Journal of German Linguistics 17(3). 183–217.

Levin, Beth. & Malka Rappaport-Hovav. 1995. Unaccusativity. Cambridge, Mas- sachusetts: MIT Press.

Löbner, Sebastian. 1989. German schon - erst - noch: An integrated analysis. Lin- guistics and Philosophy 22. 45–107.

Lødrup, Helge. 2002. The syntactic structures of Norwegian pseudocoordinations. Studia Linguistica 56(2). 121–143.

Maienborn, Claudia. 1996. Situation und lokation. die bedeutung lokaler adjunkte von verbalprojektionen. Tübingen: Stauffenberg.

Maienborn, Claudia. 2003. Event-internal modifiers: Semantic underspecification and conceptual interpretation. In Ewald Lang, Claudia Maienborn & Cathrine Fabricius-Hansen (eds.), Modifying adjuncts, 475–509. de Gruyter.

Merriam-Webster, Inc. 2003. Merriam-Webster’s collegiate dictionary, 11th edition.

Michealis, Laura. 2004. Type shifting in construction grammar: An integrated approach to aspectual coercion. Cognitive Linguistics 15(1). 1–67.

Newman, John. 2002. A cross-linguistic overview of the posture verbs ‘sit’, ‘stand’ and ‘lie’. In John Newman (ed.), The linguistics of sitting, standing, and lying, 1–24. John Benjamins Publishing Company.

Newman, John. 2009. English posture verbs: An experientially grounded approach. Annual Review of Coginitive Linguistics 7. 30–57.

Newman, John & Sally Rice. 2004. Patterns of usage for English sit, stand, and lie: A cognitively-inspired exploration in corpus linguistics. Cognitive Linguistics 15. 351–396.

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Rothstein, Susan. 2000. Secondary predication and aspectual structure. ZAS Papers in Linguistics 17 741–763.

Schultze-Berndt, Eva & Nikolaus P. Himmelmann. 2004. Depictive secondary predicates in crosslinguistic perspective. Linguistic Typology 8. 59–131.

Spalek, Alexandra Anna. 2014. Verb meanings adn combinatory semantics: A corpus- based study of spanish change of state verbs. Universitat Pompeu Fabra PhD dissertation.

Spalek, Alexandra Anna. 2015. Spanish change of state verbs in composition with atypical theme arguments: Clarifying the meaning shifts. Lingua 157. 36–53.

de Swart, Henriette. 1998. Aspect shift and coercion. Language & Linguistic Theory 16(2). 347–385.

author contact information Katherine Fraser University of the Basque Country (UPV/EHU) [email protected]

OSLa volume 10(2), 2018 Alexandra Anna Spalek and Matthew Gotham (eds.) Approaches to Coercion and Polysemy, Oslo Studies in Language 10(2), 2018. 29–45. (ISSN 1890-9639 / ISBN 978-82-91398-12-9) https://www.journals.uio.no/index.php/osla

i’m done my homework: complement coercion and aspectual adjectives in canadian english

PATRICKMURPHY University of Toronto abstract Self-paced reading and eye-tracking studies have generally found that combining aspectual verbs (like begin and finish) with entity nouns (like the book or the coffee) is associated with increased reading times on and around the noun (McElree et al. 2001; Traxler et al. 2002; Pickering et al. 2005). This processing cost is widely interpreted as evidence of complement coercion— aspectual verbs semantically select for an event (like dancing or the dance) and can take entity objects only if they are coerced into an event through a computationally costly process of type-shifting (Pustejovsky 1995; Jackendoff 1997). This paper presents an eye-tracking study of the Canadian English be done NP construction, e.g., I am done/finished my homework (not to be con- fused with the dialect-neutral I am done/finished with my homework) to mean I have finished my homework. Results suggest a processing penalty for entity- denoting nouns like the script (compared to event description nouns like the audition) in this construction, which supports Fruehwald & Myler’s (2015) proposal that done and finished in this construction are aspectual adjectives that behave like aspectual verbs in requiring complement coercion and type- shifting for entity-denoting nouns.

[1] introduction The focus of this paper is complement coercion, such as in the sentence the child began the book (Briscoe et al. 1990; Pustejovsky 1991, 1995; Jackendoff 1997; Asher 2011; Egg 2003). According to the literature on coercion, aspectual verbs like begin select as their complement an event description like to dance, dancing, or the dance. However, the book denotes an entity; such a mismatch can be solved if the entity- denoting noun is reinterpreted as an event involving that entity. In the case of the child began the book, the book is likely to be understood as reading the book or looking at the book (other interpretations, such as writing the book, are also possibilities depending on the subject and context). Note that the event interpretation of the book is specifically tied to its position as the complement of an aspectual verb, and is not universally available. As noted by Asher (2011), a sentence like the child’s book [30] patrick murphy

will begin in two minutes (meaning the child’s {reading, writing, etc.} of the book will begin in two minutes) is semantically odd. In addition to aspectual verbs, psychological verbs like enjoy have traditionally been analyzed as event-selecting verbs that require complement coercion for entity-denoting objects (although more recently, Katsika et al. 2012 have presented evidence that psychological verbs do not fit into this category). The term coercion was introduced to linguistics by Moens & Steedman (1988), and it has also been used for mass/count and aspectual mismatches. Early processing studies of complement coercion using self-paced reading and eye-tracking techniques discovered that the combination of event-selecting verb and entity-denoting NP is slower or more difficult to process compared to other verb and object combinations (McElree et al. 2001; Traxler et al. 2002; Pickering et al. 2005—but see also de Almeida 2004). These early studies generally presented or cited the enriched composition view of coercion, which involves a (computationally costly) semantic repair mechanism, commonly called type-shifting, acting on the noun to satisfy the selectional requirements of the verb (Piñango et al. 1999; Pylkkänen & McElree 2006; Pustejovsky 1991, 1995; Jackendoff 1997; Katsika et al. 2012). However, these studies primarily focused on providing psycholinguistic evidence that these coercion sentences are unique, rather than distinguishing between different theories about what coercion involves. Later studies used reading measures (and other evidence) to delve more deeply into understanding the mechanisms underlying coercion. One alternative possibility is that complement coercion involves extra structure in the form of a silent VP between the coercion verb and the noun, and that this (rather than an operation such as type-shifting) is the reason for the increased processing requirements of coercion (de Almeida & Dwivedi 2008). However, Pylkkänen & McElree (2006) present evidence against coercion involving a silent VP, including an inability to adverbially modify the supposed silent VP. Another possible explanation that does not rely on type-shifting is that the processing effect of coercion is a result of pragmatically having to infer an event from an entity (e.g., to determine whether began the book refers to reading, writing, looking at, etc.). However, multiple studies find that varying the need to infer the event (Traxler et al. 2005 by providing a context sentence, and Frisson & McElree 2008 by choosing coercion sentences with more or fewer possible interpretations) does not affect the processing effect of coercion. The type-shifting view of coercion remains common in the literature (e.g., Katsika et al. 2012), although note that the nature of complement coercion is still an ongoing area of research and there are other current proposals (Asher 2011; Piñango & Deo 2016). The linguistic phenomenon of interest in this paper is the be done NP construction seen in (1) and (2), which is found in Canadian English and in a few varieties of American English, specifically in Philadelphia and Vermont (Yerastov 2008, 2012;

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Fruehwald & Myler 2015). Both done and finished are possible.

(1) I’m finished my homework. (2) I’m done my homework.

The meaning is equivalent to the aspectual verb finish in the perfect, as in (3).

(3) I’ve finished my homework.

The meaning of the Canadian construction has overlap with the (dialect-neutral) prepositional be done with NP construction in (4) and (5), but they are not the same. The Canadian construction requires that the object be completely finished, while the prepositional construction also allows cases where the subject has lost interest (if someone completes half of their homework and moves to another task, they are done with their homework but not done their homework).

(4) I’m finished with my homework. (5) I’m done with my homework.

The difference in interpretation between the Canadian construction and the prepositional construction is evidence that the Canadian construction should not be analysed as involving a silent preposition, or at least not one equivalent to with. Yerastov (2008, 2012) argues that the Canadian construction is best analyzed as the regular English perfect like in (3) but with a non-standard auxiliary (be instead of have), based in part on parallels with the be-perfect in Scottish English. However, Fruehwald & Myler (2015) argue against the be-perfect analysis for this Canadian English construction for a variety of reasons. Notably, all is compatible with the Canadian construction (6) and with adjectives (7) but not perfect parti- ciples (8).

(6) I’m all done my homework. (7) I’m all ready for school. (8) *I’ve all done my homework.

In addition, they note that the Canadian construction (9) and adjectives (10) can be embedded under the perfect, but the perfect itself (11) cannot be embedded under another perfect.

(9) I have been done my homework for a while now. (10) I have been ready for school for a while now. (11) *I have had done my homework for a while now.

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Instead, Fruehwald & Myler propose that the Canadian construction involves an adjective that directly takes as its complement an NP (without a silent interven- ing PP or VP). This is not common in English, but is also not unprecedented (as in be worth NP). Because done and finished are adjectival versions of aspectual verbs, Fruehwald & Myler argue that these aspectual adjectives semantically select for an event description and require complement coercion and type-shifting for interpretation of entity-denoting nouns. Given that complement coercion with aspectual verbs has been investigated and supported with reading measures, Frue- hwald & Myler’s proposal should also be testable with reading measures. The present study is an eye-tracking experiment testing this analysis of the Canadian construction by comparing reading times of entity-denoting nouns and event description nouns in the Canadian construction, with the hypothesis that entity-denoting nouns will be associated with more processing difficulty. Sen- tences in the dialect-neutral prepositional construction will also be tested, although Fruehwald & Myler’s analysis does not have any specific predictions here. Note that this paper will be assuming the type-shifting or enriched composition analysis of coercion, in line with the language used by Fruehwald & Myler in their analysis, although this experiment was designed to determine whether the Cana- dian construction exhibits coercion effects, rather than to distinguish between different reasons or explanations for coercion effects (like Traxler et al. 2005 and Frisson & McElree 2008 comparing pragmatic and semantic analyses).

[2] canadian english be done np experiment

This experiment tests whether there is a penalty for entity nouns compared to event nouns in the Canadian English be done NP construction and in the dialect- neutral be done with NP construction.

[2.1] Method Participants Thirty-six native speakers of Canadian English (mean age = 25, sd = 11), primarily from Southern Ontario, took part in this experiment at the University of Toronto, for $10 or course credit. An additional 28 participants took part but were excluded from analysis: five due to excessive blinks or track loss, 21 for not being native speakers of Canadian English,1 and two for indicating that the be done NP construction did not sound natural or acceptable to them. They provided written informed consent prior to partaking in the experiment.

[1] Students participating for course credit were not prescreened for language background, to avoid restricting opportunities for course credit.

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Items The stimuli for this experiment contrasted event description nouns (like the audition and the interview) with entity-denoting nouns (like the script and the resume) in the Canadian English be done NP construction and in the dialect-neutral be done with NP construction. Crossing these two factors resulted in four conditions, as seen below.

(12) After the girl was finished the fight against the playground bully, she went for a walk. (Canadian construction + event object) (13) After the girl was finished the comic about flying superheroes, she went for a walk. (Canadian construction + entity object) (14) After the girl was finished with the fight against the playground bully, she went for a walk. (Prepositional construction + event object) (15) After the girl was finished with the comic about flying superheroes, she went for a walk. (Prepositional construction + entity object)

In total there were 32 such quadruplets. They all followed a similar structure of a preposed subordinate clause (which included the construction of interest) and a shorter main clause. However, there were also differences between the quadruplets: half had a singular subject and half a plural subject, half had the adjective done and half had the adjective finished, and they also varied regarding their conjunction and temporal reference (past with after, present with because, and future with when). Participants only saw one sentence from each quadruplet, which means that they saw either an event description object or an entity-denoting object. The object that they did not see could be reused and shown to them in a later quadruplet, and so in the 32 quadruplets there were a total of 16 event description nouns and 16 entity-denoting nouns (rather than 32 of each). The nouns are provided below.

(16) Entities: comic, resume, prescription, script, report, autobiography, article, album, juice, coffee, hamburger, message, letters, essay, champagne, software (17) Events: fight, interview, presentation, audition, lecture, speech, conversation, concert, party, celebration, visit, gala, battle, competition, game, discussion

The mean length of the event nouns (7.625 characters) and entity nouns (7.25 characters) did not differ significantly, according to an independent t-test (t29.293 = 0.40018, p = 0.69). In addition, the (log-transformed) frequencies of the event nouns and entity nouns did not differ significantly in the usenet-based Hyper- space Analogue to Language (HAL) corpus (event: 9.69, entity: 9.47, t28.157 = -

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0.39698, p = 0.69) or in the movie subtitle-based SUBTLEX corpus (event: 3.15, entity: 2.92, t29.982 = 1.1263, p = 0.27), both of which were accessed through the English Lexicon Project (Balota et al. 2007). Reading times would not be expected to vary between the two groups of nouns as a result of their length or frequency.

Procedure Participants were seated in a height-adjustable chair wearing the EyeLink II head- mounted video-based eye-tracker (which had a sampling frequency of 250 Hz). The text was displayed on a computer screen in black 25 pt Times New Roman font on a white background. They were instructed to read each sentence at a normal reading pace, well enough to understand the sentence and answer comprehension questions (which followed every trial). Comprehension questions were asked about different parts of the sentence (the subject, the object, or the event in the second clause). For example, the comprehension question after When the musician is finished the concert at the new venue, he will take some time off asked what the musician will do, and the participant chose from a set of options. The eye- tracker was calibrated using a series of three fixed targets across the display at the beginning of the experiment, and recalibration was performed later on when judged necessary by the experimenter. Each trial began with a fixation target on the screen in the position that would be taken by the first letter of the sentence. Participants were instructed to fix their gaze on this target, at which point the experimenter started the trial and made the sentence appear on the screen, all on one line. After reading silently, participants pressed the trigger at the back of a game controller to bring up the comprehension question, which they answered with the triggers as well. Feed- back was not provided. After selecting their response, participants were immediately brought back to the screen with the fixation target, and the next trial started once they fixated on that target. Viewing was binocular, but only the left eye was recorded. All participants performed very well on the comprehension questions. Participants encountered the stimuli in a random order, mixed in with stimuli from three other eye-tracking experiments that they were simultaneously participating in. The present experiment comprised 32 of the 120 total sentences that each participant saw.2 Each participant was assigned to one of four lists, which affected which of the four sentences in each stimulus quadruplet they saw. The entire session took approximately 30 minutes.

[2.2] Results Each sentence was divided into six regions, as in (18). Region 3 was the object, and thus the critical region.

[2] Regarding order effects, reading times for this experiment (total time, as defined below, for all interest areas in this experiment) were 9% faster in the second half of the 120-trial session than the first half.

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(18) [R1 After the girl] [R2 was finished (with)] [R3 the fight] [R4 against] [R5 the playground bully,] [R6 she went for a walk.] Five reading measures are reported here for the critical region (R3): first-pass time (a.k.a gaze duration), first-pass regression ratio, go-past time (a.k.a. regression path duration), second-pass time, and total time. First-pass time is the time from first entering the region before moving on or looking back; first-pass regression ratio is the likelihood of reading a region for the first time and then re- reading an earlier region; go-past time is the time from first entering a region until moving on to a later region (including time spent re-reading an earlier region); second-pass time is the time from entering the region for a second time before moving on or looking back; and total time is all of the time spent in the area regardless of when it happened. The reading measures selected were those used in previous eye-tracking studies of coercion (Traxler et al. 2002, 2005; Pick- ering et al. 2005). Manual cleanup of the data was performed to remove trials with blinks or track loss on the critical region (or one saccade away from it) on first-pass reading and trials where the fixations indicate that the participant did not read the whole sentence (for example, they only fixated at the beginning of the sentence and then pressed the trigger to move on, possibly accidentally). Comprehension questions were used to encourage participants to read the simuli carefully, but incorrect comprehension questions were not used to exclude trials (on multiple occasions, participants remarked to the experimenter that they pressed the wrong button, suggesting that they were paying attention). In total, 11.2% of the trials were deleted. The five reading measures for R3 are shown below, separated by construction for better visibility. Keep in mind when looking at the results that a longer reading time (or more regressions) for entities compared to events is the finding that suggests coercion effects. In the tables, FP Time is first-pass time, FP Reg is first- pass regressions, GP Time is go-past time, and SP time is second-pass time.

table 1: Scores for critical region (R3) for be done NP

Object FP Time FP Reg GP Time SP Time Total Time Entity 381 ms 27.4% 545 ms 319 ms 650 ms Event 359 ms 25.4% 480 ms 263 ms 586 ms

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table 2: Scores for critical region (R3) for be done with NP

Object FP Time FP Reg GP Time SP Time Total Time Entity 330 ms 17.8% 395 ms 270 ms 494 ms Event 324 ms 20.5% 411 ms 288 ms 518 ms

R(R Core Team 2017) and lmerTest (Kuznetsova et al. 2017) were used to perform a linear (or logistic, in the case of first-pass regressions) mixed effects analysis of the relationship between each of these five reading measures, the noun type, and the construction. Fixed effects were noun type (event or entity) and construction (Canadian or prepositional). The contrast coding chosen for these two categorical factors (noun type and construction) was simple coding, rather than R’s default treatment coding, in order to test main effects rather than simple effects. This means that the effect of noun type presented below is tested across levels of construction, and the effect of construction is similary tested across noun types. These are the desired hypotheses to be tested (in addition to the interaction between noun type and construction). For these two-level factors, this involved coding one level as -0.5 and the other level as 0.5. “Event” was the reference level (-0.5) for noun type and “prepositional” was the reference level for construction. The analyses were planned with the maximal random effects structure justified by the experimental design (Barr et al. 2013), which means random intercepts for subjects and items (36 participants and 32 nouns), along with by-subject random slopes for noun type and construction, and by-item random slopes for construction (by-item slopes for noun type were not possible because each item was either one noun type or the other). This random effect structure was used for first-pass time, go-past time, and total time. For first-pass regression ratio and second-pass time, a model with random slopes failed to converge, and so the results from a simpler model (with only random intercepts) will be presented instead. The analyses for each of the five reading measures are presented below, as well as violin plots for each of the five measures (data averaged by participant for each condition). The significance markers are as follows: “***” < 0.001 < “**” < 0.01 < “*” < 0.05 < “.” < 0.1.

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First-pass time

Prepositional Construction Canadian Construction 700

600

500

400

First−pass time (ms) 300

200

event entity event entity

figure 1: Violin plot, first-pass time, critical region (R3)

table 3: Mixed effects model, first-pass time, critical region (R3)

Fixed Effects Estimate Std. Error df t-value Pr(>|t|) Sig (Intercept) 348.73 14.500 37.34 24.046 < 2e-16 *** Noun Type 17.21 13.52 32.51 1.273 0.21193 Construction 41.27 12.61 87.02 3.273 0.00153 ** Noun:Construction 15.76 22.83 644.13 0.690 0.49024

First-pass time is the time from first entering the region before moving on or looking back. In interpreting this model (and following models), attention should primarily be paid to the main effect of noun type and the interaction between noun type and construction. A main effect of noun type (with a positive estimate) would indicate a coercion effect across both constructions, while an interaction (with a positive estimate) could indicate stronger coercion effects in the Canadian construction, although neither the main effect nor the interaction were found at a statistically significant level for this reading measure. A main effect of construction would indicate that one construction resulted in overall longer reading times on the noun, across noun types. This was statistically significant in this reading measure (with a positive estimate, meaning that the Canadian construction had overall longer reading times for the noun), although

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this is of less interest because it is not relevant for coercion.

First-pass regressions

Prepositional Construction Canadian Construction

0.8

0.6

0.4

0.2 First−pass regressions (probability)

0.0

event entity event entity

figure 2: Violin plot, first-pass regressions, critical region (R3)

table 4: Mixed effects model, first-pass regressions, critical region (R3)

Fixed Effects Estimate Std. Error z-value Pr(>|z|) Sig (Intercept) -1.32892 0.13291 -9.999 < 2e-16 *** Noun Type -0.05234 0.18142 -0.289 0.77295 Construction 0.42588 0.16096 2.646 0.00815 ** Noun:Construction 0.32141 0.32141 1.000 0.31732

First-pass regression ratio is the likelihood of reading a region for the first time and then re-reading an earlier region. As with first-pass time, there was a significant effect of construction but no effect of noun type and no interaction between construction and noun type.

Go-past time

table 5: Mixed effects model, go-past time, critical region (R3)

Fixed Effects Estimate Std. Error df t-value Pr(>|t|) Sig (Intercept) 455.66 23.19 43.31 19.646 < 2e-16 ***

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Fixed Effects Estimate Std. Error df t-value Pr(>|t|) Sig Noun Type 26.16 24.73 32.01 1.058 0.2982 Construction 103.69 20.75 49.45 4.998 7.66e-06 *** Noun:Construction 82.82 36.23 70.75 2.286 0.0253 *

Go-past time is the time from first entering a region until moving on to a later region (including time spent re-reading an earlier region). The analysis found a significant effect of construction, no effect of noun type, and an interaction between construction and noun type. This interaction is important. Post-hoc analyses found that entity nouns were read significantly longer than event nouns in the Canadian construction according to a by-subjects analysis (paired t-test: t35 = -2.240, p = 0.032), although this did not quite reach significance in a by-items analysis (independent t-test: t23.091 = -1.673, p = 0.108). There was no difference between noun types in the prepositional construction in either the by-subjects (t35 = 0.77491, p = 0.444) or by-items analysis (t29.77 = 0.813, p = 0.423).

Second-pass time

table 6: Mixed effects model, second-pass time, critical region (R3)

Fixed Effects Estimate Std. Error df t-value Pr(>|t|) Sig (Intercept) 283.948 7.562 30.462 37.551 < 2e-16 *** Noun Type 18.703 13.775 444.782 1.358 0.17522 Construction 13.084 13.770 443.439 0.950 0.34251 Noun:Construction 73.684 27.508 437.494 2.679 0.00767 **

Second-pass time is the time from entering the region for a second time before moving on or looking back. The analysis found no effect of construction or noun type, but there was an interaction between construction and noun type. Post-hoc analyses using independent t-tests found that entity nouns had a significantly longer second-pass time than event nouns in the Canadian construction (by-items: t19.041 = -2.552, p = 0.019) but there was no difference between noun 3 types in the prepositional construction (by-items: t24.526 = 0.933, p = 0.360).

Total time

[3] Not all trials had a second-pass time. By-subjects analysis was not possible due to missing data, and so only by-items analysis is presented.

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Prepositional Construction Canadian Construction

1250

1000

750

Go−past time (ms) 500

250

event entity event entity

figure 3: Violin plot, go-past time, critical region (R3)

table 7: Mixed effects model, total time, critical region (R3)

Fixed Effects Estimate Std. Error df t-value Pr(>|t|) Sig (Intercept) 560.65 32.14 47.73 17.443 < 2e-16 *** Noun Type 19.51 36.28 31.97 0.538 0.5945 Construction 106.62 22.32 107.87 4.777 5.64e-06 *** Noun:Construction 78.93 43.25 157.08 1.825 0.0699 .

Total time is all of the time spent in the area regardless of when it happened. The analysis found a significant effect of construction, no effect of noun type, and a marginal interaction between construction and noun type. A visual inspection of the data finds the longest total time for entities in the Canadian construction.

Summary The following table shows a summary of the significant results on each measure. The relevance of these findings will be discussed below. In the table, FP Time is first-pass time, FP Reg is first-pass regressions, GP Time is go-past time, and SP time is second-pass time.

table 8: Summary of results (significance codes: 0 *** 0.001 ** 0.01 * 0.05 marginal 0.1 n/s 1)

Effect FP Time FP Reg GP Time SP Time Total Time Noun Type n/s n/s n/s n/s n/s OSLa volume 10(2), 2018 Construction ** ** *** n/s *** Interaction n/s n/s * ** marginal

[2.3] Discussion In none of the five measures was noun type significant, which rules out an overall coercion effect: a penalty for entity nouns compared to event nouns that applies to both constructions. In four of the five measures (second-pass time was the exception), there was a significant effect of construction, as a result of the objects in the Canadian construction having longer reading times (and more regressions) than objects in the prepositional construction. The reason for this is not evident; there is no clear precedent in the previous literature that would suggest this, as there has been (to my knowledge) no processing study of the Canadian construction. It is possible that the Canadian construction is less common than the prepositional construction. The most important result is the interaction. In two of the five measures (go- complement coercion and aspectual adjectives in canadian english [41]

Prepositional Construction Canadian Construction 700

600

500

400

300 Second−pass time (ms)

200

event entity event entity

figure 4: Violin plot, second-pass time, critical region (R3) past time and second-pass time) there was a significant interaction between noun type and construction, and in one other measure (total time) the interaction was marginal. The meaning and implication of this interaction will be discussed below, but first it is important to mention that failure to find this result on every measure is not unexpected. Go-past time is based on first-pass time and first-pass regressions, so smaller (non-significant) trends in those measures can compound into a larger effect that is visible (and statistically significant) in go-past time. The measures where a significant or marginal interaction was found (go-past time, second- pass time, and total time) in this experiment line up with the reading measures where a significant or marginal coercion effect was found in Traxler et al. (2002), the original study establishing coercion effects in eye-tracking. As for the meaning of this interaction, post-hoc t-tests showed that the interaction was a result of entity-denoting nouns having longer go-past time and second-pass time in the Canadian construction but there being no difference between noun types in the prepositional construction. The penalty for entity-denoting nouns found in the Canadian construction on these measures is consistent with the processing effects of coercion, and so this result supports Fruehwald & Myler’s 2015 proposal that the adjectives in this construction select for an event description and require complement coercion for interpretation of an entity-denoting noun (in a similar manner to finish and other aspectual verbs). The lack of difference between the noun types in the prepositional context could indicate that the preposition anticipates the upcoming type-shifting operation and attenuates the processing cost, or that it eliminates the selectional requirement for an event description (and thus the need for type-shifting when en-

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Prepositional Construction Canadian Construction

900

600 Total time (ms) Total

300

event entity event entity

figure 5: Violin plot, total time, critical region (R3)

countering an entity-denoting noun). Various authors have remarked that adding prepositions to aspectual verbs changes the interpretation in ways that are relevant for coercion. Verspoor (1997) compares begin and begin on, arguing that the prepositional version “indicates only that something is being done with the NP object, leaving a more specific interpretation to be established using contextual information”—which could mean anticipating the type-shifting operation.4 Look- ing at the equivalent in Dutch, beginnen aan, Honselaar (1980) (cited and translated in Sweep 2012) argues that beginnen needs to be combined with an event object while beginnen aan combines much more freely; Sweep (2012) argues that beginnen aan “makes logical metonymy [referring to complement coercion sentences like ‘Mary began the book’] easier to understand”. A deeper semantic analysis of coercion (or the lack of coercion) in the done with NP prepositional construction is outside the scope of this paper, although these precedents in the literature regarding prepositions and aspectual verbs does support the plausibility of the preposition anticipating type-shifting or eliminating the need for type-shifting.

[3] conclusion Previous literature has shown that entity-denoting objects have a processing cost when following event-selecting verbs (like begin the book). This cost has been associated with the need to coerce and reinterpret the book as an event in that context

[4] This has precedent in the processing literature. Processing difficulty related to mass-to-count coercion (like in yesterday, I bought imported beers [...]) has been shown to be attenuated when a numeral is provided before the object to make the reader anticipate a count interpretation (yesterday, I bought three imported beers [...])(Frazier & Frisson 2005).

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(begin [the book] to begin [reading the book]). Results from an eye-tracking study presented here found that entity-denoting objects also have a processing cost in the Canadian English be done NP construction (I’m done the book), suggesting that these aspectual adjectives behave similarly to aspectual verbs in selecting for event descriptions and requiring coercion for interpretation of entity-denoting nouns, as was argued by Fruehwald & Myler (2015). acknowledgments I would like to thank Margaret Grant, Philip Monahan, Guillaume Thomas, and Suzi Lima for their involvement in this project, as well as Mercedeh Mohaghegh, Kelly-Ann Blake, Kristen DonPaul, and Erin Pettibone for various kinds of help. I also want to thank the audience of the Workshop on Approaches to Coercion and Polysemy (CoPo 2017) at the University of Oslo for their feedback. references de Almeida, Roberto G. 2004. The effect of context on the processing of type- shifting verbs. Brain and language 90(1-3). 249–261. de Almeida, Roberto G. & Veena D. Dwivedi. 2008. Coercion without lexical decomposition: Type-shifting effects revisited. Canadian Journal of Linguistics 53(2/3). 301–326.

Asher, Nicholas. 2011. Lexical Meaning in Context: A Web of Words. Cambridge Uni- versity Press.

Balota, David A., Melvin J. Yap, Keith A. Hutchison, Michael J. Cortese, Brett Kessler, Bjorn Loftis, James H. Neely, Douglas L. Nelson, Greg B. Simpson & Re- becca Treiman. 2007. The English lexicon project. Behavior Research Methods 39(3). 445–459.

Barr, Dale J., Roger Levy, Christoph Scheepers & Harry J. Tily. 2013. Random effects structure for confirmatory hypothesis testing: Keep it maximal. Journal of memory and language 68(3). doi:10.1016/j.jml.2012.11.001. https://www.ncbi. nlm.nih.gov/pmc/articles/PMC3881361/.

Briscoe, Ted, Anne Copestake & Bran Boguraev. 1990. Enjoy the paper: lexical semantics via lexicology. In Proceedings of the 13th International Conference on Computational Linguistics, 42–47. Helsinki.

Egg, Markus. 2003. Beginning Novels and Finishing Hamburgers: Remarks on the Semantics of to begin. Journal of Semantics 20(2). 163–191. doi:10.1093/jos/20.2. 163. https://academic.oup.com/jos/article/20/2/163/1621112.

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Frazier, Lyn & Steven Frisson. 2005. Carving up word meanings: Portioning and grinding. Journal of Memory and Language 53(2). 277–291.

Frisson, Steven & Brian McElree. 2008. Complement coercion is not modulated by competition: Evidence from eye movements. Journal of Experimental Psychology: Learning, Memory, and Cognition 34(1). 1–11.

Fruehwald, Josef & Neil Myler. 2015. I’m done my homework—Case assignment in a stative passive. Linguistic Variation 15(2). 141–168.

Honselaar, Wilhelmus J. J. 1980. Valenties en diathesen: een bijdrage tot russische valentie- en genustheoriee ̈n en een toepassing daarvan bij de semantisch-syntactische descriptie van enige verba, deictische woorden en preposities in het Nederlands. Uni- versiteit van Amsterdam. Google-Books-ID: lbJyjgEACAAJ.

Jackendoff, Ray. 1997. The architecture of the language faculty. Cambridge, MA: MIT Press.

Katsika, Argyro, David Braze, Ashwini Deo & Maria Mercedes Piñango. 2012. Com- plement coercion: Distinguishing between type-shifting and pragmatic infer- encing. The Mental Lexicon 7(1). 58–76.

Kuznetsova, Alexandra, Per Bruun Brockhoff & Rune Haubo Bojesen Christensen. 2017. lmerTest: Tests in linear mixed effects models. https://CRAN.R-project. org/package=lmerTest.

McElree, Brian, Matthew J. Traxler, Martin J. Pickering & Rachel E. Seely. 2001. Reading time evidence for enriched composition. Cognition 78(1). B17–B25.

Moens, Marc & Mark Steedman. 1988. Temporal ontology and temporal reference. Computational Linguistics 14(2). 15–28.

Piñango, Maria Mercedes & Ashwini Deo. 2016. Reanalyzing the Complement Coer- cion Effect through a Generalized Lexical Semantics for Aspectual Verbs. Journal of Semantics 33(2). 359–408. doi:10.1093/jos/ffv003. https://academic.oup. com/jos/article/33/2/359/2413887.

Piñango, Maria Mercedes, Edgar Zurif & Ray Jackendoff. 1999. Real-time processing implications of enriched composition at the syntax-semantics interface. Journal of Psycholinguistic Research 28(4). 395–414.

Pickering, Martin J., Brian McElree & Matthew J. Traxler. 2005. The difficulty of coercion: A response to de Almeida. Brain and Language 93(1). 1–9.

Pustejovsky, James. 1991. The generative lexicon. Computational Linguistics 17(4). 409–441.

OSLa volume 10(2), 2018 complement coercion and aspectual adjectives in canadian english [45]

Pustejovsky, James. 1995. The generative lexicon. Cambridge, MA: MIT Press.

Pylkkänen, Liina & Brian McElree. 2006. The syntax–semantics interface: On-line composition of sentence meaning. In Matthew J. Traxler & Morton A. Gerns- bacher (eds.), Handbook of Psycholinguistics, vol. 2, 539–581.

R Core Team. 2017. R: A language and environment for statistical computing. R Found- ation for Statistical Computing. https://www.R-project.org/.

Sweep, J. 2012. Metonymical object changes: a corpus-oriented study on Dutch and German. UtrechtLOT9789460930911. https://dare.uva.nl/search? identifier=849907fc-d37e-4e85-b567-b6c74c0627cc.

Traxler, Matthew J., Brian McElree & Rihana S. Williams. 2005. Context effects in coercion: Evidence from eye-movements. Journal of Memory and Language 53(1). 1–25.

Traxler, Matthew J., Martin J. Pickering & Brian McElree. 2002. Coercion in sentence processing: evidence from eye-movements and self-paced reading. Journal of Memory and Language 47(4). 530–547.

Verspoor, Cornelia Maria. 1997. Contextually-Dependent Lexical Semantics, .

Yerastov, Yuri. 2008. I am done dinner: A case of lexicalization. In Proceedings of the 2008 annual conference of the Canadian Linguistic Association, Vancouver, BC.

