DOCSLIB.ORG

Continuation’ Semantics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Continuation’ Semantics A Mechanism to Restrict the Scope of Clause-Bounded Quantifiers in ‘Continuation’ Semantics Anca Dinu Faculty of Foreign Languages and Literatures, University of Bucharest [email protected] To filter out these impossible interpretations, we Abstract first need to understand the scope behavior of each scope-taking lexical entry: its maximal scope limits and the scope precedence preferences w.r.t. other lexical entries. Second, This paper presents a formal mechanism to we should force the scope closing of the properly constrain the scope of negation and of quantifiers by applying a standard type shifter certain quantificational determiners to their Lower (which is equivalent to identity function minimal clause in continuation semantics application), once their scope limits were framework introduced in Barker and Shan (2008) and which was subsequently extended reached. But the actual mechanism that ensures from sentential level to discourse level in Dinu the scope closing was left underspecified in (2011). In these works, type shifting is previous work on continuation semantics. employed to account for side effects such as In what follows, we propose such a pronominal anaphora binding or quantifier mechanism, designed to ensure that no lexical scope. However, allowing arbitrary type entry having the scope bounded to its minimal shifting will result in overgenerating clause (such as not, no, every, each, any, etc) will interpretations impossible in natural language. ever take scope outside, thus getting right To filter out some of these impossible discourse truth conditions. interpretations, once the negation or the The programming language concept of quantifiers reach their maximal scope limits (that is their minimal clause), one should force continuations was successfully used by Barker their scope closing by applying a standard type and Shan in a series of articles (Barker 2002, shifter Lower. But the actual mechanism that Barker 2004, Shan 2005, Shan and Barker 2006, forces the scope closing was left Barker and Shan 2008) to analyze intra-sentential underspecified in previous work on linguistic phenomena (focus fronting, donkey continuation semantics. We propose here such anaphora, presupposition, crossover, superiority, a mechanism, designed to ensure that no etc). Moreover, (de Groote, 2006) proposed an lexical entries having the scope bounded to elegant discourse semantics based on their minimal clause (such as not, no, every, continuations. Continuations are a standard tool each, any, etc) will ever take scope outside. in computer science, used to control side effects of computation. They are a notoriously hard to 1 Introduction understand notion. Actually, understanding what The starting point of this paper is the a continuation is per se is not so hard. What is continuation semantics introduced in Barker and more difficult is to understand how a grammar Shan (2008) and extended from sentential level based on continuations (a „continuized‟ to discourse level in Dinu (2011). In this grammar) works. The basic idea of continuizing framework, type shifting is used to account for a grammar is to provide subexpressions with side effects such as pronominal anaphora binding direct access to their own continuations (future or quantifier scope. However, allowing arbitrary context), so subexpressions are modified to take type shifting will result in overgenerating a continuation as an argument. A continuized interpretations impossible in natural language. grammar is said to be written in continuation 495 Proceedings of Recent Advances in Natural Language Processing, pages 495–502, Hissar, Bulgaria, 12-14 September 2011. passing style. Continuation passing style is in continuization in which only the category S has fact a restricted (typed) form of λ-calculus. been continuized. Historically, the first continuation operators This is by no means a coincidence, MG only were undelimited (e.g., call/cc or J). An continuizes the noun phrase meanings and undelimited continuation of an expression dynamic semantics only continuizes the sentence represents “the entire (default) future for the meanings, rather than continuizing uniformly computation” of that expression. Felleisen (1988) throughout the grammar as it is done in introduced delimited continuations (sometimes continuation semantics. called „composable‟ continuations) such as control („C‟) and prompt („%‟). Delimited 2 