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Home , Bound variable pronoun, Cataphora, Distributive case, English pronouns, Part of speech, Reciprocal construction

A Unified Analysis of Reflexives and Reciprocals in Synchronous Tree Adjoining

A DISSERTATION PRESENTED

BY

CRISTINA AGGAZZOTTI

TO

THE DEPARTMENT OF

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FORTHEDEGREEOF

DOCTOROF PHILOSOPHY

INTHESUBJECTOF

LINGUISTICS

HARVARD UNIVERSITY

CAMBRIDGE,MASSACHUSETTS

APRIL 2019 ©2019 – CRISTINA AGGAZZOTTI ALL RIGHTS RESERVED. Dissertation Advisor: Stuart Shieber Cristina Aggazzotti

A Unified Analysis of Reflexives and Reciprocals in Synchronous Tree Adjoining Grammar

ABSTRACT

Reflexives and reciprocals share a similar syntactic distribution so are often grouped together under the term anaphor, even though differ semantically. They are a challenging test case for any theory due to their reliance on either or another , which can sometimes be non-local, to supply their meaning. An approach that preserves the antecedent-anaphor dependency without requiring extra computational power, and can additionally generalize these two phenomena into mechanism, is desirable. This dissertation provides one such unified analysis. Using the framework of synchronous tree adjoining grammar, present a parallel analysis for reflexives and reciprocals that captures their , , and . The analysis builds on a previous STAG analysis of reflexives by Frank (2008) to not only provide the first STAG account of reciprocals, but also unify this account with one for reflexives. By employing semantic operators, the analysis abstracts out the notions of reflexivity and reciprocity into a formalization that captures the various possible readings of each anaphor. I also propose a novel of the STAG framework in which the basic unit, a lexicalized elementary tree, is decomposed into smaller units—morphological elementary trees. These word level trees obey the same rules to form lexicalized trees as level STAG trees do to form sentences. English reflexives are used as a test case but future work will apply the analysis crosslinguistically to with morphologically richer anaphors. Additional contributions include a clarification of the vast literature on reflexives in particular and a corpus investigation into the distribution of reflexives and any differences across the reflexives. Through a combination of corpus, computational, and theoretical work investigating the syntax, semantics, and morphology of anaphors, this dissertation provides a comprehensive and versatile model of both reflexives and reciprocals as unified phenomena.

iii Contents

ACKNOWLEDGMENTS viii

LIST OF FIGURES x

LISTOF TABLES xii

1 THE LANDSCAPE:PRESENTINGTHE CHALLENGE 1 1.1 Goals and contributions ...... 1 1.2 Three sides of anaphors ...... 2 1.2.1 Syntax ...... 2 1.2.2 Semantics ...... 4 1.2.3 Morphology ...... 7 1.3 Synchronous tree adjoining grammar ...... 7 1.4 Dissertation outline ...... 8

2 THE FOREST:UNDERSTANDING THE DATA 10 2.0.1 Terminology ...... 11 2.0.2 Contributions ...... 12 2.1 Survey of the range of reflexives ...... 13 2.1.1 Reflexive anaphors ...... 13 2.1.2 Intensifiers ...... 14 2.1.3 Override reflexives ...... 16 2.1.4 Previous taxonomies ...... 22 2.2 Corpus overview ...... 27 2.2.1 Data ...... 27 2.2.2 Method ...... 27 2.3 Survey and corpus results ...... 28 2.3.1 A new reflexive taxonomy ...... 28 2.3.2 Reflexive corpus findings ...... 36 2.3.3 Reciprocals ...... 40 2.4 Summary and future work ...... 41

3 THE TREES:INTRODUCINGTHE MODEL 43 3.0.1 Why STAG? ...... 43 3.0.2 Notation and terminology ...... 45 3.1 Background ...... 46 3.1.1 Synchronous Tree Adjoining Grammar ...... 46 3.1.2 Previous work on reflexives in TAG ...... 52 3.1.3 The analysis of Frank (2008) ...... 56 3.2 Multiple link MCTAG ...... 59 3.3 A new analysis ...... 60 3.3.1 Frank’s analysis revised ...... 60 3.3.2 of analyses ...... 62 3.3.3 Adding reciprocals ...... 64 3.3.4 Anaphor properties in the analysis ...... 65 3.4 Applications ...... 67

iv 3.4.1 ...... 67 3.4.2 Anaphors with control ...... 68 3.4.3 Anaphoric arguments of ditransitive verbs ...... 71 3.5 Extensions with delayed tree-locality ...... 77 3.5.1 Anaphors in picture-DPs ...... 77 3.5.2 Anaphors in adjuncts ...... 79 3.5.3 Anaphors with raising verbs ...... 80 3.5.4 Anaphors with ECM verbs ...... 81 3.5.5 Anaphors with control verbs ...... 82 3.5.6 Multiple anaphors ...... 84 3.6 Summary and future work ...... 85