Yerastov, Yuri. 2012. Transitive be perfect: An experimental study of Canadian English. Canadian Journal of Linguistics 57(3). 427–457.

author contact information Patrick Murphy University of Toronto [email protected]

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Alexandra Anna Spalek and Matthew Gotham (eds.) Approaches to Coercion and Polysemy, Oslo Studies in Language 10(2), 2018. 47–64. (ISSN 1890-9639 / ISBN 978-82-91398-12-9) https://www.journals.uio.no/index.php/osla

dispensing with unwanted polysemy: verbal idioms and the lexicon

JANWIŚLICKI University of Warsaw abstract The paper focuses on verbal idioms and their place in the lexicon. I discuss their morphosyntactic properties and effects observed for copredication. The data show that verbal idioms can be neither stored as atomic items, nor can their parts be treated as polysemous, i.e. as including “standard” and idiomatic meaning. I argue that a plausible result can be achieved by combining the framework of Distributed Morphology with Chomsky’s recent version of cyclic derivation. Viewed from that angle, idioms can be treated as emerging from derivational layers yielding a kind of structural coercion in the sense of Harley & Noyer (2000).

[1] introduction In his recent work, Cooper (2017) treats coercion as a mean for keeping chaos easily emerging in natural languages under (partial) control. There is a plenty of effects, so the argument goes, e.g. the lack of fixed interpretation, polysemy and problems with decidability, modifying meanings by the users of language on the fly, that increase the distance between natural and formal languages. Coercion, if sufficiently regular, can be conceived of as a part of grammar ramifying these potential sources of chaos in systematic mechanisms. Adopting to certain extent this idea, I discuss some closely related problems observed for verbal idioms (VIs) as those presented below:

(1) a. Mary showed Peter the door. Mary dismissed Peter. b. Mary gave Peter the cold shoulder. Mary ignored Peter/treated him in an unfriendly way.

A closer look into such expressions, especially into their morphosyntactic properties, unearths quite severe problems in assigning them the proper status in the lexicon. These primary observations give rise to further steps. First, I show that the standard coercion is not the right mechanism for resolving these complications. Second, I argue that a plausible result can be obtained at the presemantic level of computation, under a more relaxed, derivative approach to lexicon proposed by [48] jan wiślicki

Alec Marantz (1996 et seq.). In this regard Marantz’s lexicalization resembles to much extent coercion as presented by Cooper. The general conclusion is that VIs deliver strong arguments supporting a programmatic approach to lexicon. The paper is organised as follows. In section [2] I present data showing conflicting properties of VIs; the data suggest that VIs should be treated as both atomic and complex. Basing on these observations, in section [3] I sketch a general theoretical background combining Marantz’s idea of lexicalization with that of cyclic derivation as proposed by Chomsky (2013 et seq.). I show that the machinery naturally accounts for the effects discussed in section [2]. Finally, in section [4] I compare the offered solution with potential alternatives.

[2] the data: atomic properties of verbal idioms Let us start from taking a closer look at some data. What is especially puzzling from the point of view of the present discussion is that such constructions show conflicting properties. On the one hand, effects observed for movement, pronoun indexing and compositionality suggest that VIs should be treated as atomic lexical items (LIs). On the other, their morphosyntactic properties show that the grammar must secure their internal structure. I address each of the two demands in subsection [2.1] and [2.2], respectively.

[2.1] Idioms and their atomic properties Let us first have a look at the most obvious aspect of the atomic behaviour of idioms, viz. the lack of compositionality. Parts of idioms proper are not straightforwardly compositional, either under the functional or substitutional version of compositionality (cf. Pagin & Westerståhl 2010):

(2) [Mary showed Peter the door]

a. ≠ λze.λye.λxe.Mary(x)&P eter(y)&door(z)&showed(x, y, z) b. ≠ [Mary showed Peter the doorway]

The general observation is trivial: it is not the case that show and the door pick out the action of showing predicated upon the door. Still, this does not tell anything about the source of the non-compositional character of VIs. Much more can be inferred from relations observed in syntactic derivation. Let us start from a minor yet puzzling effect. As exemplified in (3), VIs do not allow co-indexing defined on their idiomatic parts:1

(3) a. She showed Peter the book1, but I couldn’t find it1. # b. She showed Peter the door1, but I couldn’t find it1.

[1] Unless stated otherwise, # marks the lack of an expected idiomatic reading.

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This fact pushes the previous observation one step further. While (2) states that VIs cannot be standardly composed from its parts, (3) shows that syntax cannot identify the idiomatic NP as an object for co-indexing. These effects fit well with those observed for movement. A brief look shows that idioms are islands for their proper parts. First of all, they block wh-movement, as in (4):

# (4) a. What1 did Mary show Peter t1? # b. What1 did Mary do t1 with the door?

A slightly weaker yet similar obstacle can be observed for passivization:

(5) a. #The door was shown by Mary to Peter.

The problem is more complex than the previous one because it is not the case that VIs universally block passivization. The classical example is to make headway which, while in general allowing passivization, is more restrictive w.r.t. other elements of verbal domain:

(6) a. Some real headway was made today. b. Much headway was made on this project. (from Salzmann 2017) c. ??Much headway on this project was made. (from Salzmann 2017)

For further details I send the reader to the vast literature on the topic (see Chom- sky 1980, Hulsey & Sauerland 2006, Salzmann 2017 and much related work). For the present purpose it will suffice to point out that passivization of VIs involving movement of their idiomatic parts is rarely possible. If it is, insertion of other constituents between idiomatic parts poses further problems. Finally, VIs block movement to topic-marked positions. Interestingly, this applies also to adjuncts as in (7), more often than not quite flexible for that kind of operation:

(7) a. At the castle1, John will meet the police t1. # b. At bay1, John will keep the police t1.

So, to sum up, proper parts of idioms pose serious obstacles for movement of its parts, regardless of the landing site ([Spec, CP], [Spec, TP] or [Spec, TopP]) or the category (nominal, verbal or adjunct). To close this part of discussion I will point out yet another important fact. As illustrated below, neither problems for co-indexing as in (8), nor those for movement as in (9), equally arise for non- idiomatic arguments occurring within VIs:

(8) Yesterday she showed Peter1 the door, but today she hired him1 again.

(9) a. Whom1 did Mary show t1 the door?

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b. Peter was shown the door by Mary.

This fact seems to suggest that strictly local relations hold only within idioms proper, not within the whole verbal domain. Most of operations interfering in that kind of relations result in blocking the idiomatic reading. The provisional conclusion is that VIs behave like atomic units, under the simplest approach like single LIs. Indeed, had show the door been a single lexical entry, neither of the abovementioned problems would have arisen. However, in the next subsection I discuss data showing that this cannot simply be the case.

[2.2] Idioms and their structural properties In what follows, I am going to show that, while plausible for the abovementioned reasons, treating VIs as atomic LIs is untenable. I present two arguments, one of a purely empirical, another of a conceptual nature. First of all, it cannot passed unnoticed that, though highly limited, nominal idiomatic parts of VIs allow merger with non-idiomatic modifiers and determiners, sometimes obligatorily:

(10) He was just pulling your leg He was just teasing you. (11) We have made a great headway towards self-sufficiency. (12) a. Peter kicked the proverbial bucket. b. Peter kicked the goddamn bucket.

This class of expressions is not homogeneous and, to my knowledge, still under- studied (see Zwart 2009 for some interesting comments connected with his layered, top-down approach to derivation). First, there seems to be a correlation between the type of verb and the acceptability of modifiers. Light verb constructions (take, make, get, …) are more permissive in this regard:

(13) a. We have made an impressive headway. b. He took a long nap. (14) #He was pulling your long leg.

Second, there are interesting semantic effects hidden behind some of those examples. That is, neither of the two sentences in (12) means that Peter kicked (in the idiomatic sense of kicking) an x which is a bucket (in the idiomatic sense) and that x is proverbial/goddamn. Rather, the two modifiers seem to work like operators. The former looks like a metalinguistic operator marking the fact that the phrase kick the bucket is not used in its literal meaning. The latter seems to mark speaker’s attitude (anger, sadness, sorrow, …) towards Peter’s death. Nev- ertheless, regardless of the exact semantics of such units, all the abovementioned modifiers and determiners must be somehow combined with nominals. For this

OSLa volume 10(2), 2018 dispensing with unwanted polysemy: verbal idioms and the lexicon [51] to be possible, idioms like kick the bucket in (12) or pull someone’s leg in (10) must be syntactically structured, thus non-atomic. The second argument is more of a conceptual character. That is, idioms show absolutely standard distribution of morphological features, such as case or φ- features. In the generative tradition this sort of distribution follows, at various stages depending on the exact variant of grammar, from syntactic relations. Thus for show Peter the door to be interpretable, both the door and Peter must be assigned the proper case. Consequently, the derivation should secure the relevant local relations between verbal heads and nominals, roughly like in (15) below (see Harley 1995 and its offshoots for a detailed discussion):

0 (15) [ Subj [ v [ Peterdat [ show the dooracc]]]] assign dat assign acc Otherwise the grammar can neither secure their interpretability, nor can it block overgeneration of phrases with improper distribution of case, e.g.:

∗ (16) Mary showed to/of/for …Peter to/of/for…the door.

So, here comes the general conclusion. Under relatively weak and widely accep- ted assumptions, the possibility of combining parts of VIs with determiners/modifiers as well as the distribution of morphosyntactic features show that the two effects cannot be explained if VIs are taken as atomic LIs. At least at some level of derivation they seem to behave like standard VPs.

[2.3] Interim conclusion No. 1 In this section I had a general look at some data showing a puzzling conflict. On the one hand, VIs show a typically atomic behaviour, disallowing straightforward composition, blocking movement and co-indexing its parts with non-idiomatic pronouns. While these problems would not arise had idioms been taken as atomic LIs, further data from modification and the distribution of case show that this is not possible. The general conclusion is that we need a machinery which is able to yield the structure of VIs and close them off within an atom.

[3] lexicon and derived atoms The simplest approach to the problems shown in [2] is to assume that the grammar must derive atoms from syntactically complex structures. One potential option is coercion: idioms could be taken as expressions derived by coercing “standard” LIs. This, however, would be problematic. Apart from the non-trivial problem of what should be the idiomatic meaning of shoulder in give someone the cold shoulder p q resulting from coercion of λxe.shoulder(x) , there is an argument from accidental polysemy in the sense of Asher (2011). Actually, VIs behave like bank (fin-

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ancial institution and form of land) in that they do not allow copredication with its parts as taken in the idiomatic reading:

(17) a. #The bank specializes in IPOs and is steep and muddy and thus slip- pery. (from Asher 2011, # marks semantic deviancy) # b. She had found t1 and then gave him the cold shoulder1.

This observation makes the puzzle designed so far even more complex. If copredication is the right test for the accidental/logical polysemy distinction (cf. Cruse 1986), then the “standard” and the idiomatic shoulder must have been mere hom- onyms. On the other hand, the analysis in section [2] showed that VIs cannot be generated as atoms. The relevant question arises, then, in what form are they stored in the lexicon. I am going to argue that the discussed data deliver a strong argument in favour of taking lexicalization as following from syntactic derivation. The approach is conceptually cognate with Cooper’s view on coercion as mentioned above. That is, one reason of introducing coercion into his semantics is that, within dialogues, users of language can create meaning of the fly (cf. Cooper 2012; 2016; 2017). Ac- cordingly, there is a serious threat for any formal grammar to run into chaos. Coercion, rather than giving causing disturbance within natural language, may allow to keep this potential chaos under control, provided it can be shown to be sufficiently regular. I claim that there is an analogy between such presented coercion and the properly defined lexicalization resembling to some extent what Harley & Noyer (2000) call structural coercion. Lexicalization defined in this way is a recursive syntactic operation that can be conceived of as a way grammar keeps a lexical chaos under control. The required regularity can be achieved by combining the view on lexicon as proposed by Marantz with cyclicity as proposed in the Minimalist syntax.

[3.1] Lexicon in Distributed Morphology The idea underlying Marantz’s (1996; 1997) view on lexicon is that it should correspond to three computation-wise distinct notions:

• pure lexicon – set of morphosyntactic features relevant only for syntactic computation, and not for semantic/phonological interpretation;

• vocabulary – set of connections between LIs and phonological features;

• encyclopedia – set of connections between syntactic objects (SOs) and meanings that are irrelevant for syntactic computation.

In theories called by Marantz lexicalist, syntax combines units possessing features from all the three sets. His approach goes orthogonally to this direction. If

OSLa volume 10(2), 2018 dispensing with unwanted polysemy: verbal idioms and the lexicon [53] there is no regularity between the size of syntactic structures and the size of non- compositional semantic units, so the argument goes, then information stored as encyclopaedic meaning must be definable for syntactic complexes: There is a continuum between the meanings of atomic morph- emes and, at least, derivationally derived words that ends abruptly at the word level…Idiomatic structures ranging from “light verb” constructions like [“take a leap”, “take a leak”,…] to “The shit hit the fan” show the same properties of special meanings for roots in context as do derived words. [Marantz (1997:207)] Accordingly, Marantz takes syntax to involve two sorts of SOs. First, roots understood as carriers of conceptual information (idiosyncratic meanings assigned by encyclopedia). Second, functional heads (n0, v0,…) which assign formal features to uncategorized roots, allowing their interpretation (cf. Bobaljik 2017). Under the strictly Marantzian view, roots as such are devoid of all other features2, their role being just to enable mapping to meaningful terms in the context of functional heads, and possibly other roots (but see also Arad 2005 or Borer 2013; 2014b for non-trivially distinct approaches). Consequently, Marantz (1996) claims that at the level of syntax roots do not differ from each other. The derivation of, say, dog and cat is the same:

(18) λxe.x is a φ

√ n0 root

Roots appearing in the relevant syntactic context are assigned idiosyncratic information by encyclopedia (perhaps being in a sense overloaded, cf. Labelle 2014) that cannot be retrieved in the course of compositional computation. Once they are merged with functional heads, this information is inserted in the form of a full-fledged formal term. It is thus at the post-syntactic level where the system yields the meaning of cat (formally inserting the constant at the place of φ) as different from that of dog. What is crucial for the present discussion is that lexicalization, rather than assumed beforehand, is determined by syntactic structures (merger of functional nodes). Nevertheless, that kind of powerful machinery opens up a wide path for overgeneralization. To avoid this, it must specify why some structures undergo lexicalization, and others do not. One candidate is cyclicity: there are numerous proposals according to which lexicalization should be coordinated with derivational cycles determining chunks ready for interpretation. If this line of reasoning, as supported by wide range of data (cf. Marantz 2007, Borer 2013; 2014a and

[2] Merchant (2018) goes event further and takes roots as devoid of all selectional properties.

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Bauke 2014, a.o.), is correct, then the account can be conceived of as a plausible constraint. That is, for lexicalization to be justified, the whole structure must meet two requirements. First, correlation between the lexicalized material and the cycle must exemplify some more general pattern of cyclicity. Second, the lexicalized structure must show cyclic properties, again defined as a part of a general architecture of cyclicity. In what follows I show that VIs do conform to the combination of lexicalization and cyclicity as defined in Chomsky’s recent framework of the so-called lower phase.

[3.2] Lexicalisation and syntax The view that LIs are in fact products of syntactic derivations, together with the result in the form of a more flexible lexicon (either as in Pustejovsky 1995 or a more traditional form) has two faces. On the one hand, it could be taken as an open path for stipulated lexicalization. Nevertheless, there is also a way for drawing an analogy between that kind of flexible lexicalization and Cooper’s view on coercion as mentioned above. Lexicalization determined by syntactic structures and defined upon Marantz’a lexicon might serve a similar purpose as coercion: to allow speakers to shift “standard” meanings and build different yet regularly derivable ones. For this to be possible, the particular lexicalization must exemplify an independently motivated pattern, a ‘helpful regularity’ to borrow Cooper’s (2017) phrase. Given the absolutely free Merge (cf. Chomsky 2008; 2018), the com- binatorial operation itself is not a candidate. However, as suggested above, such a more general mechanism can be naturally formulated within the account of verbal phase as presented in Chomsky (2013, 2015). It is essential for the overall view on syntax in Chomsky (2001) et seq. that derivations are sliced into cycles called phases. Chomsky (2013, 2015) recognizes two phases (see also Grohmann 2003; Bošković 2014, a.o. for a wider range of varieties): one responsible for building a transitive verb and its complete argument ∗ ∗ structure (v P), another for a full proposition (CP). Under this view, v and C0 are primary phase heads (PH0s) whose merger marks reaching the phase level. This signal triggers further steps. First, Feature Inheritance (FI) – a mechanism which, for syntax-internal reasons, must remove all features from PH0s (cf. Richards 2007). In the strictly Chomskyan account (cf. Chomsky 2013; 2015; 2018), FI iden- ∗ tifies the next lowest head (V0 for v and T0 for C0) as a goal for transmitting such features. This can be illustrated at the following schema:

0 0 ∗ 0 (19) [ C ... [ T [β ... [ v ... [ V α]]]]]

fi2 fi1 At each cycle the sister of the SO that receives the relevant features via FI, here α and β, becomes inaccessible for further operations. This effect is called Phase

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Impenetrability Condition (PIC; see Chomsky 2001 et seq.) Still, the two cycles are not identical to each other. The crucial difference is ∗ that the verb is inserted as an uncategorised root and raises to v where it under- goes lexicalization. Accordingly, the lower phase of the transitive verb email as presented by Chomsky (2013, 2015) looks as follows (irrelevant details omitted):

(20) β

∗ DPsubj v P

λye.λye.email(x,y) …

√ ∗ v email α

lexicalization √ 0 raising V : email DPacc to v

The root is lexicalized as a transitive verb (and not, say, as a nominal) after rais- 3 ∗ ing to v . This structure identifies [v∗ email] as the goal for post-syntactic insertion of encyclopaedic information concerning its lexicalized meaning. As it stands, the structure in (20) cannot yield the expected results for VIs. Applied straightforwardly, it would lexicalise the verb, say show, not the whole phrase show the door as required by the idiomatic reading. Nevertheless, if syntax, as widely assumed, is the level of computation responsible for recursion (cf. Zwart 2011) and lexicalization is defined by syntactic structures, then there is no principled reason for which lexicalization could not work in a recursive way. 4 One might think of a layered verbal structure as sketched in (21):

(21) [ v2-γ [ ... [ v1-α [ α β ]]]]

In that kind of structure successive cycles could recursively lexicalize, first, the

[3] This step is not assumed in all approaches (see Embick 2015, Alexiadou & Lohndal 2017 and references therein for some alternative approaches). In Chomsky’s recent framework based on labeling, the light ∗ head v cannot be merged directly with the α, since this would be problematic for satisfying the EPP feature on V, among others. Since this detail does not affect the discussion at hand, I leave this problem open. [4] Actually, Harley & Noyer (2000) explicitly state that there are no constraints concerning the size of material to be lexicalized. Some constraints might follow from the discussion in Den Dikken & Dékány (2018). However, the discussed constraints do not apply to the present proposal, which takes the whole lower phase head to be incorporated into the higher one.

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verb α, and next a wider scope of material γ containing α. This, indeed, would be a powerful tool allowing to create lexicalized semantic atoms bigger than “standard” LIs. Still, to block overgeneration lurking behind that kind of proposal it must be shown that the v2 layer is really phasal, i.e. that it shares the relevant properties with other phasal structures. In the next subsection I show that VIs indeed meet these requirements.

[3.3] Deriving verbal idioms With this picture in mind, let us recall two demands posed by VIs, as discussed in section [2]. First, the derivation must yield both structural and atomic (see subsection [2.1] and [2.2], respectively) properties of VIs. Second, it must account for the fact that some SOs, mostly indirect objects, occurring within VIs do not share properties of the surrounding idiomatic context. Bearing all of this in mind I propose the following strategy, basically instantiating the idea envisaged in (21). VIs are first derived as standard, extensional VPs. Next, their strictly idiomatic parts undergo another process of lexicalization, resembling in some relevant respect structural coercion in the sense of Harley & Noyer (2000). The upper layer marks the second verbal phase. To see how this might work, consider the following structure (irrelevant details omitted):

(22) ζ

λye.λxe.show_the_door(x,y) δ

∗ v2 ϵ Peter γ

show the door show β

√ v2 0 v1 show Peter α √ show the door v1 v2

Let us have a look at the above derivation step by step. First, syntax builds the standard double object structure γ. The√ core of this stage is the first process of 0 verb-formation, which is triggered by the show-to-v1 raising. The result is a full-

OSLa volume 10(2), 2018 dispensing with unwanted polysemy: verbal idioms and the lexicon [57] fledged ditransitive verb show.5 Thanks to this step at the level of γ the two NPs, i.e. the door and Peter, can be assigned case as standard arguments. For reasons that will become clear soon, instead of generating subject verb-internally, the non-idiomatic Peter is moved over show, that is outside the phase (to the edge). This is the last step forming the first phase. ∗ The second phasal layer is marked by the merger of v2, a light head which lex- icalizes the incorporated material as a transitive verb. Basically, it instantiates the same mechanism as the lower one; the difference lies in the scope of lexicalization. The relevant material is that corresponding√ to the whole idiom. Accord- ∗ 0 ingly, the door raises to v2 together with show ( show pied-piped to v1). The result is a transitive verb lexicalized as show the door, whose first argument is (the higher copy of) Peter. This upper verbal layer, though derived by the same mechanism, is not trivial from the point of view of cyclic derivation. In√ particular, the material incorpor- ∗ 0 0 − ated to v2 contains the lower PH , i.e. v1 show. For Chomskyan framework that kind of operation gives rise to the effect of phase sliding/cancellation (see Gallego 2010, as well as Bobaljik & Wurmbrand 2013 or Epstein et al. 2016 for related ideas): raising a phasal head cancels its primary phase. In (22) this means that the root is first categorized as a ditransitive verb, but, as a result of rais- ∗ ing and incorporation to v2, it does not form a phase which is shipped off to the semantic and phonological interface. This fact is remarkable. Note that in this [ ∗ show the door] structure the only full-fledged phase is the one identified on v2 . As a next step after forming the phase, all the features of the (complex) PH0 are inherited by the next lowest head, viz. [ 0 show], as discussed in the context of v1 (19). After FI, the sister of [ 0 show], viz. β, is identified as a phase complement v1 and thus closed off as an impenetrable whole (PIC). However, this does not apply to the higher copy of Peter which is raised to the edge of [ 0 show]. v1 Let us now have a look at some immediate consequences. The first result is that the structure in (22) resolves the main puzzle sketched above, viz. the mixture of atomic and complex behaviour of idioms. On the one hand, the lower verbal layer provides the complete structure for a ditransitive verb. This allows the proper distribution of morphosyntactic features as well as merger with modifiers/determiners (if acceptable), as discussed in subsection [2.2]. On the other hand, the verbal phase reached at the level of higher verbal layer accounts for the atomic character of VIs as discussed in subsection [2.1]. The crucial step is lexic-

[5] Since I focus on the problem of deriving the idiomatic predicate as a transitive verb, I draw a simplified picture of the derivation of ditransitives (perhaps it should be extended to the one fitting with the general pattern discussed by Harley 1995 and the related work). I also do not go into problems of linear ordering. The issue, especially under the copy theory of movement, is highly complicated (cf. van Urk 2018; Collins & Groat 2018) and of a minor importance for the general architecture (cf. Chomsky et al. 2018). I assume that the syntax-phonology mapping is able to retrieve the right ordering at the level of the lower verbal layer (γ).

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alization yielding two expected effects. First, it secures the non-compositional meaning of idioms.6 Second, it accounts for the islandhood of idiomatic parts. ∗ Note that once show and the door are incorporated to v2, constraints on movement would require pied-piping of the whole show the door. This, in effect, blocks various types of movement of either of the two SOs, i.e. show or the door, as discussed in the context of (4)-(7). Finally, the higher level of lexicalization provides a natural explanation of the lack of copredication as shown in (17). It follows from the fact that, in the final output of derivation, there is no semantic argument in the ∗ form of idiomatic the door, just the predicate show the door, a single verbal head v . All of this shows that VIs indeed fit with the general pattern of Chomsky’s verbal phase within a cyclic derivation. To close this part of discussion, it is worth pointing out that these plausible effects support Marantz’s view on lexicon as shaped in subsection [3.1]: syntactic derivation marks the proper points for lexicalization, instead of being fed by already lexicalized units. The data from copredication showed that there is no reason to assume any relevant connection between idiomatic and non-idiomatic the door. Accordingly, the question of how the door understood as a part of idiom can be stored in the lexicon has emerged as an especially puzzling one. Marantz’s view on the lexicon, together with the Chomskyan account of verbal phase, offer an explanation. What is “stored” is a conceptual information that can become a lexicalized item within the proper syntactic structure. If properly derived, the mere fact that this structure is formally complex does not play any role. In this sense the derivation may first lexicalize the ditransitive show, and then the transitive show the door without any inconsistencies.

[3.4] Interim conclusion No. 2 In this section I applied the general Chomsky-Marantz framework to the data discussed in Section [2]. It has been shown that the puzzling properties of VIs, i.e. the fact that they must be treated as both atomic and complex, can be accounted for by making use of two crucial ideas. First, the syntax-driven view on lexicon, according to the scope of lexicalization follows from particular syntactic structures, and thus they are not fed by already lexicalized items. Second, phasal derivation thanks to which the operation of lexicalization can be defined recursively, target- ing some previously lexicalized SOs. This allows to derive VIs as following neither from an extended account of lexicon which assumes polysemous units, nor from more complex compositionality, but rather from a cyclic account of lexicalization.

[6] I leave aside the problem of whether the encyclopaedic source of information required for show the door is exactly the same as that for “standard” LIs (see Embick 2015 for the relevant discussion). For the present sake it will suffice to derive VIs as lexicalized SOs in a way securing the relevant semantic and morphosyntactic effects.

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[4] idioms and the lexicon: the discussion One important result of the account presented in [3] is that it avoids non-trivial problems arising for lexicon: parts of idioms are not stored in the lexicon as variants of polysemous LIs. The crucial argument comes from copredication. If, as shown in (17), idioms block copredication, then their parts can be related with their non-idiomatic counterparts only via accidental polysemy. Nevertheless, there is a vast literature going in the opposite direction and suggesting that LIs are polysemous, so that the idiomatic reading can be obtained via composition (cf. Larson 2017, Rodrigues & Rio-Torto 2013, a.o.). Let us then have a quick comparative look at the proposed account and potential alternatives. First of all, any selection of the right meaning of a polysemous unit must be an additional subprocess. This automatically increases the complexity of compositionality (see Gehrke & McNally 2017 for the relevant example and further discussion). By contrast, the proposed analysis assumes no special/additional operations. Being based on cyclicity (derivation by phases) and lexicalization as proposed within DM, it recursively applies mechanisms required anyway and supported by independent factors. Second, moving the problem of computation of idioms to semantics hardly allows to tackle numerous morphosyntactic effects observed for such units. Some of them, such as wh-movement, topicalization or passivization were touched upon in this paper. Findlay (2017), though arguing for weakening lexical integrity, suggests that idioms should be associated (as LIs) with particular syntactic structures which secure the relevant morphosyntactic effects (e.g. passivization).7 This, however, hardly solves problems where idioms show constraints outside the idiomatic context. To illustrate, let us have a look at two interesting suffixes, -sa and -mi, yielding deadjectival nominals in Japanese:

(23) omo-i −→ omo-sa; fuka-i −→ fuka-sa … heavy-adj −→ heavi-nmlz; deep-adj −→ deep-nmlz … ‘heavy −→ heaviness; deep −→ deepness …’ (24) omo-i −→ omo-mi; fuka-i −→ fuka-mi … heavy-adj −→ heavi-nmlz; deep-adj −→ deep-nmlz … ‘heavy −→ heaviness; deep −→ deepness …’

As discussed by Sugioka & Ito (2016), for VIs like kosi ga omoi (lit. ‘[to have] heavy hips’, idiom. ‘to be slow to act’), the two nominalization patterns are not equivalent:

(25) kosi ga omo-i −→ kosi no omo-sa hips nom heavy-adj −→ hips gen heavi-nmlz

[7] Thanks to Matthew Gotham for bringing this paper to my attention.

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lit. [to have] heavy hips; idiom. to be slow to act −→ lit. the heaviness of one’s hips; idiom. slowness to act (26) kosi ga omo-i −→ kosi no omo-mi hips nom heavy-adj −→ hips gen heavi-nmlz lit. ‘[to have] heavy hips’; idiom. ‘to be slow to act’−→ lit. ‘the heaviness of one’s hips’; [no idiomatic reading]

The authors suggest that the two effects are rooted in scope differences and the way the idiom is derived.8 -sa, so the argument goes, takes scope over the whole idioms. Thus first the derivation forms the pure idiom, and then the adjective stem is attached to the nominalizing suffix -sa by head movement:

(27) [[ kosi no t1 ][ omo1-sa ]N ]NP

By contrast, -mi does not take such a wide scope and thus blocks the idiomatic reading. If this line of reasoning is on the right track, then the analysis proposed in Section [3] correctly predicts the expected results. Lexicalization is defined on the phrase kosi no omo- and then the adjectival stem moves in order to undergo nominalization by -sa.9 By contrast, -mi must have been attached low, so that lexicalization would target the whole nominal kosi no omo-mi, contrary to the facts. Consequently, the proposed account allows not only to derive idioms by very general mechanisms, without additional levels of computation, but also to define further operations, like those in (27).

conclusion The main aim of the present paper was to argue in favour of lexicon understood as a source of encyclopaedic information whose insertion is determined solely by syntactic derivation. In this regard, it allows to point out certain results, as well as formulate future challenges. Empirically, it discussed the problem of expressions that show both atomic and complex properties. It argued for a strictly derivational approach in which syntactic complexes undergo recursive lexicalization determined by particular syntactic structures. The analysis took into account both semantic (compositionality, copredication) as well as morphosyntactic (movement, agreement, case, nominalization) properties of verbal idioms. On theoretic grounds, the paper delivered arguments supporting the Marant-

[8] The distinction may have semantic motivations. -mi is more constrained than the very general -sa; usually, it provides a sort of intensional state: a taste/tinge of. [9] This might raise doubts in the context of the above account of wh-movement, which was taken to be blocked by the general principles of incorporation and movement. Note, however, that (27) exemplifies movement required by morphological reasons, not wh-movement. As such it is a natural candidate for excorporation (for the relevant discussion, see Roberts 1993, Jouitteau 2011), a.o.

OSLa volume 10(2), 2018 dispensing with unwanted polysemy: verbal idioms and the lexicon [61] zian view of lexicon combined with Chomsky’s recent account of cyclic derivation. It showed that the challenging material in the form of verbal idioms can be derived by recursive application of phasal heads, with lexicalization treated as its core effect. That kind of machinery allowed to avoid problematic assumptions concerning building blocks of idioms, and thus to economize lexicon. The proposed approach also opens up some paths for future research. Perhaps the most far-reaching problem arising under the free Merge approach is the scope and limitations of lexicalization. Of a particular interest might be the problem of syntactic recursion and its connection with lexicalization. Viewed from this angle, it allows to raise the widely discussed problem of dynamicity of lexicon as reducible to syntactic derivations, and not to independent (lexicon-internal) operations. Finally, the paper has not touched upon the formal semantic interpretation of lexicalization conceived of as a part of syntactic derivation; I leave this problem for future research. acknowledgments Parts of this paper were presented at Workshop on Approaches to Coercion and Poly- semy (Oslo, 2017). Critical comments from the audience, in particular Nicholas Asher, Matthew Gotham, Atle Grønn, Alexandra Spalek as well as an anonymous reviewer are gratefully acknowledged. Special thanks to Matthew and Alexandra for organizing the workshop. All errors are solely mine. references Alexiadou, Artemis & Terje Lohndal. 2017. The structural configurations of root categorization. In Leah Bauke & Andreas Blümel (eds.), Labels and roots, vol. 128, 203–232. Walter de Gruyter GmbH & Co KG.

Arad, Maya. 2005. Roots and Patterns: Hebrew Morpho-syntax. Dordrecht: Kluwer.

Asher, Nicholas. 2011. Lexical Meaning in Context: A Web of Words. Cambridge: Cam- bridge University Press.

Bauke, Leah S. 2014. Symmetry breaking in syntax and the lexicon. Amster- dam/Philadelphia: John Benjamins.

Bobaljik, Jonathan David. 2017. Distributed morphology. Oxford Research Encyclo- pedias: Linguistics .

Bobaljik, Jonathan David & Susi Wurmbrand. 2013. Suspension across domains. In Ora Matushansky & Alec Marantz (eds.), Distributed Morphology Today: Morph- emes for Morris Halle, 185–198. Cambridge, MA: MIT Press.

OSLa volume 10(2), 2018 [62] jan wiślicki

Borer, Hagit. 2013. Structuring sense: Volume iii: Taking form, vol. 3. Oxford: Oxford University Press.

Borer, Hagit. 2014a. The category of roots. In Artemis Alexiadou, Hagit Borer & Florian Schäfer (eds.), The syntax of roots and the roots of syntax, 112–148. Oxford: Oxford University Press.

Borer, Hagit. 2014b. Wherefore roots? Theoretical Linguistics 40(3/4). 343–359.

Bošković, Željko. 2014. Now I’m a Phase, Now I’m Not a Phase: On the Variability of Phases with Extraction and Ellipsis. Linguistic Inquiry 45(1). 27–89.

Chomsky, Noam. 1980. Rules and representations. New York: Columbia University Press.

Chomsky, Noam. 2001. Derivation by phase. In M. Kenstowicz (ed.), Ken Hale: a life in language, 1–52. Cambridge, MA: MIT Press.

Chomsky, Noam. 2008. On Phases. In Robert Freidin, Carlos Otero & Maria Luisa Zubizarreta (eds.), Foundational Issues in Linguistic Theory. Essays in Honor of Jean– Roger Vergnaud, 133–167. Cambridge, MA: The MIT Press.