Preliminaries continuations represent the future of the We use Barker and Shan‟s (2008) tower notation computation of the expression up to a certain for a given expression, which consists of three boundary. Interestingly, the natural-language levels: the top level specifies the syntactic phenomena discussed here make use only of category of the expression couched in categorial delimited continuations. grammar, the middle level is the expression itself For instance, if we take the local context to be and the bottom level is the semantic value: restricted to the sentence, when computing the meaning of the sentence John saw Mary., the 푠푦푛푡푎푐푡푖푐 푐푎푡푒푔표푟푦 default future of the value denoted by the subject 푒푥푝푟푒푠푠푖표푛 is that it is destined to have the property of 푠푒푚푎푛푡푖푐 푣푎푙푢푒 seeing Mary predicated of it. In symbols, the 퐶|퐵 The syntactic categories are written , continuation of the subject denotation j is the 퐴 function 휆푥. 푠푎푤 풎 푥. Similarly, the default where A, B and C can be any categories. We read future of the object denotation m is the property this counter clockwise as “the expression of being seen by John, the function 휆푦. 풔풂풘 푦 푗; functions as a category A in local context, takes the continuation of the transitive verb denotation scope at an expression of category B to form an saw is the function 휆푅. 푅 푚 푗; and the expression of category C.” continuation of the verb phrase saw Mary is the The semantic value in linear notation function 휆푃. 푃 푗. This simple example illustrates 휆푘. 푓[푘(푥)] is equivalently written vertically as 푓[ ] two important aspects of continuations: omitting the future context (continuation) k. (1) every meaningful subexpression has a 푥 Here, x can be any expression, and f[ ] can be continuation; any expression with a gap [ ]. Free variables in x (2) the continuation of an expression is can be bound by binders in f [ ]. This vertical always relative to some larger expression (layered) notational convention is meant to make containing it. the combination process of two expressions Thus, when John occurs in the sentence John easier (more visual) then in linear notation. Here left yesterday., its continuation is the property there are the two possible modes of combination 휆푥. 풚풆풔풕풆풓풅풂풚 풍풆풇풕 푥; when it occurs in Mary (Barker and Shan 2008): thought John left., its continuation is the property 휆푥. 풕풉풐풖품풉풕 (풍풆풇풕 푥) 푚 and when it occurs in 퐶|퐷 퐷|퐸 퐶|퐸 the sentence Mary or John left., its continuation 퐴/퐵 퐵 퐴 푙 푒푓푡 − 푒푥푝 푟푖푔푕푡 − 푒푥푝 is 휆푥. (풍풆풇풕 풎) ∨ (풍풆풇풕 푥) and so on. 푙푒푓푡 − 푒푥푝 푟푖푔푕푡 − 푒푥푝 = It is worth mentioning that some results of 푔[ ] 푕[ ] 푔[푕 ] traditional semantic theories are particular cases 푓 푥 푓(푥) of results in continuation semantics: 퐶|퐷 퐷|퐸 The generalized quantifier type from 퐶|퐸 퐵 퐵\퐴 퐴 Montague grammar (Montague, 1970) 푙 푒푓푡 − 푒푥푝 푟푖푔푕푡 − 푒푥푝 푙푒푓푡 − 푒푥푝 푟푖푔푕푡 − 푒푥푝 = <<<e,t>,t>,t> is exactly the type of 푔[ ] 푕[ ] 푔[푕 ] quantificational determiners in continuation- 푥 푓 푓(푥) based semantics; The <<t,t>,t> type of sentences in Below the horizontal lines, combination dynamic semantics is exactly the type of proceeds simply as in combinatory categorial sentences in continuation-based semantics. In grammar: in the syntax, B combines with A/B or fact, dynamic interpretation constitutes a partial B\A to form A; in the semantics, x combines with f to form f(x). Above the lines is where the 496 combination machinery for continuations kicks To derive the syntactic category and a in. The syntax combines the two pairs of semantic value with no horizontal line, Barker categories by a kind of cancellation: the D on the and Shan (2008) introduce the type-shifter left cancels with the D on the right. The Lower. In general, for any category A, any value semantics combines the two expressions with x, and any semantic expression f[ ] with a gap, gaps by a kind of composition: we plug h[ ] to the following type-shifter is available: the right into the gap of g[ ] to the left, to form g[h[ ]]. The expression with a gap on the left, g[ 퐴|푆 퐴 ], always surrounds the expression with a gap on 푆 퐿표푤푒푟 푒 푥푝푟푒푠푠푖표푛 푒 푥푝푟푒푠푠푖표푛 the right, h[ ], no matter which side supplies the 푓[ ] 푓[푥] function and which side supplies the argument 푥 below the lines. This fact expresses the generalization that the default order of semantic Syntactically, Lower cancels an S above the evaluation is left-to-right. line to the right with an S below the line. When there is no quantification or anaphora Semantically, Lower collapses a two-level involved, a simple sentence like John came. is meaning into a single level by plugging the value derived as follows: x below the line into the gap [ ] in the expression f[ ] above the line. Lower is equivalent to 퐷푃 퐷푃\푆 푆 identity function application. 