4 THE LEAVES:REFINING THE MODEL 87 4.0.1 Reciprocity ...... 87 4.0.2 Notation and terminology ...... 89 4.1 The phenomena ...... 89 4.1.1 Extended readings ...... 90 4.1.2 Weakened readings ...... 91 4.2 Capturing extended readings ...... 95 4.2.1 Simple cases ...... 96 4.2.2 Allowing for across-group readings ...... 96 4.2.3 Allowing for within-group readings ...... 97 4.2.4 Combining extended readings ...... 98 4.3 Capturing reflexives ...... 98 4.3.1 Reflexive readings ...... 99 4.3.2 Reflexives as operators ...... 99 4.4 Capturing weakened readings ...... 101 4.4.1 Unifying the analysis ...... 106 4.4.2 Comparison with previous analyses ...... 107 4.5 Summary and future work ...... 108

5 THE ROOTS:DIGGING DEEPERINTOTHE MODEL 109 5.0.1 Previous related work ...... 110 5.1 Building up the framework ...... 111 5.1.1 Morphology as syntax ...... 111 5.1.2 Derivational morphology ...... 114 5.1.3 Inflectional morphology ...... 119 5.1.4 Interplay between derivational and inflectional morphology ...... 130 5.2 Bracketing paradoxes ...... 131 5.2.1 Morphological bracketing paradoxes ...... 132 5.2.2 Attribute phrase bracketing paradoxes ...... 135 5.3 Capturing anaphors ...... 139 5.3.1 Brief history of the English reflexive form ...... 139 5.3.2 Current status of the English reflexive form ...... 140 5.3.3 Morphology of English reflexives in STAG ...... 141 5.4 Summary and future work ...... 145

v 6 BEYOND TREES:EXPANDING THE MODEL 146 6.1 Future directions ...... 146 6.1.1 Preliminary crosslinguistic expansion ...... 146 6.1.2 Machine learning approaches ...... 152 6.2 Conclusion ...... 154

BIBLIOGRAPHY 164

vi In dedication to my dog Hercules for helping me keep perspective, forcing me to go outside, and reminding me to get excited about the little things

vii Acknowledgments

A Ph.D. is a marathon, not a sprint. have to pace yourself and take water breaks so you don’t burn out, ’s more pleasant when you look at the scenery passing by and have others around you, and the planning fallacy almost always ensures you go faster near the end. This was certainly true for me. I often forgot that the key was endurance, but many people in various ways helped me remember.

On the academic side, this dissertation would not have been possible without my advisor, Stuart Shieber. I serendipitously took his computational linguistics class in the spring of my first year and somehow became one of the lucky ones to continue working with him ever since. His dedication to and care for his students is clear. has not only taught me how to critically examine issues from all sides, but has also served as an invaluable resource and mentor for various decisions and obstacles I have encountered. I admire his calmness and wisdom and think fondly of the anecdotal tangents have gone on during meetings. He has given me both technical and life skills, perhaps without even realizing, that I will carry with me in my future endeavors. I would also like to sincerely thank Gennaro Chierchia, for not only being on my committee and advising me in all things semantics, but for also being a caring almost fatherly figure in the department and for permitting me to branch out from linguistics to pursue a non-standard path. I am also grateful to Bob Frank, whose original STAG reflexive analysis kickstarted this entire dissertation, and whose insightful comments and reflections from years’ experience pondering TAG have greatly improved this work. It was very intimidating to have such brilliant and accomplished committee members, but my dissertation has significantly benefited because of it.