Chomsky, Noam. 2013. Problems of Projection. Lingua 130. 33–49.

Chomsky, Noam. 2015. Problems of projection: extensions. In Elisa Di Domen- ico, Cornelia Hamann & Simona Matteini (eds.), Structures, strategies and beyond: Studies in honour of adriana belletti, 1–16. John Benjamins.

Chomsky, Noam, Ángel J. Gallego & Dennis Ott. 2018. Generative Grammar and the Faculty of Language: Insights, Questions, and Challenges. Catalan Journal of Linguistics .

Collins, Chris & Erich Groat. 2018. Distinguishing Copies and Repetitions. Ms .

Cooper, Robin. 2012. Type theory and semantics in flux. In Ruth Kempson, Tim Fernando & Nicholas Asher (eds.), Handbook of the philosophy of science, philosophy of linguistics, vol. 14, 271–323. Oxford: Elsevier.

Cooper, Robin. 2016. Frames as records. In Annie Foret, Glyn Morrill, Reinhard Muskens, Rainer Osswald & Sylvain Pogodalla (eds.), Formal grammar, 3–18.

Cooper, Robin. 2017. Coercion in languages in flux. Presentation: Workshop on approahes to Polysemy and Coercion.

Cruse, D Alan. 1986. Lexical semantics. New York: Cambridge University Press.

OSLa volume 10(2), 2018 dispensing with unwanted polysemy: verbal idioms and the lexicon [63]

Den Dikken, Marcel & Éva Dékány. 2018. A restriction on recursion. Syntax 21(1). 37–71.

Embick, David. 2015. The Morpheme: A Theoretical Introduction. Berlin: Walter de Gruyter.

Epstein, Samuel D, Hisatsugu Kitahara & Daniel Seely. 2016. Phase cancellation by external pair-merge of heads. The Linguistic Review 33(1). 87–102.

Findlay, Jamie Y. 2017. Multiword expressions and lexicalism: the view from lfg. In Proceedings of the 13th Workshop on Multiword Expressions (MWE 2017), 73–79.

Gallego, Ángel J. 2010. Phase Theory. Amsterdam/Philadelphia: John Benjamins.

Gehrke, Berit & Louise McNally. 2017. Idioms and the syntax/semantics interface of descriptive content vs. reference. MS.

Grohmann, Kleanthes. 2003. Prolific Domains. On the Anti-Locality of Movement De- pendencies. Amsterdam: John Benjamins.

Harley, Heidi. 1995. Subjects, Events and Licensing. Massachusetts Institute of Tech- nology PhD dissertation.

Harley, Heidi & Rolf Noyer. 2000. Formal versus encyclopedic properties of vocabulary: Evidence from nominalizations. In Bert Peeters (ed.), The lexicon- encyclopedia interface, 349–374. Amsterdam: Elsevier.

Hulsey, Sarah & Uli Sauerland. 2006. Sorting out Relative Clauses. Natural Language Semantics 14(2). 111–137.

Jouitteau, Mélanie. 2011. Post-syntactic Excorporation in Realizational Morpho- logy : Breton Analytic Tenses. In Andrew Carnie (ed.), Formal approaches to celtic linguistics, 115–142. Newcastle: Cambridge Scholar Publishing.

Labelle, Marie. 2014. Roots in models of grammar. Theoretical Linguistics 40(3-4). 401–414.

Larson, Richard K. 2017. On “Dative Idioms” in English. Linguistic Inquiry 48(3). 389–426.

Marantz, Alec. 1996. “Cat” as a phrasal idiom: Consequences of late insertion in Distributed Morphology. MS. MIT.

Marantz, Alec. 1997. No Escape from Syntax: Don’t try Morphological Analysis in the Privacy of Your Own Lexicon. University of Pennsylvania Working Papers in Linguistics 4(2). 201–225.

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Marantz, Alec. 2007. Phases and words. In S.-H. Choe (ed.), Phases in the Theory of Grammar, 191–222. Seoul: Dong In.

Merchant, Jason. 2018. Roots don’t select, categorial heads do:lexical-selection of pps may vary by category. Ms., University of Chicago .

Pagin, Peter & Dag Westerståhl. 2010. Compositionality I: Definitions and variants. Philosophy Compass 5(3). 250–264.

Pustejovsky, James. 1995. The generative lexicon. Cambridge, MA: MIT Press.

Richards, Marc D. 2007. On feature inheritance: An argument from the phase impenetrability condition. Linguistic Inquiry 38(3). 563–572.

Roberts, Ian. 1993. Verbs and Diachronic Syntax: A Comparative History of English and French. Dordrecht: Springer.

Rodrigues, Alexandra Soares & Graca Rio-Torto. 2013. Semantic coindexation: evidence from portuguese derivation and compounding. In Pius ten Hacken & Claire Thomas (eds.), The Semantics of Word Formation and Lexicalization, Edin- burgh: Edinburgh University Press. ′ Salzmann, Martin. 2017. Reconstruction and Resumption in Indirect A -Dependencies: On the Syntax of Prolepsis and Relativization in (Swiss) German and Beyond, vol. 117. Berlin: De Gruyter Mouton.

Sugioka, Yoko & Takane Ito. 2016. Derivational affixation in the lexicon and syn- tacx. In Taro Kageyama & Hideki Kishimoto (eds.), Handbook of Japanese Lexicon and Word Formation, 347–386. Berlin: De Gruyter Mouton.

van Urk, Coppe. 2018. Pronoun copying in Dinka Bor and the Copy Theory of Movement. Natural Language & Linguistic Theory 36(3). 937–990.

Zwart, Jan-Wouter. 2009. Prospects for top-down derivation. Catalan Journal of Linguisitcs 8. 161–187.

Zwart, Jan-Wouter. 2011. Recursion in language: A layered-derivation approach. Biolinguistics 5(1-2). 043–056.

author contact information Jan Wiślicki University of Warsaw [email protected]

OSLa volume 10(2), 2018 Alexandra Anna Spalek and Matthew Gotham (eds.) Approaches to Coercion and Polysemy, Oslo Studies in Language 10(2), 2018. 65–81. (ISSN 1890-9639 / ISBN 978-82-91398-12-9) https://www.journals.uio.no/index.php/osla

semelfactives

MARKUSEGG Humboldt-Universität zu Berlin abstract The present paper discusses the aspectual class of semelfactives, which comprises expressions that introduce eventualities with inherent boundaries, often a very short duration, but no lexically defined change of state, e.g., flash and cough. After reviewing previous analyses of semelfactives (including their integration into an overall system of aspectual classification), an analysis of semelfactives that treats them as denoting singleton (rather than iterated) eventualities will be defended. As a challenge for this analysis of semelfactives, semantic construction of semelfactives with frequency adverbials will be presented and analysed in terms of a coercion operator.1

[1] introduction Semelfactives are a class of predicates (expressions that denote properties of eventualities or states of affairs). They are defined in terms of aspectual properties, where ‘aspect’ is defined as the way in which predicates present the temporal progression of an eventuality. Typical examples include flash, cough, knock, rap, or nudge, all of which introduce eventualities with inherent boundaries but no lexically defined change of state. In addition, these eventualities have a rather short duration, which has often been modelled as an aspectual property of “punctuality”. These predicates are a challenge for aspectual classification because they can be used not only to refer to singleton eventualities, they frequently are used to denote whole iterations of such eventualities. E.g., (1) is used to refer to a single coughs as well as to a whole series of coughs:

(1) Amélie coughed.

In such an iterative interpretation, the predicate has completely different aspectual properties: Such iterations do not introduce inherent boundaries, as the number of repetitions is not limited. In this way, they are cumulative, or closed under a suitable join operation for eventualities. (P is cumulative iff two adjacent P -eventualities sum up to another P -eventuality.) At the same time, they are

[1] The author wishes to thank Alexandra Spalek, an anonymous reviewer, and the participants of the 2017 Workshop on approaches to coercion and polysemy at the University of Oslo for their valuable feedback. [66] markus egg

neither stative nor fully divisive (closed w.r.t. a suitable part-of relation for eventualities), as there is a clear lower bound, e.g. for (1), one single cough. These two aspectual properties are the hallmarks of the aspectual class of process or activity predicates like run, dance, or sing. Consider for instance cough, for which either of these interpretations can be supported by appropriate linguistic contexts that are compatible with only one of the readings. This predicate lends itself to a combination with suddenly, which suggests inherent boundaries and short duration, as well as to a combination with durative adverbials like the whole night, which has traditionally been cited as a “test” (linguistic environment) that indicates process predicates (see e.g. Dowty 1979):

(2) Suddenly, Amélie coughed. (once) (3) Amélie coughed the whole night. (repeatedly)

While this pattern as exhibited by cough and other semelfactives has been familiar since Comrie (1976) or Talmy (1985), in-depth analyses and formalisations of this flexibility are of more recent origin. Short of assuming polysemy, there are two main lines of analysis, in that the iterative use of semelfactives is either included in their lexical meaning (Rothstein 2004) or the result of aspectual coercion (Moens & Steedman 1988; Smith 1991). The contribution of this paper lies in an attempt to compare and assess these two lines of analysis on the basis of appropriate formalisations. The analyses will be introduced and discussed in the following section, but before doing so I want to introduce a challenge for the semantic construction of semelfactives in combination with frequency adverbials like five times, as in (4):

(4) Amélie coughed five times.

In (4), the adverbial can count the number of repetitions of singleton eventualities, but it can also count distinct iterations of such singleton eventualities. I.e., (4) might refer either to a sequence of five coughs of Amélie, or to a group of five sequences (of undetermined number) of such coughs. I will show that these two readings require specific attention in either of the proposed analyses and, finally, I will argue for the first interpretation of semelfactives, viz., that semelfactives refer to singleton eventualities, and iteration emerges through coercion or semantic construction. The structure of the paper is the following. First I will introduce previous analyses of semelfactives (including their integration into an overall system of aspectual classification). Against this background I will defend an analysis of semelfactives that treats them as denoting singleton (rather than iterated) eventualities. As a challenge for this (and, in fact, any) analysis of semelfactives, se-

OSLa volume 10(2), 2018 semelfactives [67] mantic construction of semelfactives with frequency adverbials will be discussed and formalised in detail.

[2] two analyses of semelfactives This section presents the two major analyses of semelfactives, first, the singleton analysis, which regards them as denoting typically quite short eventualities without a change of state, and the iterative analysis, which interprets them as denoting iterations of such eventualities.

[2.1] The singleton analysis The singleton analysis of semelfactives dates back to Vendler’s (1967) classification. Here they are classified as “achievements” (predicates that introduce eventualities with inherent boundaries and are applicable to temporally minimal entities). In Vendler’s achievement class, semelfactives are grouped together with predicates that introduce a lexically defined change of state, e.g., vanish as a termination of being present. Thus, Dowty’s (1979) and Rothstein’s (2004) reconstruction of Vendler’s achievements as change-of-state predicates excludes semelfactives. Semelfactives were described in Talmy (1985) as “full-cycles”, combinations of two changes of states, in which the second one immediately follows the first one and reverts it. E.g., for flash, the first change of state would be from darkness to light, the second one, the other way round. In Moens & Steedman’s (1988) and Smith’s (1991) classification, semelfactives are assigned a class of their own (Moens and Steedman call it “point”), thus, their achievement class excludes semelfactives, too.2 They define semelfactives as predicates that denote temporally minimal entities but explicily do not introduce a change of state. Their definition of “punctuality” differs from Vendler’s in that exclusive reference to temporally minimal entities is mandatory. In Vendler’s system, “punctuality” is a feature that groups his achievement predicates together with stative predicates, because the latter also can (though need not) refer to temporally minimal entities, because of their full divisivity. An alternative definition of punctuality in terms of the absence of “stages”3 in the denoted eventualities could group predicates in the same way as Vendler’s original definition (Vendler’s achievement class together with the stative predicates). The singleton analysis of semelfactives can be based on the intuition that semelfactives refer to eventualities which are maximal w.r.t. a predicate P . There are different instantiations of this predicate P , in particular:

• an emission of sound or light (flash, cough)

[2] Dini & Bertinetto (1995) advocate such a system, too. [3] Stages are incrementally developing parts of an eventuality which start at its beginning (Landman 2008).

OSLa volume 10(2), 2018 [68] markus egg

• contact plus application of force by momentum (nudge, kick, hit)

• a combination of these (knock, rap, tap)

• movements from and then back into an initial position (twitch, wink, flap)

Formally, this maximality can be characterised in terms of an operator MAX, which is based on Löbner’s (1989, 1999) notion of the “S-phase”. An eventuality ′ e is maximal w.r.t. a predicate P if P holds for e but not for an e of which e is a proper part: ′ ′ ′ (5) ∀P ∀e.MAX(P )(e) ↔ P (e) ∧ ¬∃e .e @ e ∧ P (e )

For example, the semantics of cough could be rendered as (6), if we abstract away from details not relevant here. If one wants to follow up on Dowty’s (1979) research programme of modelling aspectual classes, in which he tried to assign to each aspectual class typical patterns of lexical decomposition with characteristic operators, one might postulate MAX as one of the aspectually relevant operators. ′ (6) λxλe.MAX(make-noise (x))(e)

This definition is fully compatible with Talmy’s (1985) intuition that two changes of state are involved in a semelfactive: Maximality of a P -phase entails that before and after this phase, ¬P must hold. The definition in terms of MAX makes semelfactives telic in the sense of Krifka (1998). For telic predicates, all parts of entities e in their extension are simultaneously an initial and a final part of e. I.e., telic predicates introduce eventualities with inherent temporal (but not necessarily spatial) boundaries: ′ ′ ′ ′ ′ (7) ∀P.TEL(P ) ↔ ∀e∀e .P (e) ∧ P (e ) ∧ e ⊑ e → INI(e , e) ∧ FIN(e , e)

What these decompositions do not capture, however, is the claim that semelfactives refer to very short eventualities, i.e., they do not incorporate any version of an aspectual feature of punctuality. However, this is deliberate, because there are two problems for such a feature. First, there is the general problem of which parts of a larger sequence of eventualities are part of eventualities in the extension of a supposedly punctual predicate. Egg (2005) discusses this question for predicates like die: Is eventually fatal physical decay already part of dying, or does the verb only refer to the end of this decay, i.e., the eventual termination of all bodily and mental activities? This problem is haunting analyses of semelfactives, too. For instance, Roth- stein (2004) states that the characterisation of semelfactives as “punctual” seems to be too strict, because some semelfactives involve trajectories (e.g., of a foot for kick), which would introduce temporal extension and internal stages. Such an

OSLa volume 10(2), 2018 semelfactives [69] analysis of kick would assign a richer semantic structure to it than my analysis in term of the operator MAX above. Thus, kick instantiates the very same problem discussed above for die and similar purported punctual predicates. I think that my analysis in terms of MAX can be defended, which would also mean that this first problem does not arise for semelfactives. This will be illustrated for the example kick. Here the crucial question is: Does the movement of a foot towards a goal before making contact with it also belong to the eventualities in the extension of kick? My answer is that the traject of the foot is not part of the eventuality, but it is implied in that the momentum that figures in the definition of the semantics of kick is the result of a movement (otherwise, the application of force would have to be described as a push or a shove). While this first general problem thus does not arise for semelfactives, there still is the second problem, the question of how to define minimal duration, even if we assume that “punctuality” is not a physical but a conceptual category. For instance, there is considerable leeway in the duration of a (singleton) flash, which intuitively does not affect its semelfactive status at all. In the same way, using the verb cough to describe a slo-mo recording of a cough would be perfectly fine (as pointed out by Comrie 1976) even though the described state of affairs would not be punctual (having temporal extension and even stages). A third problem emerges if one wants to follow Talmy (1985) in decomposing the semelfactive into two subsequent changes of state (his “full-cycles”). Even if a change of state could be instantaneous, semelfactives would require minimally two instants, hence, could not be instantaneous themselves. Therefore I suggest regarding punctuality not as an aspectual feature but as defeasible conceptual knowledge about the typical duration of events that is associated with predicates. See Egg (2005) for a worked out formalisation of this idea and Bary & Egg (2012) for an application to aspectual semantics and coercion. If one regards the singleton use of semelfactives as basic, the iterative use of semelfactives emerges by aspectual coercion or reinterpretation. Such coercions introduce a suitable operator between an aspectually sensitive operator and its predicate argument that does not fulfill the aspectual selection restriction of the operator. In this way, an impending aspectual mismatch is avoided, e.g., for semelfactives that are the complement of keep on or are modified by durative adverbials like for five hours (Talmy 1985; Moens & Steedman 1988; Smith 1991; Egg 2005). Concretely, coercion for such syntactic structures with semelfactives introduces into their semantic representations an iterative operator ITER between a semelfactive argument and an aspectually sensitive functor like the durative adverbial for five hours. The functor selects for a cumulative argument, and the application of ITER to the semantic contribution of the semelfactive returns such a cumulative argument, which fulfils this selection restriction. The formalisation of ITER is given in (8). In prose, e is a P -iteration iff it is

OSLa volume 10(2), 2018 [70] markus egg ⊔ a minimal entity “ E” that is (at least temporally) uninterrupted and contains the subeventualities of the iteration set E (such that P holds for each of these subeventualities): ⊔ ′ ′ ′ (8) ∀P ∀e.ITER(P )(e) ↔ ∃E.e = E ∧ ∀e .e ∈ E → P (e ) ⊔ The motivation for the last condition on E is that when we measure the length of an iteration, the breaks between the subeventualities are taken into account, too. This can be illustrated by an attempt to express the fact that Amélie played the Moonlight Sonata every day in June by the sentences in (9). Even though (9)b sums up the lengths of the individual performances (each of which lasts approximately 15 minutes) appropriately, the adequate description is (9)a, which also considers the breaks in between:

(9) a. Amélie played the Moonlight Sonata for 30 days. b. Amélie played the Moonlight Sonata for 7.5 hours.

After coercion, the semantic representation of the iterative use of cough would then be (10):

′ (10) λxλe.ITER(MAX(make-noise (x)))(e)

[2.2] The iterative analysis In Rothstein’s (2004, 2008) analysis, the iterative interpretation of semelfactives is the basic one. E.g., for cough, its basic semantic contribution would roughly be represented by (10). She considers the two uses of semelfactives to instantiate neither ambiguity nor aspectual coercion. Instead, the choice between the two uses emerges as a context-dependent specification of an underspecified lexical meaning. The singleton interpretation is a mere fringe case of this meaning, in which the iteration consists of only one single eventuality. Consequently, the iterative operator is present even in this fringe case, which would make semelfactives cumulative.4 At the same time, semelfactives in iterative interpretation are not fully divisive; the singleton interpretation indicates the lower bound of divisivity. This means - and Rothstein argues - that semelfactives do not emerge as achievement predicates anymore. Due to their cumulativity and limited divisivity, they can be grouped together with prototypical process or activity predicates such as move, dance, or sing. Next, Rothstein points out that semelfactives (in iterative interpretation) and prototypical activity predicates are both iterative in some sense; e.g., move is

[4] Adjacency must be defined appropriately here, because e.g. for an iterative interpretation of flash, the phases of light must be interrupted by phases of darkness.

OSLa volume 10(2), 2018 semelfactives [71] an iteration of minimal changes of location (Dowty 1979). She distinguishes the two groups of predicates in that only semelfactives are naturally atomic, i.e., have conceptually salient non-overlapping minimal eventualities. This condition is included in Landman’s (2016) concept of “neatness”. In contrast, minimal eventualities of typical activity predicates lack this property, e.g., the minimal changes of place as the foundation of (continuous) movement overlap and are not conceptually salient. In a next step, Rothstein links natural atomicity to lexical accessibility by claiming that only minimal eventualities of naturally atomic predicates are lexically accessible, e.g., countable. Consider for instance the contrast in (11), where (11)a can refer to five single coughs but (11)b cannot refer to five minimal changes of location:

(11) a. Amélie coughed five times. b. Amélie moved five times.

In sum, Rothstein’s analysis captures both uses of semelfactives in one single reading, which is a very elegant and attractive solution. Still, I feel that it is worth while reconsidering the definition of natural atomicity in terms of non-overlapping minimal events: There are process predicates that follow the pattern of (11)b but nevertheless seem to be analysable in terms of conceptually salient non-overlapping minimal events, for instance, walk. Al- though the minimal eventualities could be characterised as single steps here, walk five times refers to five iterations of taking steps, not to one single iteration with 5 steps. Similarly, lexicalised iteratives in the class of process predicates, among them tremble and jiggle, clearly have minimal eventualities (roughly, specific back and forth movements). Still, tremble five times refers to five iterations of such movements only. One might try to explain away this counterargument by pointing out that, at least under normal circumstances, one does not refer to, say, single jerks or twitches in terms of jiggle or tremble, respectively. And, if minimal jigglings or tremblings must comprise at least two jerks or twitches, these minimal eventualities would be overlapping, and, consequently, the predicates would not be naturally atomic. However, one could explain this preference in terms of lexical competition, following a similar argumentation of Gyarmathy (2016) for Hungarian semelfactives: Pairs like jiggle and jerk of tremble and twitch form Horn scales, with jerk and twitch being the stronger alternatives, as they are restricted to an interpretation as singleton eventualities. Hence, using the weaker elements jiggle or tremble (which could refer to both singleton eventualities or iterations of these eventualities) implies that the stronger elements do not hold.

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The preceding discussion argued that not all naturally atomic predicates denote eventualities with lexically accessible parts. The example of stir is a counter- example in the other direction. It is not naturally atomic because its minimal eventualities overlap (any completed round of 360 degrees would qualify), but these eventualities are accessible nevertheless and can be counted, as illustrated by a quote from a recipe for the Draught of Living Death (taken from Harry Potter and the Half-Blood Prince):

(12) (i) Add the infusion of wormwood. (ii) Add the powdered root of asphodel. (iii) Stir twice clockwise. (iv) Add the sloth brain. (v) Add the sopophorous bean’s juice. (vi) Stir seven times anti-clockwise.

The conclusion to be drawn from these examples is that natural atomicity is independent of lexical accessibility, and that accessibility is a lexical property that cannot be fully predicted. Consequently, the property of lexical accessibility is orthogonal to natural atomicity in Rothstein’s sense: Naturally atomic predicates can have it (cough in the iterative analysis) or not (e.g., tremble), similarly, naturally non-atomic predicates can have it (e.g., stir) or not (move). This property allows counting the elements of a single iteration by means of frequency adverbials like in one of the interpretations of (4). But at the same time this property entrenches the distinction between the class of activity predicates and the semelfactives, in contrary to Rothstein’s original enterprise to classify semelfactives as activity predicates.

[3] semantic construction with frequency adverbials In this section, the modification of semelfactives by frequency adverbials like five times will be discussed. This discussion is motivated by the observation that the semantic construction for these expressions provides an environment in which the two proposed approaches to semelfactives as presented in the preceding section make different predictions and hence can be compared. First, the semantic contribution of frequency adverbials of the type “n times” is specified in (13) as the operator “ITERn”. This operator is based on the definition of ITER in (8). It introduces iterations with a fixed number of repetitions in that it specifies in addition the cardinality of the underlying set of eventualities E: ⊔ ′ ′ ′ (13) ∀n∀P ∀e.ITERn(P )(e) ↔ ∃E.|E| = n ∧ e = E ∧ ∀e .e ∈ E → P (e )

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In prose, any e instantiating n times P is temporally uninterrupted and minimal w.r.t. containing n subeventualities in the extension of P . The challenge for either analysis of semelfactives is semantic construction for (4). For the singleton analysis, the reading (14) with five iterations of coughs is challenging, and for the iterative analysis, the reading (15) with five single coughs:5

′ (14) λe.ITER5(ITER(MAX(make-noise (a))))(e) ′ (15) λeITER5(MAX(make-noise (a)))(e)

The semantic representations highlight the difference between (14) and (15) in that the former but not the latter includes two iterations.

[3.1] The singleton analysis This subsection will review the way in which the different analyses can handle the two readings of (4), starting with the singleton analysis. Here deriving the reading (15) of (4) with five single coughs is straightforward (applying ITER5 to (6)).6 The derivation of the reading (14) with five iterations of coughs is less straightforward, however, as it comprises two iterations. Only one of them is introduced semantically (in the semantics of five times), which raises the question of where the other one comes from. Simply assuming an iterative coercion operator between adverbial and predicate would not suffice, though. If this operator is supposed to be more than a post hoc move, it must be motivated, and there is no impending aspectual clash to be avoided by such a move. Frequency adverbials are compatible with predicates from all aspectual classes (consider e.g. be in the pub five times), so any motivation for a coercion operator must stem from a different source. I contend that the motivation lies in the attempt to align information on the duration of an eventuality. Temporal duration is expressed in particular in durative and time frame adverbials, but also through the typical duration of the eventualities denoted by predicates, which is given by conceptual knowledge. If adverbials and verb yield potentially conflicting information on the duration of an eventuality, this can trigger coercion irrespective of aspectual compatibility (Egg 2005; Bary & Egg 2012). For instance, temporal alignment uses an iterative operator in (16), which lengthens typical durations of predicates:

(16) Amélie played the piano for years.

[5] In the semantic representations of the remainder of this article, I will occasionally make use of η-equality (λe.P (e) ≡ P , if e does not occur free in P ) in order to facilitate reading. [6] Here and in the following, the semantics of the subject Amélie is tacitly included in the form of the constant “a”.

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A single instance of playing the piano has a typical duration of minutes or hours, but not days, weeks, months, or years. However, an iteration of such playing eventualities might well last years. For our example (4) this means that the choice of readings can be influenced by temporal adverbials: Time frame adverbials can trigger an insertion of ITER for purposes of safeguarding alignment of duration information. For instance, in the following pair, the interpretation as an iteration of iterations should be more strongly preferred for the second element, which is bourne out:

(17) Amélie coughed five times in the last minute. (18) Amélie coughed five times in the last hour.

In addition, this analysis would predict that lexicalised iteratives like tremble five times have no reading in which single eventualities are counted. Predicates like tremble lexically comprise an iteration, very roughly:7 ′ (19) λxλe.ITER(MAX(move-bf (x)))(e)

Hence, combining it with a frequency adverbial will always return an expression with two iterative operators, no reading is possible in which the underlying movements of a single act of trembling are counted. This automatic blocking of potential overgeneration is an advantage of the singleton analysis of semelfactives. Finally, the singleton analysis must address the question of why semelfactives lend themselves so easily to iterative coercion. The answer is that iterating semelfactives is facilitated by the fact that the state of affairs immediately before and after such an eventuality (the “prestate” and “poststate” of Moens & Steed- man 1988) must be identical, which in our analysis is modelled by the MAX operator. I.e., immediately before and after an eventuality in the extension of MAX(P ) ¬P must obtain. Compare this to change-of-state predicates, which introduce a change from ¬P to P , hence, iterating them would presuppose the restoration of the prestate ¬P between all the subeventualities of the iteration, which makes the assumption of iterative coercion less easy for them.

[3.2] The iterative analysis For the iterative analysis of semelfactives, the challenge is the other way round: The derivation of (14) is straightforward (applying ITER5 to (10)), it is the derivation of (15) that is challenging. The problem is that there is only one iterative operator in (15), but the verb and the adverbial each provide one in their semantic contribution. But intuitively, the frequency adverbial does not introduce an additional iteration in the reading modelled by (15), it merely counts the underlying

′ [7] Here “move-bf ” is shorthand for moving out of a position and returning back to it.

OSLa volume 10(2), 2018 semelfactives [75] eventualities of the iteration, which are accessible. This raises the question of how to do semantic construction, because, the underspecified approach of Rothstein needs to be augmented in some way to be able to derive a semantic representation for this reading. To handle the interpretation of (4) with five eventualities in the iterative approach, one could assume a coercion operator that intervenes between the frequency adverbial and the predicate to “cancel out” the second iterative operator. Formally, this operator would be a function from predicates P to the set of P - atoms, where P -atoms are defined as entities in the extension of P no proper part of which is likewise in the extension of P (Krifka 1998):

(20) a. λP λe.ATOM(P )(e) ′ ′ ′ b. ∀P ∀e.ATOM(P )(e) ↔ P (e) ∧ ¬∃e .e @ e ∧ P (e )

Thus, (21), the semantics of (4) with five iterations of knocks, can be derived by applying ITER5 to (10). The semantics of (4) with five single knocks emerges by applying ITER5 to the result of applying (20)a to (10), as in (22). Here the frequency adverbial reports on the number of singleton eventualities of coughing, because atomic iterations are singleton eventualities. Consequently, (22) is equivalent to (15).

′ (21) λe.ITER5(ITER(MAX(make-noise (a))))(e) = (14) ′ (22) λe.ITER5(ATOM(ITER(MAX(make-noise (a)))))(e)

To sum up, either analysis can handle one of the two interpretations of (4) directly and needs to assume a phonologically not visible operator for the other interpretation. Still, there are two aspects in which the singleton analysis emerges as the more preferable one. First, assuming (24)b as a coercion operator in English would not be straightforward in that it would operate in a different way from other operators: The effect of ITER would be merely the cancellation of lexically introduced semantic material, while normally, coercion operators contribute additional material.8 What is more, assuming such an aspectual coercion for English raises the question of how to restrict it appropriately. In particular, we need to prevent the derivation of non-attested readings of tremble five times and the like, which have no readings where singleton eventualities are counted. For instance, tremble five

[8] At this point, it seems in order to mention as seeming counterexamples analyses of the progressive that assume coercion operators “stripping off” the culmination, e.g., Moens & Steedman (1988) or Parsons (1990). However, the ongoing discussion of the “imperfective paradox” demonstrates that the culmination is in fact not removed, only its status w.r.t. factivity changes, see e.g. Landman (1992) or Bonomi (1997), to name but a few.

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times cannot refer to a single act of trembling with five underlying minimal movements, as expressed in (23):

′ (23) *λxλe.ITER5(ATOM(ITER(MAX(move-bf (x)))))(e)

Thus, the application of ATOM to the semantics of tremble must be blocked. Such a restriction could not fall back on the property of natural atomicity, because tremble is naturally atomic. The only way out here would be recourse to the property of (not) applying to singleton entities in the iteration, which tremble lacks. However, this presupposes that there is a difference between predicates like tremble and those like cough, which is best modelled in terms of an aspectual distinction between activity predicates and semelfactives. In sum, semantic construction for frequency adverbials modifying semelfactives shows that the singleton approach to semelfactives is more advantageous. But in order to obtain further insights into the question of how to interpret semelfactives, it seems advisable to extend the perspective to at least some languages that possess a richer verbal morphology than English in order to search for morphological evidence for the operators sketched in the last two subsections. Rel- evant data from two such languages, viz., Russian and Hungarian (the latter in a much more preliminary manner), will be discussed in the next subsection.

[3.3] Semelfactives and iteratives in Russian and Hungarian In Russian, a singleton interpretation can be indicated morphologically. For instance, in “prototypical semelfactives” (Dickey & Janda 2009), the verbal affix nu- is used for this purpose (Makarova & Janda 2009), like in kašlja-nu-t’ ‘cough once’, which contrasts with kašljat’ ‘cough repeatedly’.9 The suffix nu- strongly prefers unbounded extended stems that express iterations of (typically very short) “quanta of a situation” (Dickey & Janda 2009), in other words, stems that are naturally atomic in the sense of Rothstein. Nesset (2013) points out that these “quanta” do not introduce an explicit change of state. In combination with frequency adverbials, both forms are acceptable, but they have different interpretations, which allows expressing either reading of (4) explicitly:

(24) a. pjat’ raz kašljat’ ‘cough repeatedly five times’ b. pjat’ raz kašljanut’ ‘cough five times’

This suggests that nu- is a visible version of the operator with the meaning (20)a, which maps predicates P to the set of their P -atoms. The derivation of the semantics of the examples in (24) follows the patterns sketched above for the

[9] There is a variant anu- of nu-, which is often considered to contribute an addition flavour of “intensive- ness”, see Makarova & Janda (2009) for details.

OSLa volume 10(2), 2018 semelfactives [77] iterative interpretation of semelfactives. To derive the semantics of (24)a, ITER5 is applied to (10), which returns (21). For the semantics of (24)b, we apply ITER5 to the result of applying (20)a to (10), and receive (22). Consequently, the effect of this operator, by mapping iterative predicates onto semelfactives, seems to be in line with, and to support the iterative analysis as it was suggested in Rothstein’s account of semelfactives. However, the situation in Russion is more complex, first because of an additional affix, the prefix s-, which is used to form semelfactives, too. In such semelfactives, however, the verbal bases do not express iterations of small eventualities, consider for instance s-letet’ ‘fly to a specific location and return’, whose base is letet’ ‘fly’. Even if the verb introduces natural atomicity, like in s-xodit’ ‘walk to a specific location and return’, whose base is xodit’ ‘walk’, the affix does not fall back on the level of atomicity (i.e., single steps) but introduces an external criterion of atomicity, which is not inherent in the verb. Thus, s- introduces rather than presupposes natural atomicity. As a consequence, it can also be attached to other verb stems, e.g., ones that describe a kind of behaviour like grubit’ ‘be rude’, to form verbs that describe an action that instantiates this behaviour, here, s-grubit’ ‘perform a rude action’. Nesset (2013) shows that the (historically older) affix nu- is also increasingly used to form semelfactives that lack an iterative base, a tendency emerging in particular in non-standard Russian (Sokolova 2015). The resulting semantic overlap between the two affixes motivates Dickey & Janda (2009) to analyse them as (not completely complementary) morphologically conditioned allomorphs.10 Nesset (2013) describes the history of Russian semelfactive affixes as a development from the “prototypical” cases to a more general word-formation device that introduces what one could call suitably “portions” of an eventuality that in itself does not possess inherent boundaries. While the “portioning” may fall back on inherent atomicity like kašlja-nu-t’ ‘cough once’, this is no longer necessary. Reformulating this development in terms of the analyses of semelfactives discussed in this paper, it is a development away from a situation describable in terms of the iterative approach, in which semelfactives were derived from iteratives, to a situation, in which the semelfactive is independent of underlying it- erativity, which fits in with the singleton analysis of semelfactives. Also, we note that the Russian evidence supports the observation that semelfactives do not introduce a change of state and may vary in length (hence cannot be characterised as “punctual”). Hungarian likewise does not present a uniform picture with respect to semel-

[10] They put the distribution of these affixes down to a mixture of factors, in particular, the conjugation type and the semantic class of the verb. Since verb stem class and semantic class are interdependent themselves, affix distribution depends on both. Makarova & Janda (2009) claim that phonological factors influence the distribution of semelfactive affixes, too. The semantic overlap of the affixes also shows up in doublets like s-xvastat’ and xvast-nu-t’, both of which mean ‘boast once’ (Dickey & Janda 2009).