퐽표푕푛 푐푎푚푒 = 퐽표푕푛 푐푎푚푒 The third and the last type shifter we need is 푗 푐푎푚푒 푐푎푚푒 푗 one that accounts for binding. We adopt the idea In the syntactic layer, as usual in categorical (in line with Barker and Shan (2008)) that the grammar, the category under slash (here DP) mechanism of binding is the same as the cancels with the category of the argument mechanism of scope taking. Binding is a term expression; the semantics is function application. used both in logics and in linguistics with analog Quantificational expressions have extra layers (but not identical) meaning. In logics, a variable on top of their syntactic category and on top of is said to be bound by an operator (as the their semantic value, making essential use of the universal or existential operators) if the variable powerful mechanism of continuations in ways is inside the scope of the operator.
Load more

Recommended publications
  • Continuation-Passing Style
    Continuation-Passing Style CS 6520, Spring 2002 1 Continuations and Accumulators In our exploration of machines for ISWIM, we saw how to explicitly track the current continuation for a computation (Chapter 8 of the notes). Roughly, the continuation reflects the control stack in a real machine, including virtual machines such as the JVM. However, accurately reflecting the \memory" use of textual ISWIM requires an implementation different that from that of languages like Java. The ISWIM machine must extend the continuation when evaluating an argument sub-expression, instead of when calling a function. In particular, function calls in tail position require no extension of the continuation. One result is that we can write \loops" using λ and application, instead of a special for form. In considering the implications of tail calls, we saw that some non-loop expressions can be converted to loops. For example, the Scheme program (define (sum n) (if (zero? n) 0 (+ n (sum (sub1 n))))) (sum 1000) requires a control stack of depth 1000 to handle the build-up of additions surrounding the recursive call to sum, but (define (sum2 n r) (if (zero? n) r (sum2 (sub1 n) (+ r n)))) (sum2 1000 0) computes the same result with a control stack of depth 1, because the result of a recursive call to sum2 produces the final result for the enclosing call to sum2 . Is this magic, or is sum somehow special? The sum function is slightly special: sum2 can keep an accumulated total, instead of waiting for all numbers before starting to add them, because addition is commutative.
    [Show full text]
  • Denotational Semantics
    Denotational Semantics CS 6520, Spring 2006 1 Denotations So far in class, we have studied operational semantics in depth. In operational semantics, we define a language by describing the way that it behaves. In a sense, no attempt is made to attach a “meaning” to terms, outside the way that they are evaluated. For example, the symbol ’elephant doesn’t mean anything in particular within the language; it’s up to a programmer to mentally associate meaning to the symbol while defining a program useful for zookeeppers. Similarly, the definition of a sort function has no inherent meaning in the operational view outside of a particular program. Nevertheless, the programmer knows that sort manipulates lists in a useful way: it makes animals in a list easier for a zookeeper to find. In denotational semantics, we define a language by assigning a mathematical meaning to functions; i.e., we say that each expression denotes a particular mathematical object. We might say, for example, that a sort implementation denotes the mathematical sort function, which has certain properties independent of the programming language used to implement it. In other words, operational semantics defines evaluation by sourceExpression1 −→ sourceExpression2 whereas denotational semantics defines evaluation by means means sourceExpression1 → mathematicalEntity1 = mathematicalEntity2 ← sourceExpression2 One advantage of the denotational approach is that we can exploit existing theories by mapping source expressions to mathematical objects in the theory. The denotation of expressions in a language is typically defined using a structurally-recursive definition over expressions. By convention, if e is a source expression, then [[e]] means “the denotation of e”, or “the mathematical object represented by e”.