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factives. Iteratives may be formed from semelfactives with the affix -gAt,11 e.g., kacsint-gat ‘wink repeatedly’ from kacsint ‘wink (once)’. But the perfective marker meg-, which is used to introduce an inherent final boundary, e.g., in meg-épit ‘build’, see Kiss 2011 for details) may also be used to derive semelfactives from suitable iteratives, e.g., in meg-kapar ‘scratch’. In addition, semelfactives and iteratives can sometimes be derived from the same stem with different suffixes, compare e.g. köh-int ‘cough (once)’ and köh-ög ‘cough repeatedly’ (Gyarmathy 2016). At a first glance, this suggests that the iterating operator ITER is expressed in the affixes -gAt and -Og, which suggests semantic composition along the lines of the singleton approach. However, there are also morphologically marked semelfactives like meg-épit and köh-int. Especially for the general perfectivising marker meg-, further research is called for in order to explain why it can introduce semel- factivity into the semantics of meg-kapar and the like. Consequently, the case of Hungarian cannot as yet be adduced as evidence to contribute to a comparison between the singleton and the iterative approach to semelfactives.12 In sum, the evidence from Russian and Hungarian corroborates the insight that semelfactives and iteratives are closely related. Still, the evidence does not yet yield conclusive evidence in favour of either of the two approaches to semelfactives that were compared in this paper. For English semelfactives, their interpretation in the context of modification by frequency adverbials suggests a preference for the singleton approach.

[4] conclusion To sum up, the paper presented and compared two analyses of semelfactives. The first one was the singleton analysis, which regards them as referring to typically quite short eventualities that have inherent boundaries but do not introduce a change of state. Here an additional iterative coercion operator must be assumed to derive the fact that semelfactives can refer to whole series of such eventualities in specific contexts, for instance, the progressive. In contrast, the iterative analysis of semelfactives needs to assume a minim- ising coercion operator that cancels out iteration in order to model the fact that a combination of a semelfactive with a frequency adverbial may refer to one series of eventualities only, in which the adverbial counts the number of the eventualities in the series. The paper argued for the first of the two analyses, claiming that the iterative use of semelfactives is either due to processes of lexical construction or to aspectual coercion. As a next step, it seems advisable to continue investigating semelfactives by

[11] Due to vowel harmony, the vowels in the affixes may be realised in different ways, which is indicated by the capital letters. [12] See also Gyarmathy (2016) for a detailed account on semantic differences between the affixes.

OSLa volume 10(2), 2018 semelfactives [79] analysing in detail data from further languages, in particular, those with a richer verbal morphology. Furthermore, proposed analyses for semelfactives and related iteratives need to be tested along the lines of Bott & Gattnar (2015); Piñango & Deo (2016): If, like claimed in the present paper, expressions like e.g. cough for five hours are indeed the result of aspectual coercion (rather than contextual restriction of a lexically underspecified item), their processing should be more costly than the processing of non-coerced expressions, and the additional processing effort should be demonstrable experimentally. references Bary, Corien & Markus Egg. 2012. Variety in Ancient Greek aspect interpretation. Linguistics & Philosophy 35. 111–134.

Bonomi, Andrea. 1997. The progressive and the structure of events. Journal of Semantics 14. 173–205.

Bott, Oliver & Anja Gattnar. 2015. The cross-linguistic processing of aspect – an eyetracking study on the time course of aspectual interpretation in Russian and German. Language, Cognition and Neuroscience 30. 877–898.

Comrie, Bernard. 1976. Aspect. Cambridge: Cambridge University Press.

Dickey, Stephen & Laura Janda. 2009. Xoxotnul, sxitril: the relationship between semelfactives formed with -nu- and s- in Russian. Russian Linguistics 33. 229–248.

Dini, Luca & Pier Marco Bertinetto. 1995. Punctual verbs and the linguistic ontology of events. Quaderni del Laboratorio di Linguistica 7. 123–160.

Dowty, David. 1979. Word meaning and Montague grammar. Dordrecht: Reidel.

Egg, Markus. 2005. Flexible semantics for reinterpretation phenomena. Stanford: CSLI Publications.

Gyarmathy, Zsófia. 2016. Semelfactives in English and in Hungarian: A countability-based analysis. In Proceedings of IATL 32, 57–76.

Kiss, Katalin. 2011. Contributions to the analysis of activity verbs and telicity marking in English and Hungarian. Argumentum 7. 107–120.

Krifka, Manfred. 1998. The origins of telicity. In Susan Rothstein (ed.), Events and grammar, 197–235. Dordrecht: Kluwer.

Landman, Fred. 1992. The progressive. Natural Language Semantics 1. 1–32.

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Landman, Fred. 2008. 1066. On the differences between the tense-perspective- aspect systems of English and Dutch. In Susan Rothstein (ed.), Theoretical and cross-linguistic approaches to the semantics of aspect, 107–166. Amsterdam: Ben- jamins.

Landman, Fred. 2016. Iceberg semantics for count nouns and mass nouns: classifiers, measures and portions. Baltic International Yearbook of Cognition, Logic and Communication 11. 1–48.

Löbner, Sebastian. 1989. German schon - erst - noch: an integrated analysis. Lin- guistics & Philosophy 12. 167–212.

Löbner, Sebastian. 1999. Why German schon and noch are still duals: a reply to van der Auwera. Linguistics and Philosophy 22. 45–107.

Makarova, Anastasia & Laura Janda. 2009. Do it once: a case study of the Russian -nu- semelfactives. Scando-Slavica 55. 78–99.

Moens, Marc & Mark Steedman. 1988. Temporal ontology and temporal reference. Computational Linguistics 14. 15–28.

Nesset, Tore. 2013. The history of the Russian semelfactive: the development of a radial category. Journal of Slavic Linguistics 21. 123–169.

Parsons, Terence. 1990. Events in the semantics of English. Cambridge: MIT Press.

Piñango, Maria Mercedes & Ashwini Deo. 2016. Reanalyzing the complement coercion effect through a generalized lexical semantics for aspectual verbs. Journal of Semantics 33. 359–408.

Rothstein, Susan. 2004. Structuring events: an essay on the semantics of lexical aspect. Oxford: Blackwell.

Rothstein, Susan. 2008. Two puzzles for a theory of lexical aspect. In Johannes Dölling, Tatjana Heyde-Zybatow & Martin Schäfer (eds.), Event structures in linguistic form and interpretation, 175–197. Berlin: de Gruyter.

Smith, Carlota. 1991. The parameter of aspect. Dordrecht: Reidel.

Sokolova, Svetlana. 2015. “rabotnul na slavu-gul’ni smelo!”:-nu-as a universal aspectual marker in non-standard russian. In Mitsushi Kitajo (ed.), Aspektual’naja semanticheskaja zona: tipologija sistem i scenarii diakhronicheskogo razvitija. Sbornik statej V Mezhdunarodnoj konferencii Komissii po aspektologii Mezhdunarodnogo ko- miteta slavistov , 271–277. Kyoto: Tanaka Print.

OSLa volume 10(2), 2018 semelfactives [81]

Talmy, Leonard. 1985. Lexicalization patterns: semantic structure in lexical forms. In Timothy Shopen (ed.), Language typology and syntactic description vol. 3: Gram- matical categories and the lexicon, 55–149. New York: Cambridge University Press.

Vendler, Zeno. 1967. Verbs and times. In Z. Vendler (ed.), Linguistics in philosophy, 97–121. New York: Cornell University Press.

author contact information Markus Egg Humboldt-Universität zu Berlin [email protected]

OSLa volume 10(2), 2018

Alexandra Anna Spalek and Matthew Gotham (eds.) Approaches to Coercion and Polysemy, Oslo Studies in Language 10(2), 2018. 83–96. (ISSN 1890-9639 / ISBN 978-82-91398-12-9) https://www.journals.uio.no/index.php/osla

coercion in languages in flux

ROBINCOOPER University of Gothenburg abstract The classical view of semantics that we inherited from Montague is that natural languages are formal languages where semantics specifies the interpretations which can be associated with expressions of the language. In this context coercion might be seen as a slight but formally specifiable disturbance in the formal semantics which shows how the canonical interpretation of an expression can be modified by its linguistic context. In recent years an alternative to the formal language view of natural language has developed which sees the interpretation of language as a more local and dynamic process where the interpretation of expressions can be modified for the purposes of the utterance at hand. This presents linguistic semantics as a dynamic, somewhat chaotic, system constrained by the need to communicate. An interpretation of an expression will work in communication if it is close enough to other interpretations your interlocutor might be familiar with and there is enough evidence in the ambient context for her to approximate the interpretation you intended. On this view of language as a system in flux, coercion is not so much a disturbance in the semantic system but rather a regularization of available interpretations leading to a more pre- dictable system. I will present some of the reasons why I favour the view of language in flux (but nevertheless think that the techniques we have learnt from formal semantics are important to preserve). I will look at some of the original examples of coercion discussed in the Pustejovskian generative lexicon and suggest that the possibilities for interpretation are broader than might be suggested by Pustejovsky’s original work. Finally, I will suggest that coercion can play a central role in compositional semantics taking two examples: (1) individual vs. frame-level properties and (2) dynamic generalized quantifiers and property coercion.

[1] how formal are natural languages? The view of natural languages as formal language was extremely important in 20th century linguistics since it gave us a mathematical approach to making precise the apparent chaos of natural language. The formal approach includes formal grammar where languages are seen as sets of strings and associating such strings with structural descriptions as in various forms of transformational grammar. With the advent of formal semantics interpreted languages could be seen as sets [84] robin cooper

of string-meaning pairs. There is, of course, the famous quote from Montague’s Universal Grammar which became a slogan for a formal approach to semantics:

There is in my opinion no important theoretical difference between natural languages and the artificial languages of logicians; indeed I consider it possible to comprehend the syntax and semantics of both kinds of languages within a single natural and mathematically precise theory. (Montague 1974, pg. 222)

How well does coercion fit with such a formal language view? Perhaps it can be regarded as a slight disturbance or adjustment, rather similar to Montague’s treatment of ambiguity, a feature of natural languages which is not shared with formal languages, by allowing more than one derivation tree to be associated with single strings in the language. I think many current approaches to coercion are attempting to include it with minimal disruption to a general view of natural language as a formal language. However, there are a number of other aspects of natural languages which give pause for thought. Consider the notion of grammaticality. The idea in a formal language is that you characterize the set of (grammatical) expressions in the language. However, grammaticality judgements by speakers of natural languages are often in terms of degrees of grammaticality. An expression which seems ungrammatical can often be “improved” by thinking of it used in a particular context. Speakers adapt the language to new situations and domains, changing grammaticality judgements (Clark & Clark 1979, a classic paper). When it comes to meaning it seems that words and phrases do not have a fixed range of interpretations as would be suggested by the formal language view but rather that speakers adapt the meaning to fit the subject matter under discussion. Furthermore speakers seem to negotiate the interpretation of expressions during the course of a dialogue. Examples of this include using the same proper noun to refer to different individuals and discussion of the interpretation of words referring to abstract or theoretical concepts such as democracy or meaning (as a concept in linguistic theory). In order to meet this kind of consideration Cooper & Ranta (2008) proposed to think of a language as a collection of resources (a “toolbox”) which can be used to construct a language in the formal language sense. The idea here was to maintain the insights and precision gained from the formal language view while at the same time taking account of the fact that speakers of a natural language are constantly in the process of creating new language to meet the needs of novel situations in which they find themselves. Such innovation can be a motor for historical change in language, as discussed for example in the Introduction to Cooper & Kempson (2008).

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If this process of innovation is unconstrained, how can it be that we manage to communicate with each other? Let us look at some examples of how wild it can be:

(1) a. a common noun meaning ‘step’ ⇒ a negative particle: French pas b. a proper noun referring to a sandwich spread ⇒ an adjective, A, such that AN means ‘N which people either love or hate’: Marmite c. mass noun meaning ‘small stones’ ⇒ verb meaning ‘spread something on roads to stop traffic skidding in winter weather’: grit d. a noun/adjective referring to nationals of a country ⇒ noun/adjective meaning ‘of smugly narrow mind and of conventional morality whose materialistic views and tastes indicate a lack of and an indifference to cultural and aesthetic values’ (Wikipedia): Philistine e. a noun referring to bread browned by radiant heat ⇒ a predicative expression meaning ‘finished’ (in terms of career): toast

At a more micro-level of lexical semantics, Cooper (2010, 2012) discusses subtle variation in meaning of the verb rise which we summarize here:

(2) a. the temperature rises (temperature changes, location – or path – constant) b. the price rises (price changes, product and location constant) c. the Titan rises1 (location of Titan changes, Titan constant) d. China rises2 (‘gains in economic power and political influence’) e. Mastercard rises3 (‘value of shares goes up’) f. dog hairs rise4 (explanation after clarification request: they rise upstairs)

Basically, as de Saussure (1916) pointed out, you can use a linguistic sign to express any arbitrary meaning. But there is an important constraint provided by the fact that people have to use language for more or less successful communication. This means that the speaker tries to maximize the probability that the hearer will understand what is said in approximately the way it was intended. The hearer, for her part, tries to adjust her semantic interpretation so that what the speaker says makes sense (or is true) in the context in order to maximize the probability that she has understood what the speaker intended. This will not happen if people assign random interpretations to linguistic expression. There has to be a

[1] description of a video game, http://en.wikipedia.org/wiki/Risen_(video_game), accessed 4th February, 2010 [2] http://www.foreignaffairs.com/articles/63042/g-john-ikenberry/the-rise-of-china- and-the-future-of-the-west, accessed 4th February, 2010. [3] http://blogs.barrons.com/stockstowatchtoday/2010/02/03/visa-up-on-q1-beat- forecast-mastercard-moves-in-sympathy/?mod=rss_BOLBlog, accessed 4th February, 2010 [4] BNC file KBL, sentence 4201

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way for the speaker and hearer to compute a novel meaning for an expression on the basis of meanings that they have already associated with words in an expression. One way to do this is through semantic coordination which has been discussed extensively in the psycholinguistic literature (Clark & Wilkes-Gibbs 1986; Garrod & Anderson 1987; Pickering & Garrod 2004; Brennan & Clark 1996; Healey 1997; Mills 2007; Healey et al. 2007) but less so in the theoretical linguistic literature (Cooper & Ranta 2008; Larsson 2010; Larsson & Cooper 2009). On this view of language, coercion, rather than being a slight disturbance as it was on the formal language view, emerges as an additional technique providing helpful regularities which enable people to predict how meaning may be changed. Consider a classic example discussed by Pustejovsky (1995):

(3) a. The child began a new book b. The author began a new book

Here we tend to assume that the child began reading a new book and that the author writing one. Reading and writing are standard activities associated with books and Pustejovsky puts this information into the lexical entry for book. How- ever, coercion based on information contained in the lexicon will not alone be sufficient to explain how we interpret such sentences. Consider:

(4) Sam began a new book

Which interpretation you get depends on what you know about Sam. Is she a child or an author? But still there may be questions the answers to which may not be decidable. Note, for example, that it is not just straightforward probability that decides which reading you get: most authors read more books than they write. Furthermore, there are many other things that Sam might be which might suggest an alternative relation to books that could be used in the coercion: an illus- trator, an editor, a translator, a Nazi, a goat, a copying machine, …. Furthermore the general context might influence which exact coercion we use to interpret the sentence. In the unlikely scenario that the world suddenly lurches to a philistine extreme right in which the possession and reading of books is proscribed, it is possible that the most probable interpretation of the sentence is that Sam began destroying a book in order to remove the evidence. Nevertheless it seems important to know that begin followed by a noun-phrase coerces the interpretation of that noun-phrase into a property and that the result behaves like a subject-control construction, that is, what begins is an event of the subject having the property resulting from the coercion. Exactly which property is involved may not be decidable in the general case but at least we know that we are looking for a relation that might hold between the subject and the object of the sentence. Such general coercion patterns are, I believe, an important part of

OSLa volume 10(2), 2018 coercion in languages in flux [87] our linguistic knowledge which help us to efficiently compute interpretations for utterances despite that fact that our language is in a constant state of flux. In the remainder of the paper I will look at a couple of coercions which I have worked on previously from this perspective. They represent two different kinds of coercions that occur in natural language. The first, in Section [2], is a kind of coercion which yields an additional interpretation for an expression above and beyond what we might think of as the basic interpretation. The second, in Sec- tion [3], is a coercion which is so to speak part of the fabric of compositional semantics, that is, it is involved in computing what we might regard as the basic meaning of a certain kind of expression. As we will see, the exact nature of the coercions varies from utterance to utterance in the manner one might expect from a system in flux. Nevertheless there is a common pattern which puts some order into the chaos.

[2] coercion of individual level properties to frame level properties Cooper (2016) makes a connection between the following two puzzles:

(5) Partee puzzle From The temperature is rising The temperature is 90 we cannot conclude 90 is rising (Montague 1973) (6) Individual to event coercion A sentence like Four thousand ships passed through the lock has a reading where there are four thousand ship-passing-through-the- lock events, some of which may involve the same ship. (Krifka 1990)

The claim is that these two puzzles can be seen as related if we introduce a notion of frame into our semantics. Here we think of a frame (or frame type) as being intuitively the same as an event or situation (type) modelled as a record (type) in TTR, a type theory with records (Cooper 2012, in prep; Cooper & Ginzburg 2015). The use of frames for the Partee puzzle has been suggested by Löbner (2014, in prep) although his view of frames is rather different from mine. However, there are important similarities between the proposals by Cooper (2010, 2012, 2016) and LĄbner’s proposals.

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We define a record type AmbTempFrame corresponding to a very stripped down version of the Ambient_temperature frame5 in the Berkeley FrameNet:

(7) AmbTempFrame   x : Real  loc : Loc  e : temp(loc, x)

A record type is a set of fields which are ordered pairs of a label (displayed to the left of the ‘:’ above) and a type (displayed to the right of the ‘:’). It must define a function on the labels (no label more than once as the first member of a pair). A record is a similar structure except that objects rather than types occur as the second members of the fields. In the display we use ‘=’ rather than ‘:’. A record is of the above type if it has the following form:   x = n    loc = l  (8)   e = s …

where n is of type Real (in symbols, n:Real), that is, n is a real number, l:Loc, that is, l is a location and s:temp(l,n), that is, s is a situation where the temperature at l is n. Note that there may be more fields in the record than required by the type. A temperature rise is modelled in Cooper (2016) as a string of two records of the type AmbTempFrame where the location is the same in both records and the number in the ‘x’-field of the second is higher than that in the first. This analysis uses an adaptation of Fernando’s (2004; 2006; 2008; 2009; 2011; 2015) string theory of events to TTR. What is important for present purposes is that the analysis of Cooper (2016) makes a distinction between individual-level properties and frame-level properties: [ ] [ ] (9) a. dog — λr: x:Ind .[ e] :[ dog(r.x) ] b. temperature[ — λr] : [x:Rec . e : temperature(] r.x) c. run — λr:[x:Ind] . [ e : run(r.x) ] d. rise — λr: x:Rec . e : rise(r.x)

This makes a neat division between dog and run on the one hand where the predication is of individuals and temperature and rise on the other where the predication is of records (modelling frames/situations). However, Cooper (2016) points out

[5] https://framenet2.icsi.berkeley.edu/fnReports/data/frameIndex.xml?frame=Ambient_ temperature

OSLa volume 10(2), 2018 coercion in languages in flux [89] the Partee puzzle crops up again in cases where we have individual level properties:

(10) Partee puzzle with individual level properties From The dog is getting older The dog is nine we cannot conclude Nine is getting older

The proposed solution to this is that individual-level properties can be coerced to frame-level properties. Thus the noun dog actually has two interpretations: [ ] [ ] (11) a. λr:[x:Ind] . [ e : dog(r.x) ] b. λr: x:Rec . e : dog_frame(r.x)

A dog frame is a record of type: [ ] x : Ind (12) e : dog(x)

What additional information we put in a dog frame depends on the context and the purposes at hand. For example, if we are interested in the age of a dog, a dog frame of the following type would be appropriate:   x : Ind    e : dog(x)  (13)   age : Real cage : age_of(x,age)

Cooper (2016) makes a connection between this kind of example and cases where we get event readings as with the ships passing through the lock examples. First consider a classic example from the literature on event readings as a variant of the Partee puzzle: (14) Partee puzzle with event readings From National Airlines served at least two million passengers in 1975 Every passenger is a person we cannot conclude National Airlines served at least two million persons in 1975 (Gupta 1980)

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As Carlson (1982); Krifka (1990) point out, the first premise in this is ambiguous between an individual reading on which the inference goes through and an event reading on which it does not. The availability of the event reading is made clear by the acceptability of the following discourse:

(15) National Airlines served at least two million passengers in 1975. Each one of them signed the petition.

The analysis in Cooper (2016) involves coercing the interpretation of passenger to be a property of passenger frames rather than individual passengers using the following types and constraint:

(16) a. PassengerFrame  x : Ind    e : passenger(x)    journey : TravelFrame ctravel : take_journey(x, journey) b. TravelFrame  traveller : Ind  source : Loc  goal : Loc c. constraint on ‘take_journey’ If a:Ind and e:TravelFrame, then the type ‘take_journey(a, e)’ is non- empty (“true”) just in case e.traveller = a.

The types PassengerFrame and TravelFrame here represent natural assumptions about what is involved in events of being a passenger and travel events respectively but they are far from the only frame types that could be considered in connection with the interpretation of passenger. Depending on the type of journey involved we could consider boarding cards, ID numbers and booking numbers among other things. I would like to suggest that this kind of coercion yielding additional readings for expressions is very much part of the general process of creating language on the fly related to the view of language as a system in flux. While coercions give us some kind of regularity associated with this process, perhaps at least in part associated with the kind of enthymematic reasoning which Breitholtz (2014a,b) has talked about, it seems very likely that the frames involved can be generated on the fly given the needs of the current communicative act.

[3] dynamic generalized quantifiers and property coercion In Section [2] we talked of coercions which allow us to generate additional interpretations for expressions. In this section we will discuss a property coercion which is part of the basic compositional semantics associated with generalized

OSLa volume 10(2), 2018 coercion in languages in flux [91] quantifiers. In Cooper (2011, 2013, 2016, in prep) and elsewhere, we have been developing a view of generalized quantifiers as relations between properties in the TTR sense. This view is based on classical generalized quantifier theory. Properties are functions of the type: [ ] (17) ( x:Ind →RecType)

Examples of properties are:

′ (18) a. dog[ ] [ ] λr: x:Ind . e : dog(r.x) ′ b. run[ ] [ ] λr: x:Ind . e : run(r.x)

The “type of situations in which every dog runs” is represented by a ptype constructed using the predicate ‘every’:

′ ′ (19) every(dog , run )

In characterizing what it means for something to be of a type like this, we characterize how it relates to classical generalized quantifier theory. Here we will just illustrate this on the basis of the example with ‘every’. First we will introduce some notation. We will use [ˇT ] to represent the set of witnesses of type T :

(20) [ˇT ] represents {a | a : T }

We use [↓ P ] to represent the set of individuals which have property P : [ ] (21) {a | [ˇP ( x=a )] ≠ ∅}

Now we can say that ‘every(P , Q)’ has a witness just in case everything which has property P also has property Q:

(22) [ˇevery(P,Q)] ≠ ∅ iff [↓ P ] ⊆ [↓ Q]

Generalizing this to other quantifier relations will give us a TTR version of classical generalized quantifier theory. Now let us consider dynamic generalized quantifier theory, something along similar lines to that defined by Chierchia (1995). In order to do this we will need two more new notions. Firstly, T is a fixed point type for a property P just in case r : T guarantees r : P (r). In Cooper (in prep) and elsewhere we define a function F which will compute a fixed point type for a property. We will not go into the details here but just give an example:

OSLa volume 10(2), 2018 [92] robin cooper [ ] [ ] F (23) (λr[: x:Ind . e :] dog(r.x) ) = x : Ind e : dog(x)

Intuitively, F yields the result of merging the domain type of the property with the type returned by the property. There are details involving getting this to work out with the dependencies involved which would take us too far afield to discuss here. Secondly, we will need a notion of restricting a property by a type (also defined by Cooper (in prep) and elsewhere) such that the restriction of property, P , by type, T , P|T , is that property like P except that its domain type is the merge (as defined in Cooper (in prep) and elsewhere) of the domain type of P with T . Again, rather than go into the details of the definitions here, we will give an example. Suppose we want to restrict the property of running with the fixed point type derived from the property of being a dog: [ ] [ ] (24) λr: x:Ind . e : run(r.x) |  = x:Ind  [ ] e:dog(x) x:Ind [ ] λr: . e : run(r.x) e:dog(x)

Intuitively, the restriction takes us from the property of running to the property of being a dog that runs. We can use this notion of restriction to characterize dynamic generalized quantifiers. Here we give the dynamic version of ‘every’:

̸ ∅ ↓ ⊆ ↓ | (25) [ˇevery(P,Q)] = iff [ P ] [ Q F(P )]

Of course, this restriction of the second argument of the quantifier by the first argument is related to the conservativity property of quantifiers, a connection that Chierchia (1995) also points out, though in rather different terms than we have introduced here. As Chierchia points out, this gives us a way of getting donkey pronouns bound since the binder is repeated in the second argument. The sentence every farmer who owns a donkey feeds it gets interpreted as every farmer who owns a donkey is a farmer who owns a donkey and feeds it. From the perspective of the current discussion we can see the second argument of the quantifier as being coerced to be the original property expressed by the second argument restricted by the first argument. Given the plethora of subtly different interpretations of rise we discussed in connection with (2) this could be the beginning of an explanation why whenever we have a sentence of the form an X rises the interpretation of rises is always a rise-property of X’s, not

OSLa volume 10(2), 2018 coercion in languages in flux [93] any of the other interpretations available.6 On this view we have a kind of coercion here which is, so to speak, built into the fabric of dynamic interpretation. While it is in this sense perfectly regular, the result of the coercion will be defined by whatever is expressed by the first argument of the quantifier, which can basically be any arbitrary property. This seems to be a distinct kind of coercion from those which can be used to create additional interpretations for expressions. conclusion We started with an argument that natural languages are not quite as formal as we might have thought. They are in fact systems in a state of flux although constrained by the fact that people need to be able to use them to communicate. Thus the meaning associated with expressions must at least relate in some way to meanings that have previously been associated with similar expressions according to the memory of people participating in a dialogue. On this kind of view coercion appears to provide regularities which assist in the prediction of novel meanings that might be associated with an expression. We looked at two kinds of coercion: one where coercion is used to create extra interpretations on the basis of a standard interpretation and one where coercion is used in deriving the standard compositional semantic interpretation. For coercion used to derive additional interpretations we looked at an example of coercion related to the Partee temperature puzzle and related this to the discussion of event quantification coerced from quantification over individuals (as in ships passing through the lock). For coercion integrated into standard interpretation we looked at dynamic generalized quantifiers. acknowledgments This paper was supported in part by a grant from the Swedish Research Council (VR project 2014-39) for the establishment of the Centre for Linguistic Theory and Studies in Probability (CLASP) at the University of Gothenburg. references Breitholtz, Ellen. 2014a. Enthymemes in Dialogue: A micro-rhetorical approach. Uni- versity of Gothenburg PhD dissertation.

Breitholtz, Ellen. 2014b. Reasoning with topoi – towards a rhetorical approach to non-monotonicity. In Proceedings of AISB Symposium on “Questions, discourse and dialogue: 20 years after Making it Explicit”,.

[6] This would follow directly from what we have been discussing if we take the perhaps “old-fashioned” interpretation of indefinite descriptions as generalized quantifiers.

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Brennan, Susan E. & Herbert H. Clark. 1996. Conceptual pacts and lexical choice in conversation. Journal of Experimental Psychology: Learning, Memory and Cognition 22. 482–493.

Carlson, Gregory N. 1982. Generic Terms and Generic Sentences. Journal of Philo- sophical Logic 11. 145–81.

Chierchia, Gennaro. 1995. Dynamics of meaning: Anaphora, presupposition, and the theory of grammar. Chicago: University of Chicago Press.

Clark, Eve V & Herbert H Clark. 1979. When nouns surface as verbs. Language 767–811.

Clark, Herbert H. & D. Wilkes-Gibbs. 1986. Refering as a collaborative process. Cognition 22. 1–39.

Cooper, Robin. 2010. Frames in formal semantics. In Hrafn Loftsson, EirĄkur RĄgnvaldsson & SigrĄn HelgadĄttir (eds.), Icetal 2010, Springer Verlag.

Cooper, Robin. 2011. Copredication, Quantification and Frames. In Sylvain Po- godalla & Jean-Philippe Prost (eds.), Logical Aspects of Computational Linguistics: 6th International Conference, LACL 2011 (Lecture Notes in Artificial Intelligence 6736), 64–79. Springer.

Cooper, Robin. 2012. Type theory and semantics in flux. In Ruth Kempson, Nich- olas Asher & Tim Fernando (eds.), Handbook of the philosophy of science, vol. 14: Philosophy of Linguistics, 271–323. Elsevier BV. General editors: Dov M. Gabbay, Paul Thagard and John Woods.

Cooper, Robin. 2013. Clarification and Generalized Quantifiers. Dialogue and Dis- course 4(1). 1–25.

Cooper, Robin. 2016. Frames as records. In Annie Foret, Glyn Morrill, Reinhard Muskens, Rainer Osswald & Sylvain Pogodalla (eds.), Formal Grammar: 20th and 21st International Conferences FG 2015, Barcelona, Spain, August 2015, Revised Selected Papers FG 2016, Bozen, Italy, August 2016, Proceedings (LNCS 9804), 3–18. Springer.

Cooper, Robin. in prep. Type theory and language: from perception to linguistic communication. Draft of book chapters available from https://sites. google.com/site/typetheorywithrecords/drafts.

Cooper, Robin & Jonathan Ginzburg. 2015. Type theory with records for natural language semantics. In Lappin & Fox (2015) 375–407.

OSLa volume 10(2), 2018 coercion in languages in flux [95]

Cooper, Robin & Ruth Kempson (eds.). 2008. Language in flux: Dialogue coordination, language variation, change and evolution, vol. 1 Communication, Mind and Language. London: College Publications.

Cooper, Robin & Aarne Ranta. 2008. Natural Languages as Collections of Resources. In Cooper & Kempson (2008) 109–120.

Fernando, Tim. 2004. A finite-state approach to events in natural language semantics. Journal of Logic and Computation 14(1). 79–92.

Fernando, Tim. 2006. Situations as strings. Electronic Notes in Theoretical Computer Science 165. 23–36.

Fernando, Tim. 2008. Finite-state descriptions for temporal semantics. In Harry Bunt & Reinhart Muskens (eds.), Computing meaning, volume 3, vol. 83 Studies in Linguistics and Philosophy, 347–368. Springer.

Fernando, Tim. 2009. Situations in LTL as strings. Information and Computation 207(10). 980–999. doi:DOI:10.1016/j.ic.2008.11.003.

Fernando, Tim. 2011. Constructing Situations and Time. Journal of Philosophical Logic 40. 371–396. doi:10.1007/s10992-010-9155-1.

Fernando, Tim. 2015. The Semantics of Tense and Aspect: A Finite-State Perspect- ive. In Lappin & Fox (2015).

Garrod, Simon C. & Anthony Anderson. 1987. Saying what you mean in dialogue: a study in conceptual and semantic co-ordination. Cognition 27. 181–218.

Gupta, Anil. 1980. The Logic of Common Nouns: An Investigation in Quantified Model Logic. New Haven: Yale University Press.

Healey, Patrick G. T., Nik Swoboda, Ichiro Umata & James King. 2007. Graphical Language Games: Interactional Constraints on Representational Form. Cognit- ive Science 31(2). 285–309.

Healey, P.G.T. 1997. Expertise or expertese?: The emergence of task-oriented sub-languages. In M.G. Shafto & P. Langley (eds.), Proceedings of the 19th annual conference of the cognitive science society, 301–306.

Krifka, Manfred. 1990. Four Thousand Ships Passed through the Lock: Object- induced Measure Functions on Events. Linguistics and Philosophy 13. 487–520.

Lappin, Shalom & Chris Fox (eds.). 2015. The Handbook of Contemporary Semantic Theory. Wiley-Blackwell 2nd edn.

OSLa volume 10(2), 2018 [96] robin cooper

Larsson, Staffan. 2010. Accommodating innovative meaning in dialogue. In Paweł Łupkowski & Matthew Purver (eds.), Aspects of Semantics and Pragmatics of Dia- logue. SemDial 2010, 14th Workshop on the Semantics and Pragmatics of Dialogue, 83– 90. Poznań: Polish Society for Cognitive Science.

Larsson, Staffan & Robin Cooper. 2009. Towards a formal view of corrective feedback. In Afra Alishahi, Thierry Poibeau & Aline Villavicencio (eds.), Proceedings of the workshop on cognitive aspects of computational language acquisition, 1–9. EACL.