    [Show full text]
  • Degrees As Kinds Vs. Degrees As Numbers: Evidence from Equatives1 Linmin ZHANG — NYU Shanghai
    Degrees as kinds vs. degrees as numbers: Evidence from equatives1 Linmin ZHANG — NYU Shanghai Abstract. Within formal semantics, there are two views with regard to the ontological status of degrees: the ‘degree-as-number’ view (e.g., Seuren, 1973; Hellan, 1981; von Stechow, 1984) and the ‘degree-as-kind’ view (e.g., Anderson and Morzycki, 2015). Based on (i) empirical distinctions between comparatives and equatives and (ii) Stevens’s (1946) theory on the four levels of measurements, I argue that both views are motivated and needed in accounting for measurement- and comparison-related meanings in natural language. Specifically, I argue that since the semantics of comparatives potentially involves measurable differences, comparatives need to be analyzed based on scales with units, on which degrees are like (real) numbers. In contrast, since equatives are typically used to convey the non-existence of differences, equa- tives can be based on scales without units, on which degrees can be considered kinds. Keywords: (Gradable) adjectives, Comparatives, Equatives, Similatives, Levels of measure- ments, Measurements, Comparisons, Kinds, Degrees, Dimensions, Scales, Units, Differences. 1. Introduction The notion of degrees plays a fundamental conceptual role in understanding measurements and comparisons. Within the literature of formal semantics, there are two major competing views with regard to the ontological status of degrees. For simplicity, I refer to these two ontologies as the ‘degree-as-number’ view and the ‘degree-as-kind’ view in this paper. Under the more canonical ‘degree-as-number’ view, degrees are considered primitive objects (of type d). Degrees are points on abstract totally ordered scales (see Seuren, 1973; Hellan, 1981; von Stechow, 1984; Heim, 1985; Kennedy, 1999).
    [Show full text]
  • A Descriptive Study of California Continuation High Schools
    Issue Brief April 2008 Alternative Education Options: A Descriptive Study of California Continuation High Schools Jorge Ruiz de Velasco, Greg Austin, Don Dixon, Joseph Johnson, Milbrey McLaughlin, & Lynne Perez Continuation high schools and the students they serve are largely invisible to most Californians. Yet, state school authorities estimate This issue brief summarizes that over 115,000 California high school students will pass through one initial findings from a year- of the state’s 519 continuation high schools each year, either on their long descriptive study of way to a diploma, or to dropping out of school altogether (Austin & continuation high schools in 1 California. It is the first in a Dixon, 2008). Since 1965, state law has mandated that most school series of reports from the on- districts enrolling over 100 12th grade students make available a going California Alternative continuation program or school that provides an alternative route to Education Research Project the high school diploma for youth vulnerable to academic or conducted jointly by the John behavioral failure. The law provides for the creation of continuation W. Gardner Center at Stanford University, the schools ‚designed to meet the educational needs of each pupil, National Center for Urban including, but not limited to, independent study, regional occupation School Transformation at San programs, work study, career counseling, and job placement services.‛ Diego State University, and It contemplates more intensive services and accelerated credit accrual WestEd. strategies so that students whose achievement in comprehensive schools has lagged might have a renewed opportunity to ‚complete the This project was made required academic courses of instruction to graduate from high school.‛ 2 possible by a generous grant from the James Irvine Taken together, the size, scope and legislative design of the Foundation.
    [Show full text]
  • A Theory of Names and True Intensionality*
    A Theory of Names and True Intensionality? Reinhard Muskens Tilburg Center for Logic and Philosophy of Science [email protected] http://let.uvt.nl/general/people/rmuskens/ Abstract. Standard approaches to proper names, based on Kripke's views, hold that the semantic values of expressions are (set-theoretic) functions from possible worlds to extensions and that names are rigid designators, i.e. that their values are constant functions from worlds to entities. The difficulties with these approaches are well-known and in this paper we develop an alternative. Based on earlier work on a higher order logic that is truly intensional in the sense that it does not validate the axiom scheme of Extensionality, we develop a simple theory of names in which Kripke's intuitions concerning rigidity are accounted for, but the more unpalatable consequences of standard implementations of his theory are avoided. The logic uses Frege's distinction between sense and reference and while it accepts the rigidity of names it rejects the view that names have direct reference. Names have constant denotations across possible worlds, but the semantic value of a name is not determined by its denotation. Keywords: names, axiom of extensionality, true intensionality, rigid designation 1 Introduction Standard approaches to proper names, based on Kripke (1971, 1972), make the following three assumptions. (a) The semantic values of expressions are (possibly partial) functions from pos- sible worlds to extensions. (b) These functions are identified with their graphs, as in set theory. (c) Names are rigid designators, i.e. their extensions are world-independent. In particular, the semantic values of names are taken to be constant functions from worlds to entities, possibly undefined for some worlds.
    [Show full text]
  • EISS 12 Empirical Issues in Syntax and Semantics 12
    EISS 12 Empirical Issues in Syntax and Semantics 12 Edited by Christopher Pinon 2019 CSSP Paris http://www.cssp.cnrs.fr/eiss12/ ISSN 1769-7158 Contents Preface iv Anne Abeillé & Shrita Hassamal 1–30 Sluicing in Mauritian: A Fragment-Based Analysis Aixiu An & Anne Abeillé 31–60 Number Agreement in French Binomials Micky Daniels & Yael Greenberg 61–89 Extreme Adjectives in Comparative Structures and even Emilie Destruel & Joseph P. De Veaugh-Geiss 91–120 (Non-)Exhaustivity in French c’est-Clefts Regine Eckardt & Andrea Beltrama 121–155 Evidentials and Questions Yanwei Jin & Jean-Pierre Koenig 157–186 Expletive Negation in English, French, and Mandarin: A Semantic and Language Production Model Fabienne Martin & Zsófia Gyarmathy 187–216 A Finer-grained Typology of Perfective Operators Vítor Míguez 217–246 On (Un)certainty: The Semantic Evolution of Galician seguramente Emanuel Quadros 247–276 The Semantics of Possessive Noun Phrases and Temporal Modifiers EISS 12 iii Preface This is the twelfth volume of the series Empirical Issues in Syntax and Semantics (EISS), which, like the preceding eleven volumes of the series, is closely related to the conference series Colloque de Syntaxe et Sémantique à Paris (CSSP). The nine papers included in the present volume are based on presentations given at CSSP 2017, which took place on 23–25 November 2017 at École Normale Supérieure (http: //www.cssp.cnrs.fr/cssp2017/index_en.html). CSSP 2017 had a small thematic session entitled Discourse particles, but since the number of papers from the thematic session submitted to the volume was low, they are not grouped separately. I would like to take this opportunity to thank the reviewers, whose comments aided the authors in revising the first drafts of their pa- pers, sometimes substantially.
    [Show full text]
  • RELATIONAL PARAMETRICITY and CONTROL 1. Introduction the Λ
    Logical Methods in Computer Science Vol. 2 (3:3) 2006, pp. 1–22 Submitted Dec. 16, 2005 www.lmcs-online.org Published Jul. 27, 2006 RELATIONAL PARAMETRICITY AND CONTROL MASAHITO HASEGAWA Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502 Japan, and PRESTO, Japan Science and Technology Agency e-mail address: [email protected] Abstract. We study the equational theory of Parigot’s second-order λµ-calculus in con- nection with a call-by-name continuation-passing style (CPS) translation into a fragment of the second-order λ-calculus. It is observed that the relational parametricity on the tar- get calculus induces a natural notion of equivalence on the λµ-terms. On the other hand, the unconstrained relational parametricity on the λµ-calculus turns out to be inconsis- tent. Following these facts, we propose to formulate the relational parametricity on the λµ-calculus in a constrained way, which might be called “focal parametricity”. Dedicated to Prof. Gordon Plotkin on the occasion of his sixtieth birthday 1. Introduction The λµ-calculus, introduced by Parigot [26], has been one of the representative term calculi for classical natural deduction, and widely studied from various aspects. Although it still is an active research subject, it can be said that we have some reasonable un- derstanding of the first-order propositional λµ-calculus: we have good reduction theories, well-established CPS semantics and the corresponding operational semantics, and also some canonical equational theories enjoying semantic completeness [16, 24, 25, 36, 39]. The last point cannot be overlooked, as such complete axiomatizations provide deep understand- ing of equivalences between proofs and also of the semantic structure behind the syntactic presentation.