Löbner, Sebastian. 2014. Evidence for frames from human language. In Thomas Gamerschlag, Doris Gerland, Wiebke Petersen & Rainer Osswald (eds.), Frames and Concept Types, vol. 94 Studies in Linguistics and Philosophy, 23–68. Heidel- berg, New York: Springer.

Löbner, Sebastian. in prep. Functional Concepts and Frames. Avail- able from http://semanticsarchive.net/Archive/jI1NGEwO/Loebner_ Functional_Concepts_and_Frames.pdf.

Mills, Greg J. 2007. The development of semantic co-ordination in dialogue: the role of direct interaction. Queen Mary, University of London PhD dissertation.

Montague, Richard. 1973. The Proper Treatment of Quantification in Ordinary English. In Jaakko Hintikka, Julius Moravcsik & Patrick Suppes (eds.), Ap- proaches to Natural Language: Proceedings of the 1970 Stanford Workshop on Grammar and Semantics, 247–270. Dordrecht: D. Reidel Publishing Company.

Montague, Richard. 1974. Formal Philosophy: Selected Papers of Richard Montague. New Haven: Yale University Press. Ed. and with an introduction by Richmond H. Thomason.

Pickering, M.J. & S. Garrod. 2004. Toward a mechanistic psychology of dialogue. Behavioral and Brain Sciences 27(02). 169–190.

Pustejovsky, James. 1995. The generative lexicon. Cambridge, Mass.: MIT Press.

de Saussure, Ferdinand. 1916. Cours de linguistique générale. Lausanne and Paris: Payot. edited by Charles Bally and Albert Séchehaye.

author contact information Robin Cooper University of Gothenburg [email protected]

OSLa volume 10(2), 2018 Alexandra Anna Spalek and Matthew Gotham (eds.) Approaches to Coercion and Polysemy, Oslo Studies in Language 10(2), 2018. 97–119. (ISSN 1890-9639 / ISBN 978-82-91398-12-9) https://www.journals.uio.no/index.php/osla

counting constructions and coercion: container, portion and measure interpretations

PETERR.SUTTON&HANAFILIP Heinrich Heine University abstract Counting constructions with mass terms like two beers have at least two coerced interpretations depending on context. For example, two beers can have either a container (count) interpretation of ‘two glasses filled with beer’ or a portion (count) interpretation of ‘two portions of beer, each (equivalent to) the contents of one glass’. The intriguing puzzle we address, which has escaped attention, is why it is hard to get a measure (mass) interpretation of ‘beer to the amount of two glassfuls’, despite the fact that this and the other two interpretations are available for full pseudo-partitives such as two glasses of beer. Our proposal rests on an idea, backed up by co-predication data, that the measure interpretation is derived from the portion interpretation. It follows from this that coerced measure interpretations of counting constructions with mass terms would require coercing an implicit portion concept such as glass into a measure interpretation, something which, we argue, cannot easily be done.

[1] introduction [1.1] Interpretations of pseudo-partitives It has been observed that pseudo-partitives like two glasses of beer are ambiguous between at least two interpretations (i.a. Doetjes 1997; Rothstein 2011): (i) the container interpretation (‘two glasses containing beer’); (ii) the measure interpretation (‘beer to the measure of two glassfuls’). Landman (2016) argues that they are at least four ways ambiguous, with three count interpretations and one mass interpretation. For two glasses of beer, the four interpretations with their paraphrases are given in Table 1. In this paper, we will not distinguish between the contents and free portion interpretations, however, because this subtle distinction will not play a role in our analysis. Hence, the focus of this paper will be the semantics of the following three interpretations of the pseudo-partitive construction: container, portion, and the mass measure interpretation, where ‘portion’ means free portion or contents. These three interpretations can be disambiguated in context, as is illustrated in the examples in (1): [98] sutton & filip

Interpretation Paraphrase Countability container two glasses filled with beer count contents two portions of beer, each the contents count of a glass free portion two one-glassful sized portions of beer count measure beer to the amount of two glassfuls mass

table 1: Paraphrases for two glasses of beer from Landman (2016)

(1) a. He turned to reach the two glasses of wine that stood on a bedside table. [BNC] b. i (sic.) should set the record straight with Clayart that two glasses of red wine a day have beneficial health results. [UKWaC] c. Two glasses of wine is equal to 3 standard drinks of any alcoholic beverage. [UKWaC]

In (1-a), two glasses of wine has a container interpretation, because the verbs reach and stand lexically select solid objects as denotations of their direct object. In (1-b), two glasses of red wine has a portion interpretation, because it is the contents, red wine contained in two glasses, that has the beneficial effect on health. (1-b) also, plausibly, has a measure interpretation of approximately ‘wine to the measure of two glasses-worth’, which has health benefits. In (1-c), two glasses of wine has a measure interpretation. The expressed equivalence relation here holds between the alcoholic contents of the alcoholic beverages contained in the respective containers. Moreover, the singular agreement on the verb excludes a container or a portion interpretation of two glasses of wine. On count interpretations, two glasses of wine is a plural count numerical NP requiring the plural agreement on the verb. The mass interpretation of a measure construction can govern either the singular or plural agreement on the verb (Rothstein 2016, p.16).

[1.2] Mass-to-count coercion in numerical NPs Many mass nouns can be coerced into count interpretations in count syntactic en- vironments in order to resolve a type mismatch and restore compositionality. In English, such contexts include direct modification with numerical expressions in counting constructions (three wines) or quantified DPs with distributive quantifiers (each/every wine). In order to resolve the type mismatch between a numerical expression and a mass noun, two different shifted count interpretations are read- ily available, as we see with two white wines in the following examples:

(2) a. John carried two white wines to the table. b. Philippa drank two white wines.

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Given that the verb carried lexically selects solid objects in the denotation of its direct object argument, in (2-a), the shift of the mass term white wines into a count interpretation requires the retrieval of implicit, contextually salient containers from context. In (2-b), two wines has a portion reading, because the verb drink lexically selects direct objects denoting liquids. Assuming that common containers for wine are glasses, two wines might, here, be naturally understood as meaning ‘two portions of wine, each (equivalent to) the contents of a glass’. In contrast, the measure interpretation of a counting construction consisting of a numerical expression and a mass noun is either hard to get or not available at all. In (3), for example, left in the bottle makes a measure interpretation of two wines be the most likely interpretation: e.g. ‘wine to the amount of two glassfuls’. Yet this interpretation does not seem to be available for many speakers, and hence the whole sentence is infelicitous.

(3) #There are about two wines left in the bottle.

This novel observation gives us a window on both the semantics of the pseudo- partitive construction, as well as on mechanisms underlying mass-to-count shifts. If a coerced interpretation of two wines, for instance, is the same as the interpretation of a full pseudo-partitive like two glasses of wine, then assuming that the latter has at least three available interpretations, a container, portion and measure, the same three interpretations should also be available for a coerced interpretation of two wines. On this assumption, one would not expect any differences in the availability of the container, portion and measure interpretations for two wines, but as we have just seen, this prediction is not borne out, because the measure interpretation is not available in some contexts at all. The main question we address is: question: Why should a measure interpretation for numerical NPs like two wines be either hard to get or even not available at all? Our answer is motivated by two independently motivated theses: (i) in pseudo- partitives formed with classifier-like expressions (e.g. two glasses of wine), the measure interpretation (‘wine to the measure of two glassfuls’) is derived from the portion interpretation (‘two portions of wine, each the (equivalent to) contents of a glass’); (ii) when mass nouns are directly modified by numerical expressions (as in two wines), the measure interpretation is blocked, since it would require coercing an implicit portion concept glass, something that, we argue, is not possible. The outline of the paper is as follows. In Section [2], we give a brief overview of two state-of-the-art accounts of the semantics of pseudo-partitives. One, which focuses on their container and measure interpretation, is provided by Roth- stein (2011), while the other, proposed by Landman (2016), also concerns the container, contents and measure interpretations. (We subsume the contents and free

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portion interpretations under the one portion interpretation.) Our analysis of pseudo-partitives is couched within Type Theory with Records (TTR) (i.a. Cooper 2012) and our previous work on countability and on pseudo-partitives (Sutton & Filip 2017, 2016a; Filip & Sutton 2017) which we introduce in Sections [3.1]-[3.2]. In Section [3.3], we argue for an asymmetry between the measure interpretation, on the one hand, and the container and portion interpretations, on the other hand, based on asymmetries in the acceptability of mixed readings in co-predications. In Sections [3.4]-[3.5], we give a semantic analysis of the pseudo-partitive construction. Finally, in Section [3.6], we show how this analysis allows us to motivate why the coerced measure interpretation of a numerical NP built from a numerical expression and a mass noun, such as two wines, is odd or infelicitous.

[2] background: two analyses of pseudo-partitives [2.1] Rothstein (2011): The container and measure interpretations of pseudo-partitives Rothstein (2011)’s account of the container interpretation of a pseudo-partitive construction like three glasses of wine is based on a function REL that applies to the interpretation of its head glass and shifts it to a container classifier. The deriv- ∪ ation for three glasses of wine is given in (4). In (4), wine denotes a kind, wine ∗ denotes a predicate, X indicates the upward closure of the set X under mereological sum, and ⊔X is the (sum) entity that is the supremum of the set X.1 ∗ JglassesK= λx.∃X ⊆ GLASS : x = ⊔X Jglasses of wine K= (REL(JglassesK))(JwineK) ∗ = (λz.λx.∃y.∃X ⊆ GLASS : x = ⊔X ∪ ∧ CONTAIN(x, y) ∧ y ∈ z)(wine) ∗ (4) = λx.∃y.∃X ⊆ GLASS : x = ⊔X ∪ ∧ CONTAIN(x, y) ∧ y ∈ wine ∗ Jthree glasses of wineK= λx.∃y.∃X ⊆ GLASS : x = ⊔X ∪ ∧ CONTAIN(x, y) ∧ y ∈ wine ∧ CARD(x) = 3 The measure interpretation can be understood in terms of a function FUL in (5), which we extrapolate from Rothstein (2011, p. 9). According to Rothstein, it is realised either by the explicit morpheme -ful or by its null correlate, yielding the measure interpretation for three glasses of wine, as in (6)(Rothstein 2011, p. 9). J K J∅ K ⟨ ⟩ -ful = ful = FUL = λP.λn.λx.MEASvolume(x) = P, n (5) J K ⟨ ⟩ three glasses = λx.MEASvolume(x) = GLASS, 3 J K ∈ ∪ ∧ ⟨ ⟩ (6) three glasses of wine = λx.x wine MEASvolume(x) = GLASS, 3 In summary, we have two functions REL and FUL which apply to the basic interpretation of a receptacle noun, such as glass, to derive from it a container classifier and a measure classifier interpretation, respectively.

[1] For an introduction to extensional mereology, see Champollion & Krifka (2016) and references therein.

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[2.2] Landman (2016): The container, contents and measure interpretations of pseudo- partitives Landman (2016) is grounded within ‘iceberg semantics’, a theory in which counting does not depend on atomicity. The mass/count distinction applies to lexical nouns, and also to NPs and DPs, which are interpreted as pairs consisting of a body and a base: ⟨body, base⟩. Assuming a complete Boolean algebra B, the base gener- ∗ ates the body under the sum operation: body(X) ⊆ base(X). I.e. all elements of the body are sums of elements of the base. For count nouns, the base is the set in terms of which the members of the body are counted. What allows counting is the requirement that the base of their interpretation be (contextually) disjoint. The base is thought of as forming a perspective on the body, which is a subset of an unsorted interpretation domain. The idea is to define the mass/count distinction and the singular/plural distinction in relation to the base, which is taken to allow a simpler and more elegant analysis of mass-count interactions. Under its sortal interpretation, the singular noun glass and the plural noun glasses are counted in terms of the same disjoint base GLASSw,t:

w,t JglassK = ⟨GLASSw,t, GLASSw,t⟩ w,t ∗ (7) JglassesK = ⟨ GLASSw,t, GLASSw,t⟩

While count nouns are interpreted as i-sets with a disjoint base, mass nouns are i-sets with an overlapping base. Receptacle nouns can be shifted to container and contents interpretations via the classifier function, or to the measure interpretation via the measure function (following Khrizman et al. (2015)). The classifier function is illustrated below, where (X] stands for the part set of X: {x | x @ y, y ∈ X}:

classifier(JglassKw,t) = λP.⟨body , (body ] ∩ base((JglassKw,t))⟩ P P (8) if P is mass or plural. ⊥ otherwise.

The container and contents interpretations differ with respect to how bodyP is interpreted. For the contents interpretation, the interpretation of bodyP in (8) is given in (9). This enters into the derivation for glass of wine in (10): the set of glasses the contents of which are wine.

∧ bodyP = λx.GLASSw,t(x) body(P )(contents[GLASS,P,c],w,t(x)) (9) Jglass of wineKw,t = ⟨base, base⟩, such that: ∧ (10) base = λx.GLASSw,t(x) WINEw,t(contents[GLASS,WINE,c],w,t(x))

The container interpretation amounts to the set of wine portions that are glass

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contents and the interpretation of bodyP in (8) is as follows: ∧ −1 bodyP = λx.body(P )(x) GLASSw,t(contents[GLASS,P,c],w,t (x)) (11) Jglass of wineKw,t = ⟨base, base⟩ such that: ∧ −1 (12) base = λx.WINEw,t(x) GLASSw,t(contents[GLASS,WINE,c],w,t (x))

Turning to the measure interpretation, the function measure applies to the J Kw,t sortal receptacle concept glass . In (13), glassw,t is a measure function for glassfuls of stuff of type ⟨n, et⟩. ↑ is a function from sets of objects to sets of object- measure value pairs. ↓ is the inverse of ↑. m is a contextually given measure value. For glass of wine, on the measure interpretation, this yields (14). J Kw,t ⟨ ⟩ measure( glass ) = λN.λP. bodyP,N , baseP,N if P is mass or plural. ⊥ otherwise, such that: J Kw,t ◦ ∩ bodyP,N = (body( glass ) N) body(P ) (13) ↑ ∩ J Kw,t baseP,N = (bodyP ] base( glass ) {⟨ ⟩ | ≤ ∧ ∃ ∧ ⊑ } = y, glassw,t(y) glassw,t(y) m x[base(P )(x) y x] Jglass of wineKw,t= ⟨body, base⟩, such that: ∧ body = λn.λx.glassw,t(x) = n WINEw,t(x) (14) {⟨ ⟩ | ≤ ∧ ∃ ∧ ⊑ } base = y, glassw,t(y) glassw,t(y) m x[WINEw,t(x) y x]

The body is a function from numbers n to a set of amounts of wine that measure n with respect to the measure glassw,t. The base is a set of pairs of amounts of stuff which are parts of something that is wine and numbers on a measure scale n such that n is less than a contextually specified amount m. For Landman, it is ↓ vital that the set of y in the base ( base) is an overlapping set in order to derive that the measure interpretation is mass. For our analysis, what matters the most is the following feature of Landman’s and Rothstein’s accounts: both rely on specific functions to derive the measure interpretation, as opposed to the contents and container interpretations, all of which apply directly to the interpretation of receptacle nouns, such as glass.

[3] analysis Our analysis is guided by the following two hypotheses concerning the interpretation of nouns like glass that form a measure phrase in pseudo-partitives: (H1) The container and portion interpretations are default interpretations, captured by the dot type container • portion. (H2) The measure interpretation is derived from the portion interpretation: measure = g(portion). (H1) and (H2) allow us to motivate the following interpretation patterns: (i) The relative ease with which full pseudo-partitives (e.g. three glasses

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of wine) participate in co-predication over their container and portion interpretations. (ii) The general difficulty of assigning the measure interpretation to expressions like three wines. In what follows, we will first introduce Type Theory with Records (TTR) (i.a. Cooper 2012) and our mereological enrichments of the theory. We then lay out our theory of the mass/count distinction and of pseudo-partitives within mereological TTR, based on Sutton & Filip (2016a, 2017) and Filip & Sutton (2017)

[3.1] Type Theory with Records and mereological Type Theory with Records Type Theory with Records (TTR) (Cooper 2005, 2012; Cooper & Ginzburg 2015) is a theory of types which integrates lexical semantic frame-based representations in the sense of Fillmore (1975, 1976) with compositional semantics in the Montague tradition. Types are ‘rich’ in the sense that that there are many basic types instead of only e, t (and sometimes s) in Montague-style semantic theories. For example, there can be types for individuals, locations, times, and situations. In TTR, one can form arbitrarily complex sets of labelled types called Record Types (labels approximate discourse referents in DRT). Record types, displayed in tabular format (15), are sets of fields whose first member is a label and whose second member is a type:   l1 : T1  ...  (15) ln : Tn

An example of a record type is given in (16), which represents the type of situation in which a glass contains water.   x : Ind    y : Subst     sg : ⟨λv.glass(v), ⟨x⟩⟩  (16)   sw : ⟨λv.water(v), ⟨y⟩⟩ scgw : ⟨λv1, λv2.contain(v1, v2), ⟨x, y⟩⟩

We assume basic types Ind and Subst for individuals and substances, respectively. Entities of type Ind are things like a woman, a cat, an item of furniture, a grain of rice. Entities of type Subst are things like mud, water, and air. In other words, Ind and Subst track the prelinguistic distinction between substances and objects in the sense of Soja et al. (1991). The record type in (16) also contains predicate types (pTypes). They are built from predicates, which are a kind of type constructor. For example, ⟨λv1, λv2.contain(v1, v2), ⟨x, y⟩⟩ is a function which takes the values for labels x and y and returns the type of situation in which the value for x contains the value for y. Such types are dependent types in the sense that the final type

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depends on how values are assigned to labels in other fields. For convenience, we will use the abbreviated conventional notation for pTypes as in (17).   x : Ind    y : Subst     sg : glass(x)  (17)   sw : water(y) scgw : contain(x, y)

Assignments of values to labels, in TTR, are represented as records: sets of fields, whose first member is a label (to the left of the ‘=’ in (18)) and whose second member is a value for this label (to the right of the ‘=’ in (18)):   x = v1  ...  (18) y = vn

Records are the entities of which record types are true or false (‘proofs’ of propositions in type-theoretic terminology, ‘witnesses’ in a natural language setting). For example, (19) specifies a situation in which there is an individual, a, some stuff, b, and three witnesses/proofs p1, p2 and p3. Witnesses can be thought of as situations or parts of the world that make type judgements true or false.   x = a    y = b     sg = p1  (19)   sb = p2 sgbw = p3

Individuals in the domain are typed. The record in (19) is a witness for the record type in (16)/(17) iff:

a is of type Ind, p1 is a witness of glass(a), b is of type Subst, p2 is a witness of water(b), p3 is a witness of contain(a, b)

In summary, we have record types which specify types of situations, and records which provide parts of the world which record types are true of. As such, TTR, as so far stated, is compatible with a standard formal semantics based on situations or partial worlds. However, on a more philosophical level, TTR is argued to be a more cognitively oriented theory which represents the conceptual schemes of agents and the judgements s/he makes. A judgement of the form r :A T (A judges that a record, r is of type T ) may reflect the types that A has, however, we might also take records to be reflections of A’s conceptual scheme. In this paper,

OSLa volume 10(2), 2018 counting constructions and coercion [105] we adopt this more cognitively geared approach. In particular, we will make use of individuation schemas which represent perspectives on entities that are relevant to individuation and enumeration. We give full details shortly, but in brief, the same entities may be subject to a variety of individuation perspectives. For example, for entities a, b (e.g. a set of two nesting tables), an agent may perceive them as two disjoint entities a and b, as a mereological sum a⊔b, or as overlapping and so not individuated (as a, b, and a ⊔ b simultaneously). Natural language predicates denote properties of type [x : Ind] → RecType (which we abbreviate as P pty), a function from records containing individuals, ′ ′ to a record type (where T → T is a functional type such that f : T → T iff f is ′ a function with a domain of entities of type T and a range of entities of type T ). For example, a simplified representation of glass would be as in (20) (a full-fledged semantic representation of lexical common nouns is given further below): [ ] λr :[x : Ind].( sglass : glass(r.x) ) (20)

In (21), r.x means that the value to be supplemented is the value of x in r. Hence, if provided with a record [x = a],(21) would yield the type of situation in which a is a glass: [ ] sglass : glass(a) (21) Finally, we will make use of singleton types and manifest fields as defined for TTR in Cooper (2012, p. 297). For any type T , and entity a : T , Ta is a singleton type such that for any b : T , b is a witness to the type Ta iff a = b. Singleton types are represented in Record Types via manifest fields where the Record Types in (22) and (23) are examples of notational variants (of which we will use the latter). [ ] x : Inda (22) [ ] x = a : Ind (23)

[3.2] A semantics for common nouns and the mass/count distinction Context-sensitivity has become a key factor in the grounding of the mass/count distinction in recent theories (Rothstein 2010; Chierchia 2010; Landman 2011; Sut- ton & Filip 2016b, 2017). For example, count concepts specify either contextually grounded ‘semantic atoms’ (Rothstein 2010), disjoint sets for counting relative to context (Landman 2011; Sutton & Filip 2016b, 2017), or are quantized at each context (Filip & Sutton 2017), while mass concepts do not. Such context sensitivity was first addressed in connection with a sizeable subclass of count nouns like fence, bouquet, wall for which what counts as ‘one’ entity for counting varies with context. So fencing around a square field can count as one fence in some contexts and as four fences in others (Rothstein 2010). In contrast, the lexical entry of a mass noun like mud does not specify a unique partition of individuals in any

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context (unless the relevant concept is coerced into a portion interpretation, for instance). Here we build upon Sutton & Filip (2017) and provide a semantics for common nouns that captures such context sensitivity by means of individuation schemas for counting which may vary with the context. Following Sutton & Filip (2017), we also enrich the domain, standardly assumed in TTR, to include mereological sums, such that for any two entities in the domain a, b, their sum a ⊔ b is also in the domain. Following Krifka (1989) (along with e.g. Sutton & Filip (2016b) and Landman (2016)), we presuppose a non-atomic domain (one which is not determ- inately atomic or atomless). As in standard formal semantics, and its TTR variant, common nouns like glass would specify a predicate such as λv.glass(v) which determines the application conditions for the noun such that v is restricted to be of type Ind. The plural glasses ∗ would require any single entity of type Ind, or a sum thereof (given as Ind), and ∗ for the predicate to be applicable to any single glass or sum thereof (λv. glass(v)): [ ] [ ] JglassK=λr : x: Ind . s: glass(r.x) (24) [ ] [ ] ∗ ∗ JglassesK=λr : x: Ind . s: glass(r.x) (25)

However, as argued by Landman (2016); Sutton & Filip (2017); Filip & Sutton (2017), we actually need two fields for any common noun. Roughly, one which specifies the counting base, i.e. the entities that count as ‘one’, and the other which which amounts to the standard conditions for application, that is, the extension. One reason for keeping the counting base and the application conditions separate is that plurals have the same counting base as their singular counterparts, but an extension which includes both singularities and sums. The lexical entry for the singular common noun glass is given in (26), below, in which P pty abbreviates the type [x : Ind] → RecT ype, functions from records to record types. Records as arguments to this function contain not only witnesses for individuals, but also a schema of individuation i : Sch, such that Sch abbreviates (x : Ind → P T ype) → (x : Ind → P T ype). It is analysed as a modifier of a predicate such that what a predicate applies to may vary depending on the schema being applied. For instance, a predicate that inherently denotes an overlapping set of entities, may, in relation to an individuation schema, denote some partition of this set that contains only disjoint entities. To take the example of fence once more, whereas a, b, c, and d may all fall under the predicate fence at individuation schema i1, their sum, a⊔b⊔c⊔d may fall under the predicate fence at individuation schema i2. The field labelled pcbase (the counting base field) is a manifest field which makes use of singleton types (recall that, if l=a : T , then if b : Ta, b = a). This field specifies that the witness/proof for pcbase must be of the type P pty such ′ that it is restricted to the property λr :[y : Ind].[s1 : r.i(glass)(r.y)], i.e. a type,

OSLa volume 10(2), 2018 counting constructions and coercion [107] the only witness for which is the property of being a single glass. Finally, the field labelled sapp specifies the application conditions of glass. This is a function from a record that is a witness to an individual and an individuation schema, to a type of situation in which the individual is a glass under that schema. [ [ ] ] [ ] ′ x: Ind pcbase=λr :[y : Ind]. s: r.i(glass)(r.y) : P pty JglassK=λr : . i : Sch sapp : pcbase(r) [ [ ] ] [ ] ′ (26) x: Ind pcbase=λr :[y : Ind]. s: r.i(glass)(r.y) : P pty =λr : . [ ] i : Sch sapp : s: r.i(glass)(r.x)

The lexical entry for the plural common noun glasses is given in (27) which differs from (26) only in so far as the predicate in the ptype in the field labelled ∗ sapp applies to singularities and sums represented with the operator. [ ] [ [ ] ] ∗ ′ x: Ind pcbase=λr[ :[y : Ind] s1:r.i(glass] )(r.y) : P pty JglassesK=λr : . ∗ (27) i : Sch sapp : s2: r.i(glass)(r.x)

(27) is a function from a record that is a witness to an individual or a sum individual and an individuation schema, to a type of situation in which each individual in the sum is a glass under that schema. Numerical expressions are interpreted as record types, i.e. the type of witnesses for the singleton type of real numbers equal to n, e.g. 3, below. [ ] JthreeK= n=3 : R (28) The function NMOD shifts such types to a Ppty modifier. The effect of which is to add a condition that the argument individual has some cardinality relative to the counting base property. P (r).pcbase is the path labelled pcbase in P after P is applied to r. [ ] ∗ x: Ind NMOD= λR:[n : R] λP :Ppty λr : . i : Sch [ ] (29) N_type=P (r): RecType s : Card(r.x, P (r).p , R.n) [ ] cbase ∗ x: Ind NMOD(JthreeK)= λP :Ppty λr : . i : Sch [ ] (30) N_type=P (r): RecType s : Card(r.x, P (r).pcbase, 3) [ ] ∗ x: Ind NMOD(JthreeK)(JglassesK) = λr : .  [ i : Sch ]  ′ ′ pcbase=λr[ :[y : Ind][s1 :r.i(glass] )(r .y)] : P pty (31) N_type= ∗ : RecType  sapp : s2: r.i(glass)(r.x)  scard : Card(r.x, N_type.pcbase, 3)

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The counting base property is needed since cardinality is relative to some individuating or counting property. To take an example from Link (1983), if x counts as 52 with respect to playing card, it can count as 1 with respect to deck of cards. After flattening and relabelling, this gives us the function in (32) which is the same as the entry for glasses, but with the added condition that the plural individual witnessed in the record counts as 3 with respect to the counting base.   [ ] ′ ′ ∗ pcbase=λr[ :[y : Ind][s1 :r.i(glass] )(r .y)] : P pty x: Ind  ∗  = λr : . s : s : r.i(glass)(r.x) (32) i : Sch app 2 scard : Card(r.x, pcbase, 3) Following Landman (2011, 2016); Sutton & Filip (2016b, 2017), mass nouns are distinguished from count nouns in terms of whether their counting base is disjoint. If counting base predicates specify a disjoint set of entities, the relevant noun is count, if it specifies a non-disjoint set of entities, the relevant noun is mass. Overlap in counting bases makes ‘counting go wrong’ (Landman 2011). Sutton & Filip (2017) represent this in terms of a difference in types of individuation schemas. Mass noun lexical entries specify a join individuation schema, i∨ which is formed as a join type of all specific individuation schemas. This means that if there are different ways of individuating some stuff, such as furniture, into different items, or water into different portions, at the join individuation schema, all of the different partitions are simultaneously available at a given context. This results in overlaps and a predicate that is undefined for cardinality. For a mass noun like wine we get the entry in (33). The argument record requires a Spelke substance, rather than an individual and the resulting record type specifies that the join individuation schema i∨ is to be used. (We use ‘Spelke substance’ to refer to substances in the sense of Soja et al. (1991).)   [ ] i = i∨: Sch [ ] J K  ′ ′  wine =λr : x: Subst . pcbase= [λr :[y : Subst] s]: i(wine)(r .y) : Ppty (33) sapp = s: i(wine)(r.x) Since there are many ways to partition wine into portions and since these overlap with one another, the resulting concept is mass. For treatments of object mass nouns (e.g. furniture) and granular mass nouns (e.g. rice), see Sutton & Filip (2017).

[3.3] Measure interpretations are derived from portion interpretations: The data from co-predication In standard dictionaries, receptacle nouns like glass or jar are commonly treated as polysemous between the container and the portion interpretations, while the measure interpretation is not a part of their inherent lexical entries. This would seem to be validated by data from co-predication. First, let us consider co-predications over the container (C) and portion (P) interpretations:

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(34) a. The two glasses of wine with tall, thin stems are being drunk (C-P) by Rachel and Matt. b. Loretta and Fiona are drinking the two glasses of wine with (P-C) tall, thin stems.

In (34-a), the subject NP contains glasses and its PP modifier with tall, thin stems makes salient its container (C) interpretation, and the verb drink, which follows, selects its portion (P) interpretation. In (34-b), we have the reverse (P-C) order. This shows that nouns, such as glass, bottle, pot, have simultaneously accessible container (C) and portion (P) interpretations, which can be easily accessed, mod- ulo selectional restrictions of their co-constituents. In (35-a) and (35-b) below, we have co-predication over the portion (P) and measure (M) interpretations of pseudo-partitives, which some people accept, while others find them less than fully felicitous, but in any case, they are not as straightforwardly acceptable as the co-predictions over the portion (P) and container (C) interpretations.

(35) a. (#) The two glasses of wine with a sour flavour were the last (P-M) two in the bottle from two days ago. b. (#) The last two glasses of wine in the bottle were drunk by (M-P) Carl at lunch and Harry at dinner.

The ease with which the container (C) and portion (P) interpretations of nouns like glass, bottle, pot are accessible in co-predications (but not the measure (M) interpretation) suggests that these are in a sense their ‘default’ interpretations. We can motivate this observation hypothesising that such nouns are interpreted at a dot type, in the sense of (Pustejovsky 1995)2: container • portion, where the container (C) and portion (P) interpretations are treated as two distinct and equal aspects of their lexical meaning. Pustejovsky’s paradigm example is book, as in Amy picked up and read a book, where pick up selects a physical object (phys), while read ‘informational print matter’ aspect of the meaning of book, which is taken to be of the dot type phys • info (Pustejovsky 2011, pp. 1410-1411). The relative difficulty of accessing the measure (M) interpretation of nouns like glass, bottle, pot can be motivated, if we assume that the measure (M) interpretation is derived from the portion (P) interpretation, as we hypothesise in (H2): there is a function g such that measure = g(portion). Intuitively, two glasses of wine when understood in the mass sense of ‘wine to the amount of two glassfuls’ cannot be analysed in terms of a container (C) classifier interpretation

[2] The suggestion that the semantics of receptacle nouns such as glass requires something akin to dot types was originally made in Partee & Borschev (2012). Partee & Borschev (2012) do not provide such an analysis, however.

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(which is count), and neither in terms of a portion (P) classifier interpretation (which is also count). This is because the measure (M) interpretation, which is mass, is not tied to glasses, qua physical containers or their contents/portions of stuff they contain, but rather to glass in its abstract non-standard measurement function. This also motivates why on our account the container (C) and portion (P) interpretation are unified under the dot type and treated as part of the lexical meaning of nouns like glass, bottle, pot, and the measure (M) interpretation requires a lexical shift. In support of this lexical derivational move, we propose the explanation that co-predications with the measure (M) and the container (C) interpretation are odd, because the measure (M) interpretation blocks access to the container (C) interpretation. This, we suggest, is because the measure (M) interpretation is a result of the shift from the portion constituent of the dot type container • portion, and the type for the container is ‘lost’ as a result of shifting from the portion to the measure interpretation. This is what we see in sentences such as (36-a) and (36-b).

(36) a. #The two glasses of wine with tall, thin stems were the last (C-M) two left in the bottle. b. #The last two glasses of wine in the bottle have thin stems. (M-C)

In sum, the above data and observations confirm our guiding hypotheses in (H1) and (H2) regarding the lexical semantic properties of nouns like glass, bottle, cup, pot. Hypothesising that they are of the dot type container•portion (H1) correctly predicts that their container (C) and portion (P) interpretations are simultaneously available and can be easily accessed in co-predications. Hypothesising that the measure (M) interpretation is a result of a shift from the portion constituent of the dot type (H2) motivates the observation that the measure (M) and portion (P) interpretations cannot be easily simultaneously accessed in co-predications, or are impossible to access simultaneously for some speakers at least. In Section [3.6] we will show how (H1) and (H2) jointly predict why it should be the case that the measure (M) interpretation of counting constructions like two white wines, as in (3), is hard to get, or even impossible, when the container (C) and portion (P) interpretations, as in (2-a) and (2-b), respectively, are straightforwardly available. This is the main puzzle of this paper. However, first we will turn to our formal analysis of the container (C), portion (P) and measure (M) interpretations for pseudo- partitives.

[3.4] Container and portion interpretations for pseudo-partitives We assume that container and portion interpretations of pseudo-partitives are derived via a function CL (standing for ‘classifier’) applied to the interpretation of nouns like bottles, cups, glass which have an inherently non-classifier denotation

OSLa volume 10(2), 2018 counting constructions and coercion [111] involving physical objects with a certain receptacle shape. CL is a function which turns a property like JglassK, which is not inherently relational, to a relational classifier concept (that requires a property as an argument, i.e. the contents of the receptacle). Thus CL is a function from two properties (e.g. JglassK and JwineK) to a function from a record to the TTR equivalent of a dot type (Cooper 2011), that is, where there are two fields, one for each of the types: container and portion (labelled sctr and spor) in (34). The P and Q variables stand for properties such as those expressed by JglassK and JwineK.