    [Show full text]
  • Continuation Calculus
    Eindhoven University of Technology MASTER Continuation calculus Geron, B. Award date: 2013 Link to publication Disclaimer This document contains a student thesis (bachelor's or master's), as authored by a student at Eindhoven University of Technology. Student theses are made available in the TU/e repository upon obtaining the required degree. The grade received is not published on the document as presented in the repository. The required complexity or quality of research of student theses may vary by program, and the required minimum study period may vary in duration. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain Continuation calculus Master’s thesis Bram Geron Supervised by Herman Geuvers Assessment committee: Herman Geuvers, Hans Zantema, Alexander Serebrenik Final version Contents 1 Introduction 3 1.1 Foreword . 3 1.2 The virtues of continuation calculus . 4 1.2.1 Modeling programs . 4 1.2.2 Ease of implementation . 5 1.2.3 Simplicity . 5 1.3 Acknowledgements . 6 2 The calculus 7 2.1 Introduction . 7 2.2 Definition of continuation calculus . 9 2.3 Categorization of terms . 10 2.4 Reasoning with CC terms .
    [Show full text]
  • 6.5 a Continuation Machine
    6.5. A CONTINUATION MACHINE 185 6.5 A Continuation Machine The natural semantics for Mini-ML presented in Chapter 2 is called a big-step semantics, since its only judgment relates an expression to its final value—a “big step”. There are a variety of properties of a programming language which are difficult or impossible to express as properties of a big-step semantics. One of the central ones is that “well-typed programs do not go wrong”. Type preservation, as proved in Section 2.6, does not capture this property, since it presumes that we are already given a complete evaluation of an expression e to a final value v and then relates the types of e and v. This means that despite the type preservation theorem, it is possible that an attempt to find a value of an expression e leads to an intermediate expression such as fst z which is ill-typed and to which no evaluation rule applies. Furthermore, a big-step semantics does not easily permit an analysis of non-terminating computations. An alternative style of language description is a small-step semantics.Themain judgment in a small-step operational semantics relates the state of an abstract machine (which includes the expression to be evaluated) to an immediate successor state. These small steps are chained together until a value is reached. This level of description is usually more complicated than a natural semantics, since the current state must embody enough information to determine the next and all remaining computation steps up to the final answer.
    [Show full text]
  • Compositional Semantics for Composable Continuations from Abortive to Delimited Control
    Compositional Semantics for Composable Continuations From Abortive to Delimited Control Paul Downen Zena M. Ariola University of Oregon fpdownen,[email protected] Abstract must fulfill. Of note, Sabry’s [28] theory of callcc makes use of Parigot’s λµ-calculus, a system for computational reasoning about continuation variables that have special properties and can only be classical proofs, serves as a foundation for control operations em- instantiated by callcc. As we will see, this not only greatly aids in bodied by operators like Scheme’s callcc. We demonstrate that the reasoning about terms with free variables, but also helps in relating call-by-value theory of the λµ-calculus contains a latent theory of the equational and operational interpretations of callcc. delimited control, and that a known variant of λµ which unshack- In another line of work, Parigot’s [25] λµ-calculus gives a sys- les the syntax yields a calculus of composable continuations from tem for computing with classical proofs. As opposed to the pre- the existing constructs and rules for classical control. To relate to vious theories based on the λ-calculus with additional primitive the various formulations of control effects, and to continuation- constants, the λµ-calculus begins with continuation variables in- passing style, we use a form of compositional program transforma- tegrated into its core, so that control abstractions and applications tions which preserves the underlying structure of equational the- have the same status as ordinary function abstraction. In this sense, ories, contexts, and substitution. Finally, we generalize the call- the λµ-calculus presents a native language of control.