The resulting type is given in (38). The type labelled sctr in (38) is a record type which retains the content of JglassK. par is a label for a record of the type to the right of the colon, which introduces the existential requirement that a situation witnesses individuals or substances and an individuation schema. The conditions labelled sin thereby state that, for each glass, there is some stuff to which wine can be applied in that glass. In other words, a property for glasses that each contain wine. The type labelled spor in (38) is a record type which retains the content of JwineK, but crucially, portions it in some way provided by the the schema labelled r.i. That is, we get some disjoint partition of wine. The type labelled par existen- tially binds two conditions (labelled sin), one of which states that, for each disjoint partition of wine, there is some glass it is from. In other words, a property for portions of wine, each the contents of a glass. The relation in.each(x, z) means in each x, there is z (e.g. in each glass, there is wine). The relation each.in(x, z) means in each z, there is x. For example, each (portion of) wine, is in a glass. As such these relations suppress some complexity relating to quantifier scope.3

[ ] ∗ x: Ind ∨ Subst CL = λP :Ppty λQ:Ppty λr : .   i : Sch  N_type[ =P (r): RecType]   ∗    z : Ind ∨ Subst   par:  sctr : i = i∨ :    Sch    ∗   r.x : Ind  (37)  ∧   sin : Q(par).sapp [scontain : in.each(r.x, par.z)]     N_type[ =Q(r): RecType]    ∗     z : Ind   spor:par:   i = i∨ : Sch ∧ sin : P (par).sapp [swithin : each.in(r.x, par.z)]

[3] Using predicate logic, the following approximations hold (such that contain(x,z) means that x contains z): in.each(x, z) ↔ ∀x∃zcontain(x, z); each.in(x, z) ↔ ∀z∃xcontain(x, z). However, we do not wish to be committed to there being e.g. an actual glass involved for every glass-portion reading, hence, we suspect that the relation each.in(x, z) needs to be intensionalised (such that, e.g. each portion of wine could be contained in a glass whether or not an actual glass is present in the relevant situation). We leave a TTR analysis of these relations for further research.

OSLa volume 10(2), 2018 [112] sutton & filip [ ] ∗ x: Ind ∨ Subst Jglasses of wineK = CL(JglassesK)(JwineK) = λr : .   [ i : Sch ]  ′ ′ p =λr :[y : Ind] s :r.i(glass)(r .y) : P pty   cbase 1    ∗   sapp [: r.i(glass)(r.x) ]    ∗ ∨    z : Ind Subst   par:  sctr : i = i∨ : Sch    ∗   r.x : [Ind ]      sapp : par.i(wine)(par.z)   sin :  (38)  scontain : in.each(r.x, par.z)     [ ]    ′ ′   p =λr :[y : Ind] s :r.i(wine)(r .y) : P pty   cbase 1      sapp [: r.i(wine)(r.x)]    ∗    z : Ind  spor:par:    [ i = i∨ : Sch ]    ∗  sapp : par.i(glass)(par.z) sin : swithin : each.in(r.x, par.z) One of our chief improvements over previous analyses is that the container (C) and portion (P) interpretations are both available simultaneously, somewhat along the lines akin to those captured by a dot type. This allows us to motivate why glass(es) can be straightforwardly interpreted as either container or portion within the same sentence, such as in (34-a) and (34-b).

[3.5] Measure interpretations of pseudo-partitives Measure interpretations of full pseudo-partitives, we argue, are derived from the portion interpretation of inherent receptacle nouns like glass. Take, for instance, the measure interpretation of glasses in two glasses of wine, which is a property of wine that measures 2 with respect to a contextually provided dimension (most commonly volume) and a quantity (such as glass-sized portion) that determines the value on the scale for that dimension. So a type like Measure(x, volume, litre, 2) would be a type in which x measures 2 in terms of volume in litres. Similarly, Measure(x, volume, portion_glass, 2) would be a type in which x measures 2 in terms of volume based upon glass-sized portions of wine. This idea is formally represented via a function MSR (standing for ‘measure’): [ ] ∗ y: Ind ∨ Subst MSR = λP :Ppty(Ppty) λQ:Ppty λR:[n : R] λr : .  [ ] d: Dimension  ∗ x: Ind ∨ Subst (39) par :  2 i : Sch  smsr: Measure(r.y, r.d, (P(Q)(par2).spor), R.n) MSR maps properties, such as CL(JglassK), to a function from real numbers n to a function from a property to be measured (e.g. JwineK) to a property of substances or pluralities of individuals such that they are the type of measuring n with respect to a volume scale marked in terms of contents of glasses of, e.g. wine.

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The quantity for the Measure relation is provided by applying the witness of par2 to the interpretation of e.g. CLJglassesK and selecting the record type for the portion labelled spor (which is what is meant by (P (par2).spor) in (39)). This means that, although MSR applies to JglassesK, it operates only on the portion concept (labelled spor) and the container concept drops out of the resulting record type. The result of applying MSR to CL(JglassesK) with the further argument JwineK is given in (40). [ ] ∗ y: Ind ∨ Subst MSR(CL(JglassesK))(JwineK) = λR:[n : R] λr : . [ ] d: Dimension  ∗  x: Ind ∨ Subst par2:   i : Sch     ′ ′   pcbase =λr :[y :Ind].[s1 :par2.i(wine)(r .y)] : P pty      (40)   sapp: par[ 2.i(wine])(par2.x)     ∗     z : Ind   smsr: Measure(r.y, r.d, par: , R.n)   i∨ :     [ Sch ]     ∗   sapp : par.i(glass)(par.z) sin : swithin:each.in(par2.y, par.z) This gives us the desired result, a function from real numbers n to a property of substances or pluralities of individuals such that they measure n with respect to a volume scale marked in terms of glass-sized portions of wine. An important feature of this analysis is that all access to the container interpretation is lost as a result of applying MSR and the portion interpretation is embedded within the Measure relation: shifting to a measure interpretation such as wine to the measure of two glasses blocks access to glasses-as-containers. Thus we can explain the infelicity of (36-a) and (36-b). Furthermore, given that there is no direct access to the portion interpretation after applying the MSR function, we can also motivate why full pseudo-partitives (e.g. two glasses of wine) cannot participate in co-predication over their portion and measure interpretations, according to some native speakers at least, as we have seen in (35-a) and (35-b) above.

[3.6] Mass-to-count coercion and measure interpretations Having motivated our hypotheses (H1) and (H2), and also provided a formal analysis of the container (C), portion (P) and measure (M) interpretations, we now turn to our puzzle regarding coercion: Why is it easy to get coerced container (C) and portion (P) interpretations for expressions, such as two wines, but much harder to get measure (M) interpretations? We will set out by briefly outlining what coercion is in the context of the count/mass distinction. It is triggered by a type mismatch which arises when a quantifier, a numerical or some expression of quantity selecting for a count noun is combined with a mass noun, or vice versa). To fix the type mismatch, the relevant mass or count noun must first shift into the relevant count or mass interpretation. For example, if a numerical expression two is directly combined with

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wines, a mass noun in the plural, there is a type mismatch, because both JtwoK and the plural morphology require a noun denoting a concept that specifies a disjoint counting base, but this is what JwineK fails to do. The type mismatch may be resolved by inserting into the interpretation of two wines some individuating concept (e.g. glass) that is recoverable from the context and which ‘apportions’ wine into the requisite disjoint set: e.g. JtwoK(glass(JwineK)). On our analysis, see Section [3.4], the most straightforward interpretation of numerical expressions in cases such as two wines is as a numerical determiner, i.e. NMOD(JtwoK). However, NMOD(JtwoK)(JwineK) involves a type mismatch, since JwineK does not specify a disjoint counting base. One possibility is to insert a classifier concept based on some receptacle(s) salient in the context, such as CL(JglassK) (see also Section [3.4]), which resolves the type mismatch, making available the container or the portion interpretation based on CL(JglassK).4 Now for the answer to the main puzzle. There are two considerations that mil- itate against getting the measure interpretation for a counting construction like two wines. One has to do with the way in which we derive the measure interpretation. If, as in the container and portion case, we interpret two as the numerical determiner NMOD(JtwoK) (the usual interpretation for a numerical expression that directly modifies a noun), then even if we insert the relevant measure concept, namely, MSR(CL(JglassesK)) in order to repair the type mismatch between two and wines, there is still a type mismatch. This is because the measure interpretation requires that the measure concept combine with a numeral, such as JtwoK, rather than with a numerical determiner, such as NMOD(JtwoK) (following Roth- stein (2011), i.a.). The other consideration concerns general constraints on coercion and inter- pretive effort. It is standardly assumed that a type mismatch driven coercion arises when the properties (semantic type) of the explicit argument do not match the requirements of the explicit functor. However, coercion is not standardly assumed to be driven by a type mismatch between an implicit (contextually determined) functor and an implicit (contextually determined) argument. Now, the interpretation of counting constructions like two white wines, as in (2-a), (2-b), is commonly taken to involve recovering a suitable receptacle concept, e.g. the classifier-like CL(JglassK) concept from the context. This resolves the type clash between a numerical expression and a mass noun, because it supplies the container interpretation for the wine (2-a) or an apportioning of the wine (2-b), both of which can be subjected to grammatical counting operations. Assuming that the dot type container • portion is a suitable type for receptacle nouns, such as glass, when used relationally, as well as for the corresponding contextually-determined classifier-like CL(JglassK) concept, we should then expect the type clashes in (2-a)

[4] An alternative route to an interpretation, not discussed here, would be to shift JwineK to a set of subkinds, as in The off-license has over 100 wines in stock.

OSLa volume 10(2), 2018 counting constructions and coercion [115] and (2-b) be relatively easy to resolve. For instance, carry in (2-a) will select for a physical object of type container, while drink in (2-b) for portion, following the standard assumption that dot types allow for predications which are licensed over either of the two dot constitutive types. The measure interpretation, however, would have to be derived by shifting the dot type container • portion (see (H1)) into a measure type, following our hypothesis (H2) that the measure meaning is derived from the portion one. This derivational step, on our account, is achieved by means of the MSR function. When it comes to examples like two wines, in order to get the coerced measure interpretation of say ‘wine to the measure of two glassfuls’, the MSR function would have to operate on an implicit portion meaning of the contextually-determined CL(JglassK) concept, which is the result of coercion: ‘two glass-sized portions of wine’. In other words, MSR would have to apply to implicit linguistic material, which was previously inserted to repair a mismatch between two and wines, in order to yield the intended measure interpretation. Now, if an agent has already retrieved a classifier-like portion concept from the context in order to repair a type mismatch between two and wines, there is no type mismatch to fix, and no coercion is predicted to be available, if we understand coercion in the standard way. Neither is there any other impetus to trigger the application of the MSR function to the implicit portion meaning. We can speculate that natural languages do not make such complex coercive operations available at least in part because interpreters find the reinterpretation of implicit linguistic material already used to repair e.g. the mismatch between a numerical determiner and a mass noun to be conceptually highly unwieldy. That is, once we coerce two wines to mean ‘two glass-sized portions of wine’, for instance, and thus resolve the ‘original’ type mismatch by means of the implicit classifier-like CL(JglassK) concept, it is highly cognitively costly, if not impossible, to try to coerce this shifted portion interpretation into the abstract measure interpretation, which intuitively ‘detaches’ the measure from both its container and portion anchoring, in our case, from its anchoring to the classifier-like CL(JglassK) concept, which is, albeit, implicit and recovered from context. A key feature of our analysis is thus that the measure interpretation of pseudo- partitives is generally derived from the portion interpretation of classifier-like concepts, based on receptacle nouns (e.g. glass, bottle, basket, pitcher). Accounts which derive the measure interpretation directly from nouns that inherently denote receptacles do not have the means to proffer such an explanation. summary and conclusions We have introduced two types of data points not previously discussed in the literature, First, not all interpretations of pseudo-partitives formed with classifier- like expressions are equally felicitous under co-predication. This especially holds

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of container (C) and measure (M) interpretations, as in (36-a) and (36-b). Second, when mass nouns, such as wine, are directly modified with numerical expressions, it is not easy to get a coerced measure (M) interpretation, e.g. two wines cannot (easily) mean something like ‘wine to the measure of two glasses-worth’. To account for these data we have built upon and were inspired by the work of Rothstein and Landman. Our novel contribution mainly lies in showing that the measure interpretation of pseudo-partitives formed with classifier-like expressions like glass is derived from the portion interpretation, and not directly from their inherent non-classifier interpretation of physical receptacles pure and simple. That is to say that, instead of shifting JglassK to a measure interpretation and then combining it with JwineK, as Rothstein and Landman, for instance, propose, we argue that glass has an interpretation that is akin to a dot type for a container (C) and a portion (P) interpretation, and that the portion part of this meaning is shifted to a measure (M), namely, ‘wine to the measure of a glassful’. This difference between our account and others formed the basis for our explanation for why container and measure interpretations are not easily co-predicated over. Our account suggests the following partial order for felicity of combinations: C- P/P-C >M-P/P-M > C-M/M-C. When it comes to the interpretation of full pseudo- partitives, we argued that their classifier-like container and portion interpretations are default interpretations, and proposed that they are, therefore, of the dot type container•portion. This explains the felicity of C-P/P-C co-predication. The portion (P) and measure (M) interpretations can be accessed, by some people at least, by reconstructing the portion interpretation from the measure, as the measure MSR function contains the type for the portion in that the property for portion specifies the scale for the measure function for something like ‘glassful’ (see equation 40). The measure interpretation excludes access to the container interpretation, since, on our account, the type for the container is ‘lost’ as a result of shifting from the portion to the measure interpretation. Finally, we used our proposal for full pseudo-partitive constructions to give us a window on mass-to-count coercion. On our analysis the measure interpretation is derived from the portion interpretation. This provided a reason why it is hard to access the measure interpretation when numerical expressions are directly combined with mass nouns. Finding a salient classifier in the context re- volves any type clash and so further shifting this classifier concept into a measure concept is not motivated (the original type clash is resolved), and is cognitively burdensome, since it would require reinterpreting implicit concepts.

acknowledgments We would like to thank the participants the Workshop on Approaches to Coercion and Polysemy (CoPo 2017) for helpful feedback. Thanks, especially, to Robin Cooper and Keren Khrizman for useful discussion. This research was funded by the Ger-

OSLa volume 10(2), 2018 counting constructions and coercion [117] man Research Foundation (DFG) as a part of the Collaborative Research Centre 991, project C09. references Champollion, Lucas & Manfred Krifka. 2016. Mereology. In Maria Aloni (ed.), The cambridge handbook of formal semantics, 513–541. Cambridge University Press. doi:10.1017/cbo9781139236157.014.

Chierchia, Gennaro. 2010. Mass nouns, vagueness and semantic variation. Syn- these 174. 99–149. doi:10.1007/s11229-009-9686-6.

Cooper, Robin. 2005. Records and record types in semantic theory. Journal of Logic and Computation 15(2). 99–112.

Cooper, Robin. 2011. Copredication, quantification and frames. In Sylvain Po- godalla & Jean-Philippe Prost (eds.), Logical aspects of computational linguistics, number 6736 in lecture notes in computer science, 64–79. Springer.

Cooper, Robin. 2012. Type theory and semantics in flux. In R. Kempson, T. Fernando & N. Asher (eds.), Philosophy of linguistics, handbook of the philosophy of science, 271–323. Elsevier.

Cooper, Robin & Jonathan Ginzburg. 2015. Type theory with records for natural language semantics. In Shalom Lappin & Chris Fox (eds.), Handbook of contemporary semantic theory, second edition, 375–407. Wiley.

Doetjes, Jenny. 1997. Quantifiers and selection. University of Leiden PhD dissertation.

Filip, Hana & Peter R. Sutton. 2017. Singular count NPs in measure constructions. Semantics and Linguistic Theory 27. 340–357.

Fillmore, Charles J. 1975. An alternative to checklist theories of meaning. Proceed- ings of the First Annual Meeting of the Berkeley Linguistics Society 1. 123–131.

Fillmore, Charles J. 1976. Frame semantics and the nature of language. Annals of the New York Academy of Sciences 280(1). 20–32.

Khrizman, Keren, Fred Landman, Suzi Lima, Susan Rothstein & Brigitta R. Schvarcz. 2015. Portion readings are count readings, not measure readings. Proceedings of the 20th Amsterdam Colloquium 197–216.

Krifka, Manfred. 1989. Nominal reference, temporal constitution and quantification in event semantics. In Renate Bartsch, J. F. A. K. van Benthem & P. van Emde Boas (eds.), Semantics and contextual expression, 75–115. Foris Publications.

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Landman, Fred. 2011. Count nouns – mass nouns – neat nouns – mess nouns. The Baltic International Yearbook of Cognition 6. 1–67.

Landman, Fred. 2016. Iceberg semantics for count nouns and mass nouns: The evidence from portions. The Baltic International Yearbook of Cognition Logic and Communication 11. 1–48.

Link, Godehard. 1983. The logical analysis of plurals and mass terms: A lattice- theoretic approach. In Rainer Bäuerle, Urs Egli & Arnim von Stechow (eds.), Meaning, use and the interpretation of language, 303–323. Berlin: de Gruyter.

Partee, Barbara H. & Vladimir Borschev. 2012. Sortal, relational, and functional interpretations of nouns and russian container constructions. Journal of Semantics 29. 445–486.

Pustejovsky, James. 1995. The generative lexicon. MIT Press.

Pustejovsky, James. 2011. Coercion in a general theory of argument selection. Linguistics 49(6). 1401–1431.

Rothstein, Susan. 2010. Counting and the mass/count distinction. Journal of Se- mantics 27(3). 343–397. doi:10.1093/jos/ffq007.

Rothstein, Susan. 2011. Counting, measuring and the semantics of classifiers. Baltic International Yearbook of Cognition, Logic and Communication 6. 1–42.

Rothstein, Susan. 2016. Counting, measuring and the semantics of classifiers. Baltic International Yearbook of Cognition, Logic and Communication 11. 1–42.

Soja, Nancy, Susan Carey & Elizabeth Spelke. 1991. Ontological categories guide young children’s inductions of word meaning: Object terms and substance terms. Cognition 38. 179–211. doi:10.1016/0010-0277(91)90051-5.

Sutton, Peter & Hana Filip. 2016a. Counting in context: Count/mass variation and restrictions on coercion in collective artifact nouns. Semantics and Linguistic Theory 26. 350–370. doi:10.3765/salt.v26i0.3796.

Sutton, Peter R. & Hana Filip. 2016b. Mass/count variation, a mereological, two- dimensional semantics. The Baltic International Yearbook of Cognition Logic and Communication 11. 1–45.

Sutton, Peter R. & Hana Filip. 2017. Individuation, reliability, and the mass/count distinction. Journal of Language Modelling 5(2). 303–356.

OSLa volume 10(2), 2018 counting constructions and coercion [119] author contact information Peter R. Sutton Heinrich Heine University Düsseldorf [email protected]

Hana Filip Heinrich Heine University Düsseldorf [email protected]

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Alexandra Anna Spalek and Matthew Gotham (eds.) Approaches to Coercion and Polysemy, Oslo Studies in Language 10(2), 2018. 121–141. (ISSN 1890-9639 / ISBN 978-82-91398-12-9) https://www.journals.uio.no/index.php/osla

identity criteria of common nouns and dot-types for copredication

STERGIOSCHATZIKYRIAKIDIS 1 &ZHAOHUILUO 2 1 Department of Philosophy, Linguistics and Theory of Science, University of Gothenburg 2 Royal Holloway, University of London abstract Copredication, especially when combined with quantification, provides interesting examples to support the idea that common nouns have their own identity criteria, as once argued for by Geach and subsequently studied by others. In this paper, revisiting the use of dot-types in modern type theories to model copredication, we show that, when both copredication and quantification are involved, CNs are not just types but should better be interpreted as types associated with their own identity criteria. In other words, formally, CNs are setoids – pairs whose first component is a type that interprets the domain of a CN and whose second component gives the identity criterion for that CN. For copredication with quantification, identity criteria play an essential role in giving a proper treatment of individuation and counting and hence constructing appropriate semantics to facilitate reasoning correctly. With CNs being setoids, the dot-type approach provides an adequate theory for copredication in general and for copredication with quantification in particular. It is further explained that the CNs-as-types approach is still the appropriate characterisation of our approach to interpreting CNs since, in phenomena that do not involve the interaction of copredication with quantification, the identity criteria of related CNs are essentially the same and can be safely ignored.

[1] introduction Copredication (Pustejovsky 1995) is the phenomenon in which more than one predicate (verb or adjective) that require different types of arguments are used in coordination and applied to the “same” CN argument. When combined with quantification, copredication provides interesting examples to support the idea that common nouns have their own identity criteria, an idea first discussed by Geach (1962) and further studied by others including, for example, that by the second author (Luo 2012a) in the semantic framework based on modern type theories. In this paper, revisiting the use of dot-types in modern type theories to model copredication (Luo 2010, 2012b), we show that, when both copredication and quantification are involved, CNs are not just types but should better be in- [122] chatzikyriakidis & luo

terpreted as types associated with their own identity criteria, formally called setoids.1 For copredication with quantification, identity criteria play an essential role in giving a proper treatment of individuation and counting and hence constructing appropriate semantics to facilitate reasoning correctly. With CNs being setoids, the dot-type approach provides an adequate theory for copredication in general and for copredication with quantification in particular. Consider the following example of copredication:

(1) John picked up and mastered the book.

In the above sentence, the predicates pick up and master require physical and informational objects as their respective arguments: formally, their domains are Phy and Info, the types of physical and informational objects, respectively. How- ever, they manage to be applied in coordination to the argument the book. Thus, book in this case is used in its physical sense with respect to the predicate picked up and in its informational sense with respect to the predicate mastered. The term copredication was coined by Pustejovsky (1995), according to whom lexical items like book in (1) are complex and have more than one sense, to be chosen appropriately according to the context. The topic has since been studied by many researchers and different accounts of copredication have been proposed in various semantic frameworks.2 For instance, the second author has proposed dot-types in modern type theories for the semantic study of copredication (Luo 2010, 2012b). The idea was that, the phenomenon that a single occurrence of book may be used in both physical and informational senses can be captured by stip- ulating that the type Book, that interprets book, be a subtype of the dot-type of those of physical and informational objects:3

Book ≤ P hy • Info.

The copredication phenomenon as exhibited in (1) can then be dealt with straightforwardly: the predicates pick up and master can be applied in coordination to the argument the book because, with the above stipulation in the setting of dot-types, they are both of type Book → P rop (see later for a more detailed description of dot-types and their use for copredication.)

[1] The current authors have considered the issue in (Chatzikyriakidis & Luo 2015) where, however, the necessity of considering identity criteria was not recognised – the current paper studies identity criteria in this context, based on the abstract presented at at the Workshop on Approaches to Coercion and Polysemy in Oslo (Chatzikyriakidis & Luo 2017b). [2] Besides Pustejovsky’s initial proposal (Pustejovsky 1995), these include, to mention a few among many: Asher (2012) using his Type Composition Logic, Luo (2010, 2012b) using modern type theories, Bassac et al. (2010) using second-order λ-calculus, and Gotham (2014, 2017) using a mereological account. [3] In formal semantics based on modern type theories (MTT-semantics) (Luo 2012b; Chatzikyriakidis & Luo 2018), CNs are interpreted as types (not predicates), an idea originally coming from Ranta’s work (Ranta 1994).

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When giving an account of copredication, one needs to take care of a more advanced issue – the involvement of quantification. (2) is an example, taken from (Asher 2012), where copredication and quantification interact:

(2) John picked up and mastered three books.

Because of the presence of the quantifier three in (2), individuation and counting come into play in the semantic analysis of this sentence with copredication. In other words, an adequate account of copredication must take into consideration these parameters – but, what is needed for an adequate account? To explain, let’s start by considering the following simpler sentences that do not involve copredication:

(3) John picked up three books. (4) John mastered three books.

The first example, i.e. (3), is true in case John picked up three distinct physical objects. Thus, it is compatible with a situation where John picked up three copies of a book that are informationally identical as long as three distinct physical copies are picked up. Similarly, example (4) is true in case three distinct informational objects are mastered but it does not impose any restrictions on whether these three informational objects should be different physical objects or not.4 A more explicit way of explaining this is that, intuitively, the following entailments should be the case:

(5) John picked up three books ⇒ John picked up three physical objects (6) John mastered three books ⇒ John mastered three informational objects

At first appearance, the above examples may be puzzling. The books John picked up and the books he mastered must have different individuation criteria – being physically identical is different from being informationally identical. Are they the same books? Actually, they are not. The collection of books with being physically the same as its identity criterion (call it =p) is different from the collection of books with being informationally the same as its identity criterion (call it =i). In other words, identity criteria play a crucial role in fixing collections of objects represented by CNs, although they are not made explicit in NL sentences. Books

[4] We adopt the view that two physically identical books can be informationally different, as assumed by (Asher 2012) and (Gotham 2014). However, the authors actually incline to believe that, in reality, if two books are physically identical, they cannot be informationally different. For example, Asher considers the example of several books in one volume, thinking that the same volume is involved. But we do not think that volume and the books in concern are anything comparable in such an example. But, as we said, we still adopt Asher/Gotham’s view since this is not important as far as giving the examples is concerned and it is easier for comparisons as well.

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in (3) and (5) refer to those with identity criterion =p while books in (4) and (6) refer to those with identity criterion =i. Note that it is the predicates (pick up and master) that determine which identity criterion should be: in (3), the domain of picked up is the type P hy of physical objects, and the identity criterion for books is =p (being physically the same); and in (4), the domain of master is the type Info of informational objects, and the identity criterion for books is =i (being informationally the same). Now, a further complication arises in cases like (2), where copredication and quantification interact and, therefore, in its semantic analysis, both identity criteria have to be used, i.e. we have to consider both collections of books: one with being physically the same as its identity criterion and the other with being informationally the same as its identity criterion. Giving the semantics properly, we should be able to get the following entailment:

(7) John picked up and mastered three books ⇒ John picked up three physical objects and mastered three informational objects

Here, there is some sort of double-distinctness that should be accounted for, involving both identity criteria. Any adequate theory of copredication should not only account for (5) and (6), but also for (7), dealing with counting and individuation correctly. In order to deal with copredication with quantification, this paper further develops the idea on identity criteria for CNs, studied for MTT-semantics by the second author in (Luo 2012a). We propose that, in general, CNs are interpreted as types associated with their identity criteria, i.e., they are setoids. A setoid is a pair (A, =), where A is a type (domain of the setoid) and = is an equivalence relation on A (equality of the setoid). If a setoid interprets a CN, its domain interprets that of the CN and its equality gives the identity criterion for the CN. For example, books in (3) refer to those in the collection of books whose identity criterion is =p (being physically the same), while books in (4) refer to those in the collection of books whose identity criterion is =i (being informationally the same). They are books with different identity criteria; or put in a better way, they belong to different collections of books whose identity criteria are different. In the CNs-as-setoids setting, it is shown that dot-types offer a proper treatment of copredication, not just the usual cases but also the sophisticated cases involving both copredication and quantification. At this point, one might want to ask: why do people usually say that, in MTT- semantics, CNs are interpreted as types and do not pay attention to their identity criteria? This is because most cases are not as sophisticated as copredication with quantification and, in these cases, related CNs usually have the ‘same’ identity criteria. For example, Man inherits its identity criterion from Human: two

OSLa volume 10(2), 2018 dot-types and identity criteria [125] men are the same if and only if they are the same as humans. This explains why we usually consider the entailment below induced by the subtyping relationship Man ≤ Human as ‘straightforward’ without even mentioning their identity criteria:

(8) Three men talk ⇒ Three humans talk

In other words, when interpreting a CN, its identity criterion can usually be safely ignored. Of course, this is not always the case: books in (3) and (4) are referring to different collections of books which have different identity criteria and, in (2) where both copredication and quantification are involved, more than one identity criterion will be involved in constructing appropriate semantics. In other words, in general, CNs are setoids but, in the usual cases, their identity criteria can be safely ignored and they are just types. In §[2], we shall give a brief introduction to dot-types in MTT-semantics. Then, in §[3], after an informal introduction to identity criteria for CNs, we shall study the generic semantics of numerical quantifiers. Copredication with quantification is studied in §[4], where we show how dot-type and the generic quantifier can be used together to deal with such situations. Related and future work is discussed in the last section.

[2] dot-types: a brief introduction Dot-types in MTT-semantics were introduced by the second author (Luo 2010, 2012b) to model copredication in MTT-semantics. Here is a brief introduction. Consider the copredication example (1), repeated here:

(9) John picked up and mastered the book.

Let P hy and Info be the types of physical and informational objects, respectively, and the interpretations of pick up and master have the following types:

pick up : Human → P hy → P rop master : Human → Info → P rop

In (9), pick up and master are applied in coordination to the book. In order for such coordination to happen, the two verbs must be of the same type.5 Our question is: given the above typing, can both of them be of the same type? The introduction of dot-types make this happen naturally. Informally, P hy • Info is the dot-type that satisfies the following property: it is a subtype of both P hy and Info. Then, the phenomenon according to which

[5] In MTT-semantics, the conjunction and can be given a polymorphic type ΠA : LT ype.A → A → A, where LT ype is the universe of linguistic types. See (Chatzikyriakidis & Luo 2012) for details.

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a book has both a physical and an informational aspect can be captured by stipu- lating that Book is a subtype of P hy • Info: formally, we have

Book ≤ P hy • Info ≤ P hy Book ≤ P hy • Info ≤ Info

Therefore, by contravariance of subtyping for function types, we have

pick up : Human → P hy → P rop ≤ Human → P hy • Info → P rop ≤ Human → Book → P rop

master : Human → Info → P rop ≤ Human → P hy • Info → P rop ≤ Human → Book → P rop

In other words, pick up and master are both of type Human → Book → P rop and, therefore, the coordination in (9) and its interpretation can proceed straightforwardly as intended. In general, given types A and B, we can form the dot-type A•B in the case that A and B do not share common parts (formally called components). For instance, P hy • Info is a legitimate dot-type, while P hy • (P hy • Info) is not, because in the latter, the constituent types P hy and P hy • Info share the common part P hy. Furthermore, as exemplified above, a dot-type A • B is a subtype of both of its constituent types A and B. The formal definition of component and the rules for dot-types are given in Appendix A. Note that, because of the non-sharing requirement for components and the subtyping relationships with its component types, a dot-type is not an ordinary type (like an inductive type) already available in MTTs. One has to introduce dot-types by means of the specific rules in Appendix A. As mentioned in Footnote 3, in MTT-semantics CNs are interpreted as types (rather than predicates): for instance, the CNs table and man can be interpreted as types T able and Man, respectively. Every CN corresponds to a type, but not vice versa: not every type represents a CN. Dot-types are examples: dot-types such as T able • Man do not represent any CNs in natural language.

[3] identity criteria: common nouns as setoids [3.1] Individuation and Setoids In simple terms, individuation is the process by which objects in a particular collection are distinguished from one another. Individuation provides us with the

OSLa volume 10(2), 2018 dot-types and identity criteria [127] means that enables one to count individual cats/dogs or any other type of objects and differentiate among them. At the same time, individuation also provides one with a sameness criterion, i.e. a way to decide whether two members of a particular collection are the same or not. The discussion on individuation goes back to at least Aristotle and has been the subject of enquiry of great philosophers in both the continental as well as the analytical tradition. However, it is outside the scope of the present chapter to present an overview of individuation from a philosophical point of view. Our point of departure will be individuation as discussed in the philosophy of language and linguistic semantics tradition. In linguistic semantics, individuation is very much related to the idea that a CN may have its own identity criterion, as discussed by Geach (1962). In mathematical terms, the idea amounts to the association of an equivalence relation (the identity criterion) to each CN. In fact, in the tradition of constructive mathematics, a set or a type is indeed a collection of objects together with an equivalence relation that serves as identity criterion of that collection.6 For CNs in MTT- semantics, this is the same as saying that a CN should in general be interpreted as a setoid – a type associated with an equivalence relation over the type. In our discussions of MTT-semantics, the current authors have been extensively discussing and endorsing the view that CNs are better treated as types rather than predicates. In doing so, we have been skipping some detail for the sake of simplicity. These details will now become significant, as well as handy, when discussing the issue of individuation concerning CNs. Put it in another way, these details we have been skipping are now crucial in giving an account of individuation and correct predictions in complex cases like (5) and (6) of copredication with quantification, where individuation, and the derived issue of counting, becomes significant and cannot be ignored anymore. The crucial detail that has been mostly ignored is embodied in the proposal put forward by the second author in (Luo 2012a), according to which the interpretation of a CN is not just a type, but rather a type associated with an identity criterion for that specific CN. In other words, a common noun is in general interpreted as a setoid, i.e. a pair

(10) (A, =) where A is a type and =: A → A → P rop is an equivalence relation over A. The notion of setoids is not new in type theory and reflects the view that a type is basically a setoid, meaning that it is comprised of a type plus an equivalence relation on this type. We apply this to linguistic semantics and this view makes

[6] For this, the interested readers may consult writings in constructive mathematics including, just to mention two of them, (Bishop 1967; Beeson 1985). The idea that sets/types may have different identity criteria is fundamentally different from that in classical mathematics where there is a universal equality relation between all objects of the formal theory (say, set theory).

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meanings of CNs more nuanced with respect to identity criteria: two CNs may have the same base type, but their identity criteria can be different and, if so, they are different CNs. To see how this proposal works, let’s consider some simple examples for illus- tration. In a simplified view, one would only interpret a CN as a type: for instance, human would be interpreted as a type Human, as in (11). However, in the elabor- ate view, CNs are interpreted as setoids, i.e., pairs of the form (10) and, therefore the CN human is now interpreted as in (12).

(11) [human] = Human : T ype (CNs-as-types view)

(12) [human] = (Human, =h) (CNs-as-setoids view)

where =h: Human → Human → P rop is the equivalence relation that represents the identity criterion for humans. Interpreting CNs as setoids makes explicit the individuation criteria (or identity criteria) and, based on this, we shall be able to use dot-types as introduced in the previous section to deal with copredication properly, even for the sophisticated cases when quantification is involved (see §[4]). However, before that, we shall first deal with the usual situations where the identity criteria of related CNs are essentially the same – inherited from supertypes.

[3.2] Inheritance of Identity Criteria: Usual Cases of Individuation Consider the following sentences (13) and (14) and their formal interpretations (15) and (16), respectively:

(13) A man talks. (14) A human talks. (15) ∃m : Man.talk(m) (16) ∃h : Human.talk(h)

where talk is interpreted as a predicate of type Human → P rop.7 Note that talk(m) in (15) is only well-typed because of the following subtyping relationship:

(17) Man ≤ Human 8

Then, the following is expected to be the case:

[7] When CNs are interpreted as setoids, the interpretations of verbs/adjectives should be IC-respecting predicates: for example, for talk : Human → P rop, talk(h1) ⇔ talk(h2) if h1 =h h2. [8] Such relations are intuitively true. Formally, it can be realised by more than one way: for example, Man may be defined as Σx : Human.male(x) with male : Human → P rop and then Man ≤ Human via the first projection as coercion.

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(18) (15) ⇒ (16) and, in fact, it can be easily proven because of (17). It is worth noting that, analysing the above example, we have not needed to consider the identity criteria of man and human at all, simply because that, for the simple sentences like (13) and (14), identity criteria are irrelevant. However, this is not the case anymore if we consider the following sentences (19) and (20) and their semantics (21) and (22), respectively:

(19) Three men talk. (20) Three humans talk.

(21) ∃x, y, z : Man. x ≠ M y & y ≠ M z & x ≠ M z & talk(x)&talk(y)&talk(z)

(22) ∃x, y, z : Human. x ≠ H y & y ≠ H z & x ≠ H z & talk(x)&talk(y)&talk(z) where Man = (Man, =M ) and Human = (Human, =H ) are setoids and the identity criterion for men and that for humans are used in (21) and (22), respectively, to express that x, y and z are distinct from each other. The difference of (19)/(20) with the earlier examples (13)/(14) is the presence of quantifier three (a numerical quantifier bigger than one), which makes it necessary to consider the individuation criteria explicitly by using the identity criteria =M and =H . The relationship between the setoids Man and Human is not just that the domain of the former is a subtype of that of the latter (Man ≤ Human), but their identity criteria are also essentially the same: the identity criterion for men is the restriction of the identity criterion for humans to the domain of men. Put in another way, the identity criterion for men is inherited from that for humans: two men are the same if, and only if, they are the same as human beings. In symbols, we have:

(23) (=M ) = (=H )|Man

One may wonder how =M and =H may be specified so that (23) is true. For example, if Man and Human are both base types with assumed coercion c such that ′ ′ Man ≤c Human, then given =H , we can define m =M m as c(m) =H c(m ). Then, (23) is true. Another possibility is that, in the case that the type of men is defined to be the type of humans who are male – formally, Man = Σx : ′ Human.male(x) (cf., Footnote 8), we can then define m =M m as π1(m) =H ′ π1(m ), where π1 is the operator for first projection. With this, (23) is true as well. Because of both (17) and (23), we have the following result as expected, which would not be provable if we only have (17) but not (23):

(24) (21) ⇒ (22).

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It is important to notice that, in usual cases, the relationships between related CNs are like that between man and human: one of the domains is the subtype of the other (like Man ≤ Human) and one of the identity criteria inherits the other (like =M inheriting =H as shown above). Such an inheritance relationship occurs in many cases, in fact, in all of the usual cases: examples of such pairs include man and human, red table and table, and many others. It may be useful to provide a name for this relation and this what the following definition does.

Definition (sub-setoid) We say that a setoid A = (A, =A) is a sub-setoid of B = (B, =B), notation A ⊑ B, if A ≤ B and =A is the same as (=B)|A (the restriction of =B over A). We often write =B for (=B)|A, omitting the restriction operator.

For example, besides Man ⊑ Human, we also have (RT able, =t) ⊑ (T able, =t), where RT able is the type Σx : T able.red(x) representing the domain of red tables and =t is the equivalence relation representing the identity criterion for tables (and inherited for red tables). Note that, in the restricted domain like Man or RT able, the identity criteria coincide with those in Human and T able and, in such a case, they are essentially the same and we can safely ignore them in semantic studies. Of course, there are more sophisticated cases where identity criteria are not inherited – they are in fact rather different. Copredication with quantification provides interesting examples, to be studied in §[4].

[3.3] Generic Semantics of Numerical Quantifiers Another way to consider the semantic interpretations of (19)/(20) is to define a generic semantics of the numeral quantifiers such as three and then define the semantics using the generic operator. In the following, we shall use three as an example of a numerical quantifier to show how to give generic semantics to them. A first attempt to define the semantics of three is to consider the following definition (25): for any setoid asetoidB = (B, =B), and any predicate P : B → P rop,

(25) T hree0(B,P ) = ∃x, y, z : B.D[B](x, y, z) & P (x) & P (y) & P (z)

where D[B](x, y, z) = x ≠ B y & y ≠ B z & x ≠ B z. Using T hree0, the semantics of (21) and (22) can be rewritten as (26) and (27), respectively:

(26) T hree0(Man, talk)

(27) T hree0(Human, talk)

And, similarly, we can express the semantics of (28) as (29), which is (30) after

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T hree0 is expanded, where Phy = (P hy, =p) is the setoid for the collection of physical objects and pick up : P hy → P rop:

(28) John picked up three physical objects.

(29) T hree0(Phy, pick up) (30) ∃x, y, z : P hy. D[Phy](x, y, z) & pick up(x) & pick up(y) & pick up(z)

A common feature of the examples (19), (20) and (28) is that the verb’s domain is the same as that of the object CN: for example, in (28), the domain of pick up is the same as P hy, the type of physical objects. Because of this restriction, the operator T hree0 is not generic enough,: it does not cover semantics of sentences with reference to more general situations, including (31):

(31) John picked up three pens.

(31) is an example where, first, the verb is applied to a CN whose domain is more restricted (but not the same): pick up can be applied to any physical object, not just pens; secondly, the identity criterion of the object CN is inherited from that for the domain of the verb (two pens are the same if, and only if, they are the same as physical objects). The identity criterion for pens inherits that for physical objects and can be determined from the contextual information in the sentence, more specifically, from the verb pick up: only physical objects can be picked up (the semantic type of pick up is P hy → P rop). The semantics of the CN pen is the setoid (P en, =p), whose identity criterion comes (is inherited) from the setoid of physical objects. In general, the identity criteria are determined by those of the verbs or adjectives applied to them. This has led us to the following generic definition.

Definition (T hree) Let A be a type and B = (B, =B) a setoid such that A ≤ B, and P : B → P rop a predicate over B. Then, we define the generic semantics of three as follows:

(32) T hree(A, B,P ) = ∃x, y, z : A. D[B](x, y, z) & P (x) & P (y) & P (z). where D[B](x, y, z) = x ≠ B y & y ≠ B z & x ≠ B z. Among T hree’s arguments, the type A and the domain B of setoid B are related in one of the following manners (all of them satisfy that A is a subtype of B):

(i) B = A: in this case, T hree(A, B,P ) is just T hree0(B,P ). In other words, T hree0 is a special case of T hree. For example, the semantics of (28) can be re-written as T hree(Phy, pick up).

(ii) B is different from A, but it is not a dot-type. An example of this is (31)

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whose semantics can be given as (33), which is (34) when T hree is expanded:

(33) T hree(P en, Phy, pick up) (34) ∃x, y, z : P en. D[Phy](x, y, z) & pick up(x) & pick up(y) & pick up(z)

(iii) B is different from A, but it is a dot-type – we shall discuss this in §[4]. When the setoid B interprets a CN, the predicate P is usually the interpretation of a verb phrase or an adjective. We usually require that such a predicate respect the identity criteria in the sense that, if x =B y, P (x) ⇔ P (y) (cf., Footnote 7.) Sometimes, B does not interpret a CN; an example is when B is a dot-type, which represents a typical case of copredication, to be discussed in the next section.

[4] copredication with quantification When both copredication and quantification are involved, the situation becomes more sophisticated and requires special treatment w.r.t the setoids concerned in order to give proper semantics.

[4.1] Dot-types and Quantification Dot-types in MTTs have been developed for copredication in linguistic semantics (Luo 2010, 2012b). The basic idea and formal rules are sketched in §[2], with the simple example of (9), repeated below as (35), which involves copredication, but no quantification. This is different in (2), repeated here as (36), where copredication interacts with quantification manifested in the numerical quantifier three.

(35) John picked up and mastered the book. (36) John picked up and mastered three books.

In such cases as (36) where both copredication and quantification are involved, a proper semantic treatment becomes more sophisticated and require more careful considerations. Let’s start by considering the simpler subcases (37) and (38), which do not involve copredication.

(37) John picked up three books. (38) John mastered three books.

First, it is not difficult to realise that (37) and (38) are not much different from (31), if we replace pens by books, and they should have similar semantics. Actually, they do: the semantics of (37) and (38) are (39) and (40), respectively:

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(39) T hree(Book, Phy, pick up). (40) T hree(Book, Info, master). where Phy = (P hy, =p) and Info = (Info, =i). However, it is important to note that the CN book in (37) refers to a different collection from that referred to by book in (38): for the collection of books in (37), two books are the same if they are physically the same, while for that in (38), two books are the same if they are informationally the same. Put in another way, although they share the same domain Book, their identity criteria are different and, therefore, they are different collections. This is reflected in their semantics: to compare books, =p is used in (39) and =i in (40). So, the CN book in (37) stand for a collection of books that is different from that in (38), represented by the setoids Book1 and Book2 as follows:

(41) Book1 = (Book, =p)

(42) Book2 = (Book, =i)

At this point, a question that naturally arises is how the identity criterion for books is determined: why do we use =p in (39) and =i in (40)? The answer is that it is the verb (and its semantics) that determines the identity criterion of the object CN. In (37), the verb is pick up : P hy → P rop, its domain P hy has determined that it is =p, the identity between physical objects, that should be used for the books; and in (38), the verb is master : Info → P rop, its domain Info has determined that it is =i, the identity between informational objects, that should be used for the books. In general, one may express this as follows: given a predicate V : Dom(V ) → P rop that interprets the verb, the identity criterion of the object CN N(book in the above examples) to which the verb is applied is determined by the domain of the predicate: in the case Dom(V ) ∈ {P hy, Info}, { =p if Dom(V) = P hy (43) ICN,V = =i if Dom(V) = Info

What the above does not cover is the crucial case of conjunction – for example, coordination of verbs pick up and master in (36). In order for such a coordination to happen, the two verbs must be of the same type, but the originally given types to picked up and mastered are different: Human → P hy → P rop and Human → Info → P rop, respectively. As explained in §[2], the introduction of dot-type P hy • Info and the subtyping in (44) make both verbs be of the same type and, hence, the two verbs can be coordinated.

(44) Book ≤ P hy • Info

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However, the treatment illustrated in §[2] is only for the situations when CNs are interpreted as types. As explained, (36) also involves quantification, due to the additional quantifier three, as well as copredication. This makes it necessary to consider CNs as setoids, with explicit identity criteria. As mentioned in the In- troduction, the correct semantics of sentences like (36) makes use of both identity criteria, =p for physical objects and =i for informational objects. In other words, one can update the above (43) into (45):  =p if Dom(V) = P hy (45) ICN,V ⇒ = if Dom(V) = Info  i ??? if Dom(V) = P hy • Info

The question is: what is the equivalence relation if the domain is a dot-type? Put in another way, assuming that we have the setoid Phy • Info, its domain is P hy • Info, what is =Phy•Info? This is to be defined below in the following subsection.

[4.2] Setoids for Dot-types We shall first give the definition of setoids for dot-types and then explain the related issues for clarification.

Definition (setoids for dot-types) Let A = (A, =A) and B = (B, =B) be setoids. Then the dot-setoid A • B is defined as follows:

A • B = (A • B, =A•B),

where ⟨a1, b1⟩ =A•B ⟨a2, b2⟩ if, and only if, (a1 =A a2) ∨ (b1 =B b2). Note that disjunction is used in the above definition. This is mainly because that, with this definition, the semantics by means of the generic numerical quantifier (say T hree) is exactly what we want. For instance, the semantics for (36) is (46), which is (47) when T hree is expanded, where pm : Human → P hy • Info → P rop is the interpretation of pick up and master:

(46) T hree(Book, Phy • Info, pm(j)) (47) ∃x, y, z : Book. D[Phy](x, y, z) & D[Info](x, y, z) & pm(j, x) & pm(j, y) & pm(j, z)

The semantics captures the ‘double distinctness’ as expected: that is, there are books x, y and z which are different physically and informationally. Note that this is achieved through defining the equivalence relation for dot-types by means of disjunction of both identity criteria and, then, we obtain double distinctness by negating the disjunction. At this point, one might want to question the equivalence relation for dot- types, as given in the definition above. The first question would be: Why is it

OSLa volume 10(2), 2018 dot-types and identity criteria [135] defined by disjunction of the constituent equalities? The answer to this is that, besides other reasons, the definition delivers the correct semantics by means of the generic quantifier, as shown above. Another subtler and possibly deeper question is: is the definition appropriate? Instead of answering this question directly, let us discuss two related issues which we hope would clear away some misunderstandings that may be behind asking the question and clarify the issues at hand. The first issue concerns the relationship between dot-types and linguistic entities like CNs. Although CNs can be interpreted as types, there is no CN that can be interpreted as a dot-type. In particular, the equivalence relation does not represent any identity criterion of a CN. That’s why we have been careful in not calling the equivalence relation =A•B an identity criterion – it is simply not. The other related issue is more general than the first: we think that, unlike other data types in MTTs (say, the type of natural numbers), a dot-type A•B is not a representation of a collection of objects, although its constituent types A and B may be (this concerns the detailed definition of dot-types – see, for example, (Luo 2012b) for some discussions.) Therefore, in a setoid whose domain is a dot-type, its equivalence relation is not supposed to be the equality for a collection. This explains the flexibility we have in defining the equivalence relation for dot-types. In fact, as far as correctness is concerned, as long as it is an equivalence relation, it would do. Our definition does result in an equivalence relation.

[4.3] Verbs Plus Adjectives: More Examples of Copredication with Quantification Consider the following example:

(48) John mastered three heavy books.

Interpreting the above sentence, one needs to capture that John mastered three informational objects that are also heavy as physical objects. In effect, both the verb and the adjective have a word on the decision concerning the identity criteria involved in interpreting this sentence. Formally, we have:

(49) heavy : P hy → P rop (50) master(j) : Info → P rop

So, both identity criteria for physical/informational objects are in play. This is a more sophisticated copredication phenomenon. Let us break the problem into two parts: first we look at the adjectival modification and, then, the result of three quantifying over heavy books and, then, the application of mastered(j) to the whole quantified NP three heavy books. The interpretation of the adjectival

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modification is taken to be a Σ-type:9 heavy book will be interpreted as (51), which is a subtype of Book as shown in (52):10

(51) HBook = Σ(Book, heavy) (52) HBook ≤ Book ≤ P hy • Info

The interpretation we get for the whole sentence (48) is (53), which is (54) when T hree is expanded:

(53) T hree(HBook, Phy • Info, master(j)) (54) ∃x, y, z : HBook. D[Phy](x, y, z) & D[Info](x, y, z) & master(j, x) & master(j, y) & master(j, z)

The above account can also be extended to the case when a noun is modified by more than one adjective that may induce different identity criteria, such as (55):

(55) John mastered three heavy informative books.

In such a case, what we need to capture is the fact that John mastered three informational objects that are heavy as physical objects but informative as informational objects. Let us see how this works. We first form the Σ-type in a nested manner,11 and we have similar subtyping relationships (58):

(56) IBook = Σ(Book, informative), where informative : Info → P rop. (57) HIBook = Σ(IBook, heavy), where heavy : P hy → P rop. (58) HIBook ≤ IBook ≤ Book ≤ P hy • Info.

The interpretation we get for the whole sentence (55) is the following:

(59) T hree(HIBook, Phy • Info, master(j))

Shown by the above examples, what is obvious is that the way the identity criteria are decided are a little bit more complicated, given that we might have cases where both a verb and an adjective play a role in this decision. Another related issue is how many identity criteria can be used. In all our examples, the maximum number is two. This is not an accident as it basically represents the ability that a common noun to be associated with identity criteria. This is true for common nouns like book that are associated with two aspects: in

[9] For more information on adjectival modification and modification in general in MTTs, please consult (Chatzikyriakidis & Luo 2013, 2017a) [10] (51) is just another notation for Σx : Book.heavy(x), the type of books which are heavy. [11] We note that there is another interpretation of the adjective modification: heavy informative books is seen as heavy and informative books. Then similar but slightly different analysis would follow.

OSLa volume 10(2), 2018 dot-types and identity criteria [137] the case of book, a physical and an informational one. Whether we have cases where more than three identity criteria are involved for the same common noun boils down to the question of whether common nouns with that many aspects can be found. One such case is newspaper: it is associated with three senses: (a) physical, (b) informational, and (c) institutional. However, rather interestingly, only two of the three senses can appear together. More specifically, Antunes & Chaves (2003) argue that, whereas senses (a) and (b) can appear together in a coordinated structure, sense (c) cannot appear with any of the other two:

(60) # That newspaper is owned by a trust and is covered with coffee. (61) # The newspaper fired the reporter and fell off the table. (62) # John sued and ripped the newspaper.

In (Chatzikyriakidis & Luo 2015), we have argued that one can find cases where two senses are actually coordinated:

(63) The newspaper you are reading is being sued by Mia.

Whatever the data are, however, there are no cases where all three senses are coordinated nor we know of any other common noun that allows this kind of situation. This means that an account of individuation can be reduced to dot- types with two senses, not more than that, even though in principle the account presented here, as well as other accounts like the one proposed by (Gotham 2017), could easily be generalized for n senses if there is a need to do so.

[5] related work and conclusion The dot-type approach offers an adequate account of copredication in general, and a proper treatment of individuation and counting in copredication with quantification in particular. It is shown that, in this latter sophisticated case, identity criteria should be taken into account – in another word, CNs should be interpreted as setoids. Whence the identity criteria of CNs are taken into account, correct predictions and expected reasoning results can be obtained. We have only considered the interpretation of CNs as setoids in the specific context of copredication with quantification. However, the general paradigm of CNs-as-setoids has not been developed in depth: these include, for example, its relationship with the simpler CNs-as-types paradigm and its other applications. It should be explored further in future work.

Related work. The origin of the notion of criteria of identity can be traced back to Frege (1884) when he considered abstract mathematical objects such as numbers or lines. As far as the authors know, it was Geach (1962) who first connected iden-

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tity criteria with CNs in linguistic semantics. Subsequent studies include Baker (2003), Barker (2008), Gupta (1980) and Luo (2012a), among others. For the first time, this paper has studied the issue of identity criteria in the context of copredication with quantification. As mentioned in Footnote 1, we have studied the issues of copredication with quantification in (Chatzikyriakidis & Luo 2015) but did not realise the necessity of considering identity criteria – the current paper does the job. The individuation problem was studied by Asher (2008, 2012), among others. Gotham (2017), starting from his PhD thesis (Gotham 2014), has successfully looked at the individuation problem in copredication with quantification in a mereological setting, as related to (Link 1983) among others. It is the first account to deal in depth with the problems discussed in this paper in which Gotham manages to provide a compositional account of co-predication that derives the correct identity criteria in the cases where double distinctness is needed. One of the interesting connections with our work is the assumption in the first paragraph of Section 2 of (Gotham 2017) – it is related to our disjunction-based equivalence relation for dot-types (see Definition in §[4.2]). Deeper reflections and analysis of these different approaches are called for.

acknowledgements The first author supported by by grant 2014-39 from the Swedish Research Coun- cil, which funds the Centre for Linguistic Theory and Studies in Probability in the Department of Philosophy, Linguistics, and Theory of Science at the University of Gothenburg. We are grateful to N. Asher, M. Gotham, R. Cooper and C. Retoré for providing useful discussion and comments throughout the years that we have been working on this issue.

references Antunes, S. & R.P Chaves. 2003. On the licensing conditions of co-predication. In Proc of the 2nd Inter. Workshop on Generative Approaches to the Lexicon (GL 2007),.

Asher, N. 2008. A type driven theory of predication with complex types. Funda- menta Informaticae 84(2). 151–183.

Asher, N. 2012. Lexical Meaning in Context: a Web of Words. Cambridge University Press.

Baker, Mark C. 2003. Lexical categories: Verbs, nouns and adjectives, vol. 102. Cam- bridge University Press.

Barker, C. 2008. Nominals don’t provide criteria of identity. In A. Alexiadou &

OSLa volume 10(2), 2018 dot-types and identity criteria [139]

M. Rathert (eds.), Nominalizations across languages and frameworks Intrface Ex- plorations, .

Bassac, C., B. Mery & C. Retoré. 2010. Towards a type-theoretical account of lexical semantics. Journal of Logic, Language and Information 19(2).

Beeson, M.J. 1985. Foundations of constructive mathematics. Springer-Verlag.

Bishop, E. 1967. Foundations of constructive analysis. McGraw-Hill.

Chatzikyriakidis, S. & Z. Luo. 2012. An Account of Natural Language Coordination in Type Theory with Coercive Subtyping. In Y. Parmentier & D. Duchier (eds.), Proc. of Constraint Solving and Language Processing (CSLP12). LNCS 8114, 31–51. Or- leans.

Chatzikyriakidis, S. & Z. Luo. 2013. Adjectives in a modern type-theoretical setting. In G. Morrill & J.M Nederhof (eds.), Proceedings of Formal Grammar 2013. LNCS 8036, 159–174.

Chatzikyriakidis, S. & Z. Luo. 2015. Individuation criteria, dot-types and copredication: A view from modern type theories. In Proceedings of the mathematics of language 2015, acl anthology,.

Chatzikyriakidis, S. & Z. Luo. 2017a. Adjectival and adverbial modification: The view from modern type theories. Journal of Logic, Language and Information 26(1). 45–88.

Chatzikyriakidis, S. & Z. Luo. 2017b. Identity Criteria of CNs: Quantification and Copredication. Workshop on Approaches to Coercion and Polysemy. Oslo .

Chatzikyriakidis, S. & Z. Luo. 2018. Formal Semantics in Modern Type Theories. Wiley & ISTE Science Publishing Ltd. (to appear).

Frege, G. 1884. Grundlagen der arithmetik. Basil Blackwell. (Translation by J. Austin in 1950: The Foundations of Arithmetic).

Geach, P. 1962. Reference and generality: An examination of some medieval and modern theories. Cornell University Press.

Gotham, M. 2014. Copredication, quantification and individuationy. University Col- lege London PhD dissertation.

Gotham, M. 2017. Composing criteria of individuation in copredication. Journal of Semantics 34(2). 333–371.

Gupta, A. 1980. The logic of common nouns. Yale University Press.

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Link, G. 1983. The logical analysis of plurals and mass terms: A lattice-theoretical approach. In Schwarze C. Bauerle R. & von Stechow A (eds.), Meaning, use an interpretation of language, 302–323. Mouton De Gruyter, Berlin.

Luo, Z. 1999. Coercive subtyping. Journal of Logic and Computation 9(1). 105–130.

Luo, Z. 2010. Type-theoretical semantics with coercive subtyping. Semantics and Linguistic Theory 20 (SALT20), Vancouver .

Luo, Z. 2012a. Common Nouns as Types. In D. Bechet & A. Dikovsky (eds.), Logical Aspects of Computational Linguistics (LACL’2012). LNCS 7351,.

Luo, Z. 2012b. Formal semantics in modern type theories with coercive subtyping. Linguistics and Philosophy 35(6). 491–513.

Luo, Z., S. Soloviev & T. Xue. 2012. Coercive subtyping: theory and implementation. Information and Computation 223. 18–42.

Pustejovsky, J. 1995. The generative lexicon. MIT.

Ranta, A. 1994. Type-theoretical grammar. Oxford University Press.

A rules for dot-types The following formal rules for dot-types are given in (Luo 2012b). The notion of component with notation C(_) is used in the Formation Rule below, as defined as follows.

Definition A.1 (components) Let T : T ype be a type in the empty context. Then, ′ ′ C(T ), the set of components of T , is defined as, where Sup(T ) = {T | T ≤ T }: { (T ) T X • Y C Sup if the normal form of is not of the form (T ) =df C(T1) ∪ C(T2) if the normal form of T is T1 • T2

Presenting the rules, we shall assume the knowledge of coercive subtyping (Luo 1999; Luo et al. 2012). Also, we shall use ≤ instead of < for subtyping and, for this, it may be useful to know that the coherence condition for coercive subtyping implies that, if A ≤c A, then c = [x : A]x, the identity function over A.

Formation Rule Γ valid ⟨⟩ ⊢ A : T ype ⟨⟩ ⊢ B : T ype C(A) ∩ C(B) = ∅ Γ ⊢ A • B : T ype

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Introduction Rule Γ ⊢ a : A Γ ⊢ b : B Γ ⊢ A • B : T ype Γ ⊢ ⟨a, b⟩ : A • B

Elimination Rules Γ ⊢ c : A • B Γ ⊢ c : A • B Γ ⊢ p1(c) : A Γ ⊢ p2(c) : B

Computation Rules

Γ ⊢ a : A Γ ⊢ b : B Γ ⊢ A • B : T ype Γ ⊢ a : A Γ ⊢ b : B Γ ⊢ A • B : T ype Γ ⊢ p1(⟨a, b⟩) = a : A Γ ⊢ p2(⟨a, b⟩) = b : B

Projections as Coercions Γ ⊢ A • B : T ype Γ ⊢ A • B : T ype ⊢ • ≤ ⊢ • ≤ Γ A B p1 A : T ype Γ A B p2 B : T ype

Coercion Propagation ⊢ • ⊢ ′ • ′ ⊢ ≤ ′ ⊢ ′ Γ A B : T ype Γ A B : T ype Γ A c1 A : T ype Γ B = B : T ype ⊢ • ≤ ′ • ′ Γ A B d1[c1] A B : T ype where d1[c1](x) = ⟨c1(p1(x)), p2(x)⟩. ⊢ • ⊢ ′ • ′ ⊢ ′ ⊢ ≤ ′ Γ A B : T ype Γ A B : T ype Γ A = A : T ype Γ B c2 B : T ype ⊢ • ≤ ′ • ′ Γ A B d2[c2] A B : T ype where d2[c2](x) = ⟨p1(x), c2(p2(x))⟩. ⊢ • ⊢ ′ • ′ ⊢ ≤ ′ ⊢ ≤ ′ Γ A B : T ype Γ A B : T ype Γ A c1 A : T ype Γ B c2 B : T ype ⊢ • ≤ ′ • ′ Γ A B d[c1,c2] A B : T ype where d[c1, c2](x) = ⟨c1(p1(x)), c2(p2(x))⟩. author contact information Stergios Chatzikyriakidis Department of Philosophy, Linguistics and Theory of Science, University of Gothen- burg [email protected]

Zhaohui Luo Royal Holloway, University of London [email protected]

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Alexandra Anna Spalek and Matthew Gotham (eds.) Approaches to Coercion and Polysemy, Oslo Studies in Language 10(2), 2018. 143–162. (ISSN 1890-9639 / ISBN 978-82-91398-12-9) https://www.journals.uio.no/index.php/osla

coercion as proof search in dependent type semantics

ERIKOKINOSHITA,KOJIMINESHIMA&DAISUKEBEKKI Ochanomizu University abstract This paper presents an analysis of coercion and related phenomena in the framework of Dependent Type Semantics (DTS). Using underspecified terms in DTS, we present an analysis of selectional restriction as presupposition; we then combine it with a type called transfer frame to provide an analysis of coercion. Our analysis focuses on the fact that coercion is triggered not only by type mismatch between predicates and their arguments, but also by more general inference with contextual information. We show how the analysis can be extended to copredication of logical polysemy and complement coercion. Finally, we will suggest that this analysis can shed light on an aspect of complicity that is invoked in interpreting coercion and other meaning-shifting phenomena.

[1] introduction Recently, various extended type systems have been developed to explain phenomena related to coercion (Pustejovsky 1993; Asher 2011; Luo 2012; Asher & Luo 2012; Cooper 2012; Retoré 2014; Mery & Retoré 2017). These systems are enriched with more fine-grained types than is commonly assumed in formal semantics, which enables us to analyze selectional restrictions of predicates as type matching. According to the widely held view, an operation for dealing with coercion is triggered when a predicate and its argument cause a type mismatch during the course of semantic composition. For example, the predicate escape demands that its subject is an animate entity; thus, the literal reading of (1-a) produces a type mismatch. When it is uttered in a context where there is a man who ate an omelet in a café, however, (1-a) can be understood as meaning (1-b) (Nunberg 1995).

(1) a. The omelet escaped. b. The man who ate the omelet escaped.

The coercion-as-type-mismatch view naturally accounts for this reading. However, there is a problem with the naive assumption that coercion is only triggered by type mismatch: it can be contextually triggered without any type mismatch, so as to find a more relevant interpretation. For example, (2-a) has [144] kinoshita, mineshima & bekki

the reading in (2-b), even though the literal reading does not produce a type mismatch.

(2) a. The lion escaped. b. The actor who plays the lion at The Lion King escaped (from the theater).

This suggests that coercion is not only driven by type matching in semantic composition but also by inference with contextual information. This paper proposes a formal analysis of coercion in the framework of Depend- ent Type Semantics (DTS) (Bekki 2014; Bekki & Mineshima 2017), a framework of proof-theoretic semantics that combines dependent types with the mechanism of underspecification for handling anaphora and presupposition. In this framework, selectional restrictions are analyzed as presuppositions, and the satisfaction of presuppositions is calculated at the stage of type checking that involves proof search. Using this framework, we analyze coercion at the stage of type checking rather than at the stage of semantic composition. We argue that this analysis captures the inferential aspect of coercion as shown by phenomena such as (2). We also show that it can be extended to related phenomena, including copredication and complement coercion. The structure of the paper is as follows. Section [2] gives an overview of the basic framework of DTS, focusing on how semantic underspecification works to represent and compute anaphoric elements. Section [3] provides an analysis of selectional restrictions and shows how the presuppositional behavior of selectional restrictions is derived in DTS. With this background, we present an analysis of coercion triggered by contextual inference in Section [4] and then extend it to an analyses of copredication [5.1] and complement coercion [5.2]. Finally, in Section [6] we will suggest that our analysis accounts for an aspect of interpretation called complicity involved in coercion.

[2] dependent type semantics [2.1] Dependent types Dependent types have been used to analyze various aspects of natural languages (Ranta 1994; Cooper 2012; Luo 2012). Compared with simple types, dependent types can express types depending on terms. For instance, man(x) is a type depending on a term x. We say man(x) has type type, x is a term of type entity, and man is a predicate of type entity → type. Under the so-called Curry-Howard corres- pondence, a type can be identified with a proposition; thus, the type man(x) is regarded as the proposition that x is a man. A term having such a type is called a proof term. For instance, p : man(x) expresses that a proof term p has the type man(x), that is, p is a proof for the proposition that x is a man.

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(i) (i) x : A (i) x : A . x : A . . . . A : type B : type . M : AN : B[M/x] A : type B : type [ ] (ΣF ), i (x : A) → B : type M : B [ ] (ΣI) (ΠF ), i x : A (ΠI), i x : A (x : A) → B : type : type λx.M :(x : A) → B (M,N): B B

[ ] [ ] x : A x : A M : M : M :(x : A) → BN : A B B A : type A true (ΠE) (ΣEl) (ΣEr) (@) MN : B[N/x] π1(M): A π2(M): B[π1(M)/x] (@ : A): A

figure 1: Inference rules for Π-types and Σ-types and the @-rule.

Two kinds of dependent types play an important role: (i) Π-type (dependent function type), written (x : A) → B, is a generalized form of a function type A → B; a term of type (x : A) → B is a function f that takes a term a of type A and returns a term f[(a) of type] B[a/x]. (ii) Σ-type (dependent product type), x : A written (x : A) × B or , is a generalized form of a product type A × B; B a term of type (x : A) × B is a pair (t, u) such that t is of type A and u is of type B[t/x]. The projection functions π1 and π2 are defined in such a way that π1(t, u) = t and π2(t, u) = u. When the variable x does not occur free in B, (x : A) → B and (x : A) × B can be reduced to A → B and A × B, respectively. Given the identification of types with propositions, A → B and A×B correspond to implication and conjunction, respectively.1 See Martin-Löf (1984) and Ranta (1994) for more details on dependent types. In contrast to model-theoretic semantics, the semantics of natural language based on dependent types can be called proof-theoretic semantics, where the meaning of a sentence is regarded as a proof-condition, a condition specified by inference rules, rather than as a truth-condition. By taking proof-conditions as a central aspect of meaning, semantic theories based on dependent types are particularly suitable for capturing inferential aspects of interpretations. Figure 1 shows formation rules (ΠF , ΣF ), introduction rules (ΠI, ΣI) and elimination rules (ΠE, ΣE) for Π-type and Σ-type we use in this paper. It is important to see that Π-type and Σ-type correspond to universal and existential quantification, respectively. For example, the sentences in (3-a) can be analyzed as having a semantic representation (SR) in (3-b).

(3) a. Every man entered.