    [Show full text]
  • Donkey Anaphora Is In-Scope Binding∗
    Semantics & Pragmatics Volume 1, Article 1: 1–46, 2008 doi: 10.3765/sp.1.1 Donkey anaphora is in-scope binding∗ Chris Barker Chung-chieh Shan New York University Rutgers University Received 2008-01-06 = First Decision 2008-02-29 = Revised 2008-03-23 = Second Decision 2008-03-25 = Revised 2008-03-27 = Accepted 2008-03-27 = Published 2008- 06-09 Abstract We propose that the antecedent of a donkey pronoun takes scope over and binds the donkey pronoun, just like any other quantificational antecedent would bind a pronoun. We flesh out this idea in a grammar that compositionally derives the truth conditions of donkey sentences containing conditionals and relative clauses, including those involving modals and proportional quantifiers. For example, an indefinite in the antecedent of a conditional can bind a donkey pronoun in the consequent by taking scope over the entire conditional. Our grammar manages continuations using three independently motivated type-shifters, Lift, Lower, and Bind. Empirical support comes from donkey weak crossover (*He beats it if a farmer owns a donkey): in our system, a quantificational binder need not c-command a pronoun that it binds, but must be evaluated before it, so that donkey weak crossover is just a special case of weak crossover. We compare our approach to situation-based E-type pronoun analyses, as well as to dynamic accounts such as Dynamic Predicate Logic. A new ‘tower’ notation makes derivations considerably easier to follow and manipulate than some previous grammars based on continuations. Keywords: donkey anaphora, continuations, E-type pronoun, type-shifting, scope, quantification, binding, dynamic semantics, weak crossover, donkey pronoun, variable-free, direct compositionality, D-type pronoun, conditionals, situation se- mantics, c-command, dynamic predicate logic, donkey weak crossover ∗ Thanks to substantial input from Anna Chernilovskaya, Brady Clark, Paul Elbourne, Makoto Kanazawa, Chris Kennedy, Thomas Leu, Floris Roelofsen, Daniel Rothschild, Anna Szabolcsi, Eytan Zweig, and three anonymous referees.
    [Show full text]
  • Nominal Anchoring
    Nominal anchoring Specificity, definiteness and article systems across languages Edited by Kata Balogh Anja Latrouite Robert D. Van Valin‚ Jr. language Topics at the Grammar­Discourse science press Interface 5 Topics at the Grammar­Discourse Interface Editors: Philippa Cook (University of Göttingen), Anke Holler (University of Göttingen), Cathrine Fabricius­Hansen (University of Oslo) In this series: 1. Song, Sanghoun. Modeling information structure in a cross­linguistic perspective. 2. Müller, Sonja. Distribution und Interpretation von Modalpartikel­Kombinationen. 3. Bueno Holle, Juan José. Information structure in Isthmus Zapotec narrative and conversation. 4. Parikh, Prashant. Communication and content. 5. Balogh, Kata, Anja Latrouite & Robert D. Van Valin‚ Jr. (eds.) Nominal anchoring: Specificity, definiteness and article systems across languages. ISSN: 2567­3335 Nominal anchoring Specificity, definiteness and article systems across languages Edited by Kata Balogh Anja Latrouite Robert D. Van Valin‚ Jr. language science press Balogh, Kata, Anja Latrouite & Robert D. Van Valin‚ Jr. (eds.). 2020. Nominal anchoring: Specificity, definiteness and article systems across languages (Topics at the Grammar-Discourse Interface 5). Berlin: Language Science Press. This title can be downloaded at: http://langsci-press.org/catalog/book/283 © 2020, the authors Published under the Creative Commons Attribution 4.0 Licence (CC BY 4.0): http://creativecommons.org/licenses/by/4.0/ ISBN: 978-3-96110-284-6 (Digital) 978-3-96110-285-3 (Hardcover) ISSN:
    [Show full text]