[ ] A [1] For conjunction A × B, we also use a two-dimensional notation for readability. For nested     B [x : A ] x : A Σ-types, we abbreviate  y : B  as  y : B . C C

OSLa volume 10(2), 2018 [146] kinoshita, mineshima & bekki ( [ ]) x : entity b. u : → enter(π (u)) man(x) 1

The term u has a Σ-type: it is a pair of a term (let it be x) having type entity and a proof term having type man(x) that depends on x. The Π-type universally quantifies over such pairs of terms. The term π1(u) in the argument position of enter picks up the entity that is the first element of u, namely, the entity x. Thus, the entire SR in (3-b) says that for every entity x such that x is a man, x entered. This is equivalent to the standard truth-condition for (3-a).

[2.2] Underspecification DTS (Bekki 2014; Bekki & Mineshima 2017) differs from the previous studies such as Ranta (1994) and Luo (2012) in that it has underspecified terms @ to represent context-dependent elements.2 For example, the sentence in (4-a) is given the SR in (4-b) that contains an underspecified term @.

(4) a. He whistled.( ( [ ])) x : entity b. whistle π @ : 1 man(x)

The @-term plays the role of a hole to be filled in at a later stage of interpretation called type checking. The type A in @ : A, called type annotation, specifies the type of the underspecified term @. In this case, the term @ has the Σ-type standing for the proposition that there is an entity x such that x is a man. Since a term having the Σ-type is a pair of objects, the first element is picked up by the projection function π1 and the predicate whistle applies to it. Such an underspecified SR is compositionally derived from a parse tree for a sentence.3 Then the well-formedness of an SR is proved via type-checking. This launches a derivation of A : type for the underspecified SR A, given a background context called a global context. If A contains an underspecified term @, this process of type-checking invokes a process of proof search, i.e., a process of constructing a proof term for @. This is the process of filling a hole indicated by @ with a suitable term having the type annotated to @. In the case of (4-b), the type checking to ensure that this SR is well-formed, i.e., it has type type, runs as in Figure 2. Here we use the @-rule shown in Figure 1. This

[2] Another difference between DTS and previous proposals is that in DTS, a common noun like man is analyzed as a predicate rather than as a type. Thus, (3-a) is analyzed as (3-b), not as (x : man) → enter(x). See Bekki & Mineshima (2017) and Chatzikyriakidis & Luo (2017b) for a detailed comparison of two approaches. [3] See Bekki (2014); Bekki & Mineshima (2017) for an approach to compositionality in DTS based on Com- binatory Categorial Grammar (CCG).

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. . [ . ] [ . Λ ] x : entity x : entity : type true man(x) man(x) ( [ ]) [ ] (@) x : entity x : entity @ : : man(x) man(x) ( [ ]) (ΣEl) x : entity whistle : entity → type π @ : : entity 1 man(x) ( ( [ ])) (ΠE) x : entity whistle π @ : : type 1 man(x)

figure 2: The type checking for the SR (4-b)

parse tree underspecified SR well-formed SR

semantic composition type checking (proof search)

figure 3: Two-stage process of interpretation

rule introduces an @-term with annotated type A.4 The judgement A true means that there exists a proof term having the type A. Thus, this triggers a process of proof search to construct a term having the annotated type. Starting from the root of the derivation tree in Figure 2, one needs to fill the gap in Λ by finding a term having the annotated Σ-type.5 This means that one has to construct a pair (a, t) such that a is an entity and t is a proof of the proposition that a is a man. Suppose that we can construct such a term (a, t) from the global context where a : entity and t : man(a) hold. By replacing @ in (4-b) with the constructed term (a, t), we obtain whistle(π1(a, t)), which computes to whistle(a). This yields a fully specified SR for (4-a) in this context. Figure 3 shows the two-stage process of deriving a well-formed SR. Note that semantic composition at the first stage is deterministic, while proof search at the second stage can be non-deterministic if there are more than one way to resolve an underspecified term. See Bekki & Mineshima (2017) for more discussions on anaphora, including E-type anaphora, donkey anaphora and bridging inferences.

[4] If the annotated type contains another @-term, a separate process of proof search is launched by the sub-derivation starting from A : type in the left premise of the @-rule. [5] Note that the other two branches are closed using judgements such as whistle : entity → type and man : entity → type, which we assume are contained in the global context.

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[3] selectional restrictions [3.1] Types versus predicates There are at least two approaches to representing selectional restrictions in extended type-theoretic frameworks, i.e., those frameworks that go beyond a simply- typed setting with entities and truth-values as base types. The first one is to represent selectional restrictions as types (Asher 2011; Luo 2012; Retoré 2014); for instance, taking animate as a base type, one can assign a type animate → prop to the predicate escape. According to this approach, the violation of selectional restrictions leads to type mismatch. To avoid type mismatch during the course of semantic composition, then, one needs to enrich the system with subtyping. For instance, to combine the predicate escape of type animate → prop with the term john of type human, one needs a subtyping relation human < animate and extra subtyping rules. A disadvantage is that these additional subtyping rules may make the resulting compositional semantics more complicated. The other approach is to represent selectional restrictions as predicates; for instance, if one uses the base type for entities, the selectional restriction of the verb escape can be represented as animate(x), i.e., as a predicate over entities. Although it is underdeveloped, this second approach has an advantage in that it dispenses with subtyping and thus can preserve the well-understood mechanism of the syntax-semantics interface.6 We are going to build on this second approach and integrate it with the two-stage architecture of interpretation in DTS.

[3.2] Selectional restrictions as presupposition Selectional restrictions show the behavior of presuppositions. One piece of evidence comes from presupposition projection. For instance, one can infer that John is animate not only from (5-a) but also from (5-b).

(5) a. John escaped. [⇒ John is animate] b. John didn’t escape. [⇒ John is animate]

If selectional restrictions of predicates were part of entailment, the verb escape would be assigned the meaning in (6-a), which would predict that (5-b) has the semantic representation in (6-b).

(6) a. λx.escape(x) ∧ animate(x) b. ¬(escape(john) ∧ animate(john))

Clearly, this does not account for the inference in (5-b). More generally, selectional restrictions project out of the scope of entailment-canceling operators such as negation, modals, and conditionals (Magidor 2013; Asher 2014).

[6] The choice between predicates and types is related to the analysis of common nouns in type theory; see footnote 2 and references cited there.

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Further evidence comes from the fact that selectional restrictions show the behavior of presupposition filtering as exemplified by (7):

(7) If numbers are coloured, then the number two is green. (Magidor 2013, p.135)

The violation of a selectional restriction observed in the number two is green is ab- sent in (7) due to presupposition filtering, for which the naive type-mismatch analysis would yield a wrong prediction.

[3.3] Transfer Frame In simple type theory, the predicate escape denotes a function from entities to truth-values, i.e., a function of the type e → t. In dependent type theory, we can put an additional condition for selectional restriction on arguments; thus we assign the following semantic type to the predicate escape.7 [ ] x : entity (8) escape : → type. animate(x)

The predicate escape is a function that takes a pair of an entity x and a proof of x’s being animate and returns a type (i.e., a proposition). In DTS, we can leave underspecified the second argument, i.e., a proof term for selectional restriction; that is, by filling the second argument with an underspecified term @, we do not have to find a specific proof term for selectional restriction at the stage of semantic composition. Now we can define the lexical entry for an intransitive verb as in (9).8

(9) The lexical entry for the verb escape (Version 1) [[escape]] = λx.escape(x, @ : animate(x))

Here the type of [[escape]] is entity → type. When the verb is combined with the subject NP, say, John, whose SR is [[John]] = j of type entity, we can derive the following:

(10) [[escape]]([[John]]) = escape(j, @ : animate(j)).

For this SR to be well-formed, one has to find a proof term for the type animate(j) annotated to @. This correctly predicts the behavior of selectional restriction for the verb escape.9 However, this analysis does not cover the interpretations of coercion including ones driven by contextual inference such as (2). Accordingly, we general-

[7] Note that this type is equivalent to (x : entity) → animate(x) → type. [8] This is the entry proposed in Kinoshita et al. (2016). [9] See Kinoshita et al. (2016) for more details.

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ize the entry in (9) and propose a new lexical entry for predicates, using a type TF x 10 F -target, called Transfer Frame, relativized to an entity x and a predicate F -target. In the case of escape, the new lexical entry is given in (11).

(11) The lexical entry for the verb escape (Version 2) TF x [[escape]] = λx.escape(π1(@ : animate)) TF x 11 The type F -target is defined as follows.  [ ]  y : entity  t-pair :   F -target(y)     F source : entity → type   -  def   (12) TF x ≡  p : F -source(x)  F -target  [ ] [ ]   w : entity y : entity   R : → → type   F -source(w) F -target(y)  R(x, p)t-pair

Some remarks are in order. The predicate in F -target stands for the selectional restriction imposed on the argument of the verb in question. The term x, called the source term, is the entity denoted by the NP in the argument position of a given TF x sentence. The role of F -target is to link the source term x to a term y (called the target term) that satisfies the selectional restriction in F -target by means of a relation R holding between x and y. More specifically, given a source term x and a predicate F -target, the under- TF x specified term @ : F -target searches a 5-tuple (t-pair, F -source, p, R, q) that satisfies the following conditions: (i) t-pair is a pair of a target term y and a proof term of the proposition that y has the predicate F -target; (ii) F -source is a predicate of type entity → type; (iii) p is a proof term of the proposition that the source term x has the predicate F -source; (iv) R is a relation between the source term x and the target term y12; (v) q is a proof term of R(x, p)t-pair, i.e., the proposition that R holds between the source term x and the target term y.13 If such a 5-tuple is constructed, the main predicate applies to its first projec-

[10] The transfer frame generalizes the operator arg (called argument operator) introduced in Kinoshita et al. (2016). A problem with the argument operator arg in Kinoshita et al. (2016) is that it does not derive the meaning of coercion when a sentence does not cause type mismatch. So it does not cover the case of coercion driven by contextual inference shown in (2). [11] It should be noted that TF is defined as a Σ-type, although the notation used here is similar to record types (Cooper 2012). See also the remark on the notation in footnote 1. [12] Note that the relation R takes as argument two pairs of an entity and a proof term; the proof term ensures that the entity satisfies the selectional restriction of R. [13] In the definition of TF, we use a Σ-type of the form (X : A → · · · → type) × B, which is known to cause Girard’s paradox (Hook & Howe 1986). We can avoid the inconsistency by introducing the hierarchy of universes; but discussing this problem in detail will take us too far afield from the focus of this paper.

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. . . . Λ TF j TF j animate : type animate true (@) (@ : TF j ): TF j [ ] animate [ animate ] (ΣE) x : entity x : entity escape : → type π (@ : TF j ): animate(x) 1 animate animate(x) (ΠE) TF j escape(π1(@ : animate)) : type figure 4: The type checking for (13) tion, namely, t-pair, as shown in the lexical entry in (11). Since t-pair is a pair of an entity y (the target term) and a proof term for F -target(y), it matches with the type of the predicate escape in (8).

[3.4] Literal interpretation To see how the analysis works, consider first the sentence in (5-a) with its literal interpretation. Using the lexical entry of escape in (11), one can derive the SR of (5-a) as (13), where j is the term for John. TF j (13) escape(π1(@ : animate)) The type checking of this underspecified SR goes as shown in Figure 4, in a sim- TF j ilar way to the one in Figure 2. In this derivation, animate true triggers in Λ a process of proof search to construct a 5-tuple satisfying the transfer frame. In the literal reading of (5-a), the target term should be identical to the source term j, both being an animate entity; in such a case, we can use the equality relation between animate entities for R. Thus, assuming that it is established in the global context that John is an animate entity, we can construct a 5-tuple as shown in Figure 5.14 By substituting @ in (13) with this 5-tuple, we obtain an SR escape(π1((j, t), anim, t, =, refl(j, t))), which computes to escape(j, t), where t is a proof term for animate(j). In this way, the literal interpretation of (5-a) is correctly derived.

[3.5] Presupposition projection Our analysis can account for the presuppositional inferences triggered by selectional restrictions. For presupposition projection, let us consider the case of negation. The SR of the negative sentence in (5-b) is given as (14).

[14] Here we write entity as e, type as t, animate as anim, and a tuple (a, (b, c)) as (a, b, c). The equality in dependent type theory is relativized to a type, but as a notational convenience, we make this type implicit: the equality = here should be understood as =(x:entity)×anim(x). The constructor refl for equality is also implicitly relativized to this type; see Nordström et al. (1990) for the treatment of equality in dependent type theory.

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. [ ] [ ] . w : e y : e . = : → → t refl(j, t):(j, t) = (j, t) anim(w) anim(y)  [ ] [ ]  (ΣI) w : e y : e R : → → t t : anim(j) (=, refl(j, t)) :  anim(w) anim(y)  R(j, t)(j, t)   (ΣI) p : anim(x)  [ ] [ ]   w : e y : e  anim : e → t (t, =, refl(j, t)) :  R : → → t   anim(w) anim(y)  R(j, p)(j, t)   (ΣI) F -source : e → t j : e t : anim(j)   [ ] (ΣI)  p : F -source(x)  x : e  [ ] [ ]  (j, t): (anim, t, =, refl(j, t)) :  w : e y : e  anim(x)  R : → → t   F -source(w) anim(y)  R(j, p)(j, t) (ΣI) TF j ((j, t), anim, t, =, refl(j, t)) : anim

TF j figure 5: A process of proof search for @ : animate in (13)

¬ TF j (14) escape(@ : animate) The negation has the following formation rule.15 A : type (¬F ) ¬A : type

This rule says ¬A is a type if A is a type, which means that both A and ¬A have the same well-formedness condition. Hence, it is correctly predicted that (14) has the same presupposition as the positive counterpart (13); namely, in both cases, it is required to find a proof term for the proposition animate(j). This means that John is animate projects out of the scope of negation. Our analysis can also deal with the case of presupposition filtering in (7). To simplify the matter, consider the sentence (15-a), whose SR is given in (15-b).

(15) a. If the number two is colored, the number two is green. → TF two b. (u : colored(two)) green(π1(@ : colored)) Here we assume that the predicate green imposes the property of being colored on its argument. The sentence (15-a) as a whole can be used without violating this selectional restriction of the predicate green. This filtering behavior is correctly predicated as shown in the type checking in Figure 6. Here, we assume that the relation R is set to the equality relation; then, the essential part of the derivation is to find a proof term for colored(two),

[15] Since ¬A is defined as A → ⊥, this rule can been seen as a special case of ΠF in Figure 1.

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1 u : colored(two) . . . . two colored(two): type green(π1(@ : TF )) : type colored (ΠF ), 1 → TF two (u : colored(two)) green(π1(@ : colored)) : type figure 6: The type checking for the SR (15-b) namely, the proposition that the term two satisfies the selectional restriction of the predicate green. In this case, the information in the antecedent, colored(two), is passed to the consequent using the formation rule (ΠF ) in Figure 1; according to this rule, (x : A) → B is a type if (i) A is a type and (ii) B is a type under the assumption that there is some proof term x for A. Thus, the SR as a whole can be proved to be well-formed without using any information from the global context. It has been observed that a negative sentence like (16) has a reading where the apparent violation of selectional restrictions does not lead to infelicity.16

(16) Rocks can’t have diabetes. (McCawley 1968, p.62)

This phenomena can be naturally accounted for by the mechanism of presupposition accommodation. Let us assume that (16) has the SR in (17), where Frock is a predicate such that it is meaningful to ask if rocks have that property.

(17) ¬have(rock, @ : TF diabetes) Frock

Again, we can take R to be the equality relation. Then, in the same way as the example in (14), for this SR to be well-formed, it is required to find to a proof term for the proposition Frock(diabetes). In this case, however, rocks are not the kind of things that can have diabetes, that is, we fail to find a suitable proof of Frock(diabetes) in the global context. In that case, the process of local accommodation is available, by means of which the presupposed content does not project and hence is interpreted inside the scope of negation, resulting in the ¬ ∧ SR (Frock(diabetes) have(rock, diabetes)). Although presenting a compre- hensive account of presupposition accommodation within the framework of DTS is beyond the scope of this paper17, the view to take the selectional restriction as presupposition from a proof-theoretic perspective has appealing features in accounting for a variety of presuppositional inference patterns arising from the constructions we saw in this section.

[16] We thank Robin Cooper for pointing out this issue at the CoPo2017 workshop. [17] But see Mineshima (2008) for an account of presupposition accommodation in a proof-theoretic setting.

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[4] coercion [4.1] Coercion by type mismatch Let us move on to the case of coercion triggered by type mismatch. Consider the sentence (1-a). Using the lexical entry in (11), the SR of (1-a) is derived as TF o escape(π1(@ : animate)), where o is the term for the omelet. In this case, while the predicate escape requires its argument to be animate, the source term the omelet is not an animate entity. Accordingly, unlike the case of literal interpretation, taking R to be the equality relation leads to the violation of selectional restriction. We need to find a suitable relation R in TF in the context. Suppose that there is a salient entity john who eats the omelet in the context; thus, the global context has the following information.

(18) o : entity, j : entity, animate : entity → type, edible : entity → type, [ ] [ ] y : entity x : entity eat : → → type, edible(y) animate(x)

p1 : animate(j), p2 : edible(o), p3 : eat(o, p2)(j, p1)

We can use eat instead of the equality relation for R and construct a 5-tuple TF o ((j, p1), edible, p2, eat, p3) as a term satisfying animate. By replacing @ with this 5-tuple and by computation, we can get the SR escape(j, p1), which captures the intended reading.

[4.2] Coercion by contextual inference Next, let us look at an example of coercion by contextual inference. Consider the TF l example in (2-a). The SR of (2-a) is given as escape(π1(@ : animate)), where l is the term for the lion. In this case, the predicate escape takes an animate entity as its argument. Since the source term the lion is an animate entity, the relation R can be set to the identity relation, ending up with the literal interpretation. Alternatively, R can be set to the relation x plays y at The Lion King, which leads to the coercion interpretation. Thus we can derive the coercion interpretation even when type mismatch does not occur. The literal interpretation conflicts with the common background knowledge that there is no real lion in the theater. So the coercion interpretation is usually preferred. Then, suppose that we have the following information in the global context.

(19) l : entity, actor : entity, animate : entity → type, object : entity → type,

OSLa volume 10(2), 2018 coercion as proof search [155] [ ] [ ] y : entity x : entity play : → → type, animate(y) object(x)

p1 : animate(actor), p2 : object(l), p3 : play(actor, p1)(l, p2) TF l Given this global context, we need to find a 5-tuple satisfying animate. Us- ing play instead of the equality relation for R, we can construct a 5-tuple TF l ((actor, p1), object, p2, play, p3) as a term satisfying animate. In a similar way to the case of coercion triggered by type mismatch, we can obtain the SR escape(actor, p1) for the sentence (2-a). The use of transfer frame enables us to handle coercion triggered by type mismatch and coercion triggered by contextual inference in a uniform way.

[5] copredication and complement coercion In this section, we show how the current proposal accounts for copredication and complement coercion, two phenomena that have been widely discussed in the literature on coercion and selectional restrictions.

[5.1] Copredication of logical polysemy Nouns having multiple meanings can be classified into accidental and logical polysemy (Asher 2011). For example, the noun bank in (20-a) is accidentally polysemous, while the noun book in (20-b) is logically polysemous.

(20) a. # The bank is closed and muddy. b. The book is interesting and heavy.

The structure where two or more equally connected predicates have different selectional restrictions for the same argument is called copredication. The sentence (20-b) shows that the logically polysemous noun book allows copredication, despite the fact that interesting and heavy require different objects (i.e., an informational object and a physical object) as their object argument. Let us examine sentence (20-b). Like the lexical entry of escape in (11), we define the lexical entries of interesting and heavy as follows. TF x (21) a. [[interesting]] = λx.interesting(π1(@ : Info)) TF x b. [[heavy]] = λx.heavy(π1(@ : PhyObj))

Here, Info and PhyObj are predicates of type entity → type that represent being an informational object and being a physical object, respectively. The SR of (20-b) is derived as (22), where b is the term for the book and × stands for conjunction (i.e., product type). TF b × TF b (22) interesting(π1(@1 : Info)) heavy(π1(@2 : PhyObj))

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For the logical polysemous noun book, we assume that the global context has (23-a) and (23-b), which are read as Books have informational aspects and Books have physical object aspects, respectively. Thus, ib and pb are functions that map a book to its informational aspect and its physical aspect, respectively. [ ] y : entity (23) a. ib :(x : entity) → book(x) → [ Info(y) ] y : entity b. p :(x : entity) → book(x) → b PhyObj(y)

Furthermore, the following predicates, x is an informational aspect of y (IA) and x is a physical object aspect of y (PA) can be defined as follows: [ ] [ ] x : entity y : entity (24) a. IA : → → type book(x) Info(y) ≡ where IA λx.λy.ib(π1x)(π2x) =(z:entity)×Info(z) y [ ] [ ] x : entity y : entity b. PA : → → type book(x) PhyObj(y) ≡ where PA λx.λy.pb(π1x)(π2x) =(z:entity)×PhyObj(z) y

In addition to these, let us suppose that the global context has the following information:

(25) b : entity, p1 : book(b)

Applying the functions ib and pb to b and p1 yields the informational aspect and the physical aspect of the book b, namely, ib(b)(p1) and pb(b)(p1), respectively. The type check of (22) goes as in the ones given in the previous sections. We use the relation IA to specify R for @1 and the relation PA for @2. Then, we can construct 5-tuples (ib(b)(p1), book, p1, IA, refl(ib(b)(p1))) and TF b TF b (pb(b)(p1), book, p1, PA, refl(pb(b)(p1))) for @1 : Info and @2 : PhyObj, respectively. The final SR for (20-b) is:

(26) interesting(ib(b)(p1)) × heavy(pb(b)(p1)).

This asserts that the informational aspect of the book is interesting and its physical aspect is heavy, which captures the intended reading of (20-b). There has been an ongoing debate on a construction in which a logical polysemous nouns like book appears with a numeral quantifier (Asher 2011; Cooper 2011; Gotham 2017; Chatzikyriakidis & Luo 2015, 2017a). Consider:

(27) Three heavy books are interesting.

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To analyze this kind of sentences, it is necessary to consider what three books means, more specifically, whether it counts informational aspects of the books, physical aspects of the books, or both. This is called the counting problem. Gotham (2017) argues that a sentence like (27) is true only if there are three books that are individuated both physically and informationally; thus, (27) would be false (i) when there are three copies of the same informational book that are both heavy and interesting or (ii) when there is one physical volume that binds together three informational books that are both heavy and interesting. Liebesman & Magidor (2017) doubt that (27) has these truth-conditions, arguing that (27) can be true in a situation like (i) or (ii); furthermore, they argue that it is not easy to test the existence of the reading that requires three books individuated both physically and informationally. We agree with Liebesman & Magidor (2017) that the linguistic intuition about examples like (27) is not so clear and more discussion would be needed about the data. So we will leave as future work solving the counting problem in our framework.

[5.2] Complement coercion A verb like enjoy, begin and finish takes an NP-complement denoting an entity, although it require its argument to denote an event. For example, (28) can be interpreted as “Bob is enjoying smoking the cigarette”, though the NP-complement the cigarette literally denotes an entity.

(28) Bob is enjoying the cigarette.

The analysis we have developed so far can be naturally extended to handle this type of examples: we define a transfer frame TFev for events as in (29):  [ ]  e : event  t-pair :   F -target(e)     F -source : entity → type    TF x ≡   (29) ev F -target  p : F[-source(x) ] [ ]   w : entity e : event   R : → → type   F -source(w) F -target(e)  R(x, p)t-pair

The difference from the transfer frame TF for entities is that the first element of t-pair is an event, rather than an entity. We assume that the predicate enjoy requires an event as its object argument, thus having the following type. [ ] [ ] e : event x : entity (30) enjoy : → → type φenjoy(e) animate(x)

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Here, φenjoy is a function from events to types; φenjoy(e) means the event e satisfies the selectional restriction associated with the verb enjoy.18 Then, the lexical entry of the transitive verb enjoy is given as follows.

TF y TF x (31) enjoy : λyλx.enjoy(π1(@1 : ev φenjoy ))(π1(@2 : animate))

For (28) we can derive the SR

TF cig TF bob (32) enjoy(π1(@1 : ev φenjoy ))(π1(@2 : animate))

where bob is the term for Bob and cig is the term for the cigarette.19 Now suppose that we have the following information in the global context.

(33) bob : entity, cig : entity[ , smk : event] ,[ ] x : entity x : entity smoking : event → → → type, animate(x) cigarette(x) p1 : animate(bob), p2 : cigarette(cig), p3 : smoking(smk)(bob, p1)(cig, p2), p4 : φenjoy(smk).

Here, smoking(smk)(bob, p1)(cig, p2) means that smk is an event of smoking whose subject is bob being animate and whose object is cig being a cigarette. TF cig The underspecified terms @1 having type ev φenjoy and @2 having type TF bob animate require constructing 5-tuples from the global context. Since bob has the property animate,@2 finds a 5-tuple ((bob, p1), animate, p1, =, refl(bob)) using the equality relation, in the same way as the type checking shown in Section [3.4]. On the other hand, @1 requires constructing a term having an event type that is related to the cigarette in the context. We can construct a 5-tuple shown in (34) for @1.

(34) ((smk, p4), cigarette, p2, λuλv.smoking(π1v)(bob, p1)u, p3)

Replacing @1 and @2 in (32) with these 5-tuples, we can finally get the SR:

(35) enjoy(bob, p1)(smk, p4).

This means that Bob enjoy the event of smoking the cigarette, which gives the desired interpretation of (28).

[18] Here we use the notation φF to represent the selectional restriction associated with the predicate F . Generally speaking, for an object x to satisfy the condition φF means that it is meaningful to ask whether x is an F or not. To give a characterization of the condition φ for each predicate is a long-standing issue. See Magidor (2013, pp.146–148) for some discussion. [19] For simplicity we treat a definite description as a constant, rather than as an underspecified term like one for a pronoun in (4).

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[6] concluding remark: complicity We have proposed the architecture of interpretation based on proof search for the analysis of coercion and related phenomena. According to the proposed view, the overall process of interpretation consists of two phases: (i) semantic composition, a compositional derivation of an underspecified SR φ from a given sentence S, and (ii) type checking with proof search, a process of checking the well-formedness of φ that may involve searching a suitable term for an underspecified term @ in φ. From the viewpoint of utterance interpretation, the hearer has to do inference (proof search) to understand an utterance, not just to verify the truth of the content of the utterance. On this account, the process of coercion and other meaning shift is not necessarily triggered by type mismatch during semantic composition but also by contextual inference to search for a relevant interpretation of the utterance. One notable feature of this architecture of interpretation is that a type checking inference is needed even if hearers do not accept the speaker’s utterance, that is, even if they do not think it is true. We suggest that the process of invoking an inference on the side of the hearers to understand an utterance captures an aspect of utterance interpretation called complicity (Camp 2017). A most typical instance of the effect of complicity is found in a metaphorical interpretation. For instance, consider the sentence in (36).

(36) Chairman, you are a Bolshevik! (Cohen 1978, p.8)

If the hearer feels that (36) is in a bad mood, then he is complicit in interpreting bad words even if he does not feel bad about the chairman in question. The effect of complicity also arises in other phenomena in which a meaning shift occurs. Consider the case of coercion:

(37) a. The {pig/omelet} asked for another helping of food. b. {The man who looks like a pig/The man who ate the omelet} asked for another helping of food.

Even in the absence of bad words, the effect of complicity is produced; when interpreting (37-a) as (37-b), the hearer is forced to accommodate herself to the speaker’s way of thinking to grasp what is said by the utterance. The strategy to invoke complicity in conversation is important in accounting for why the speaker chooses to use a construction like (37-a), rather than (37-b). In this type of coercion, one has to find a suitable relation R that links a source term to a target term on the fly, in order to find a relevant interpretation of the utterance given a background context. That is, in our implementation, one has to construct a relation R in a 5-tuple satisfying the transfer frame from a given global context. This may be called a creative meaning shift. The speaker’s strategy

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to invoke complicity, namely, the strategy to purposely make the hearer compute the meaning shift can be seen in the case of such creative meaning shift. By contrast, in the case of the literal interpretation that we have seen in Sec- tion [3.4], the option to take R as the equality relation is always available. Simil- arly, in the case of examples of copredication like (20-b), the relation R has not to be constructed on the fly but can be already defined in the global context. These may be classified as conventional meaning shift, in a similar way to dead (or idiomatic) metaphor in contrast to creative metaphor. Though a full defense of the present view will depend on how it can analyze other inferential phenomena such as metaphor, which is left for future work, we suggest that coercion can best be characterized in inferential terms. The proof- theoretic conception we developed in this paper has appealing features in accounting for a variety of coercion and other meaning-shifting phenomena in a formal theory, and it can contribute to a better understanding of aspects of interpretation such as complicity and creative meaning shift.

acknowledgments An earlier version of the paper was presented at the CoPo2017 workshop. We are grateful to Nicholas Asher, Stergios Chatzikyriakidis, Robin Cooper, Matthew Gotham and the audience at the CoPo2017 workshop for their useful feedback and helpful suggestions. Special thanks to Alexandra Spalek and Matthew Gotham for organizing the workshop.

references Asher, Nicholas. 2011. Lexical meaning in context: A web of words. Cambridge Uni- versity Press. Asher, Nicholas. 2014. Selectional restrictions, types and categories. Journal of Applied Logic 2(1). 75–87. Asher, Nicholas & Zhaohui Luo. 2012. Formalisation of coercions in lexical semantics. Sinn und Bedeutung 17. 63–80. Bekki, Daisuke. 2014. Representing anaphora with dependent types. In Nich- olas Asher & Sergei Soloviev (eds.), Logical Aspects of Computational Linguistics (LACL2014), 14–29. Springer. Bekki, Daisuke & Koji Mineshima. 2017. Context-passing and underspecification in dependent type semantics. In Stergios Chatzikyriakidis & Zhaohui Luo (eds.), Modern perspectives in type-theoretical semantics, 11–41. Springer. Camp, Elisabeth. 2017. Why metaphors make good insults: perspectives, presupposition, and pragmatics. Philosophical Studies 174(1). 47–64.

OSLa volume 10(2), 2018 coercion as proof search [161]

Chatzikyriakidis, Stergios & Zhaohui Luo. 2015. Individuation criteria, dot-types and copredication: A view from modern type theories. In Proceedings of the 14th international conference on mathematics of language, 39–50.

Chatzikyriakidis, Stergios & Zhaohui Luo. 2017a. Identity criteria of CNs: Quanti- fication and copredication. Talk presented at the CoPo2017 Workshop.

Chatzikyriakidis, Stergios & Zhaohui Luo. 2017b. On the interpretation of common nouns: Types versus predicates. In Stergios Chatzikyriakidis & Zhaohui Luo (eds.), Modern perspectives in type-theoretical semantics, 43–70. Springer.

Cohen, Ted. 1978. Metaphor and the cultivation of intimacy. Critical Inquiry 5(1). 3–12.

Cooper, Robin. 2011. Copredication, quantification and frames. In Logical Aspects of Computational Linguistics (LACL2011), 64–79. Springer.

Cooper, Robin. 2012. Type theory and semantics in flux. Handbook of the Philosophy of Science 14. 271–323.

Gotham, Matthew. 2017. Composing criteria of individuation in copredication. Journal of Semantics 34(2). 333–371.

Hook, James G & Douglas J Howe. 1986. Impredicative strong existential equivalent to Type: Type. Tech. rep. Cornell University.

Kinoshita, Eriko, Koji Mineshima & Bekki Daisuke. 2016. An analysis of selectional restrictions with dependent type semantics. In Proceedings of the 13th international workshop on Logic and Engineering of Natural Language Semantics (LENLS13), 100–113.

Liebesman, David & Ofra Magidor. 2017. Copredication and property inheritance. Philosophical Issues 27(1). 131–166.

Luo, Zhaohui. 2012. Formal semantics in modern type theories with coercive subtyping. Linguistics and Philosophy 35(6). 491–513.

Magidor, Ofra. 2013. Category mistakes. Oxford University Press.

Martin-Löf, Per. 1984. Intuitionistic type theory. Bibliopolis.

McCawley, James D. 1968. The role of semantics in a grammar. In Emmon Bach & R. Harms (eds.), Universals in linguistic theory, 124–169. Holt, Rinehart, and Winston.

OSLa volume 10(2), 2018 [162] kinoshita, mineshima & bekki

Mery, Bruno & Christian Retoré. 2017. Classifiers, sorts, and base types in the Montagovian generative lexicon and related type theoretical frameworks for lexical compositional semantics. In Stergios Chatzikyriakidis & Zhaohui Luo (eds.), Modern perspectives in type-theoretical semantics, 163–188. Springer.

Mineshima, Koji. 2008. A presuppositional analysis of definite descriptions in proof theory. In K. Satoh, A. Inokuchi, K. Nagao & T. Kawamura (eds.), New frontiers in artificial intelligence: JSAI 2007 conference and workshops, revised selected papers, 214–227. Springer-Verlag.

Nordström, Bengt, Kent Petersson & Jan Smith. 1990. Programming in Martin-Löf’s type theory. Oxford University Press.

Nunberg, Geoffrey. 1995. Transfers of meaning. Journal of Semantics 12(2). 109–132.

Pustejovsky, James. 1993. Type coercion and lexical selection. In Semantics and the lexicon, 73–94. Springer.

Ranta, Aarne. 1994. Type theoretical grammar. Oxford University Press.

Retoré, Christian. 2014. The Montagovian generative lexicon λtyn : a type theoretical framework for natural language semantics. 19th International Conference on Types for Proofs and Programs (TYPES2013) 202–229.

author contact information Eriko Kinoshita Ochanomizu University [email protected]

Koji Mineshima Ochanomizu University [email protected]

Daisuke Bekki Ochanomizu University [email protected]

OSLa volume 10(2), 2018