Thank you as well to Kevin Ryan for his advice on Chapter 2 and to the Linguistics Department administrators—Cheryl Murphy, Helen Lewis, and Kate Pilson—for doing more behind the scenes than we will ever know. Additionally, thank you to the incredible undergraduate students with whom I had the opportunity to work: Jennifer Hu, Brian Yu, Nicolas Sardella, Alan Dai, Anya Zhang, Elbert Gong, and Simas Sakenis. I found myself time and time again being pleasantly surprised and impressed by their and insights. Jennifer and Brian helped me implement and test my STAG reflexive analysis using OCaml; Nick, Alan, and Anya annotated hundreds of reflexive sentences and significantly contributed to developing and refining the taxonomy in Chapter 2; and Elbert and Simas ran and assessed all the various machine learning models discussed in Chapter 6.1.2.

On the personal side, I of course would not be where I am today if it weren’t for my parents, brothers, and

viii family. Their encouragement to pursue my interests, regardless of how random, their pride in my accomplishments, no matter how small, their much-needed reminders to relax, even when I thought all hope was lost, and their constant ability to make me laugh (especially my brother Ryan), have pulled me through life’s ups and downs. I consider myself extremely lucky to have such amazing, diverse, supportive, and inspiring friends. They have forced me to prioritize happiness and health, encouraged me to have (some form of) a work-life balance, commiserated with me during times of frustration, and challenged me to think creatively and critically about all topics. In particular I would like to thank my cohort—Aurore, Yuyin, and Julia—for helping me through the coursework and for venting with me at our cohort dinners, and my academic mentor and friend, Zuzanna, for advising and supporting me through countless academic and personal situations. I also want to thank my travel partner and life coach, Julian, for the numerous adventures, experiences, and life lessons—may there be many more to come. Special thanks to the other members of the “no fingerprints” crew, Aaron—for making sure I have a constant flow of new music, for instigating adventures with me and Julian, and for being a master at animal GIFs—and Robert, for having dance moves for days, for planning incredible surprise birthday activities, and for boozy research lunches. I also want to thank the many strong and admirable women in my life, including but in no way limited to Morgan, Kristina, Aviva, Rachel, Ava, Anita, Amy, Catherine, Sarah, Robyn, Emma, Kat, Carina, and Tamara, as well as the fun and supportive men, including but not limited to Andre, Fraser, Joey Sax, Greg, Gus, Sanjay, Suman, Drew, Roland, Gabe, Pete, Etienne, Morgan, Ben, and Alex. The acknowledgements would not be complete without a tribute to Carlo, for introducing me to a completely different perspective on life and challenging me more than anyone else ever has, and the other members of the core “gruppo”, which started at orientation and will continue throughout our lives: Sam, Jonas, Alex, David, Armin, Ivana, Dima, and Cesar. And finally, although he will never realize it, I am deeply grateful for my dog Hercules, to whom this dissertation is dedicated, for accompanying me on this journey (from both near and far). I met him the day I found out I got into Harvard and he has been by my side ever since. He patiently listened to numerous practice talks, quietly cuddled next to me as I worked at any hour of the day and night, and ensured I stayed healthy by reminding me to take him outside for some fresh air and exercise. More than anything though, he has shown me how to give equal treatment to anyone I meet, to have memory loss for the injustices against me, and to give limitless love to those around me.

ix List of Figures

1.1 Depiction of subplurality readings ...... 5

2.1 Traditional taxonomy of reflexives ...... 23 2.2 Huddleston and Pullum’s (2002) taxonomy of reflexives ...... 24 2.3 König and Gast’s (2002) taxonomy of reflexives ...... 26 2.4 New taxonomy of reflexive kinds and types ...... 30 2.5 Distribution of reflexive kinds for each reflexive ...... 36

3.1 Derivation of Noah saw Emma...... 48 3.2 Equivalent elementary trees using TP ...... 48 3.3 Derivation showing structures, Noah saw her...... 49 3.4 Derivation of quantifiers, No one saw Emma...... 50 3.5 Derivation of topicalization, Emma, Noah saw...... 52 3.6 Nesson’s (2009) STAG reflexive analysis using de Bruijn indices ...... 54 3.7 Storoshenko et al.’s (2008) multiple forms of the English reflexive ...... 55 3.8 Frank’s (2008) reflexive analysis ...... 57 3.9 Derivation of transitive sentence using the new reflexive analysis, Noah and Emma saw themselves...... 63 3.10 Derivation including both reflexives and reciprocals, Noah and Emma saw themselves/each other...... 65 3.11 Derivation of a cataphoric (topicalized) anaphor, Each other, Noah and Emma saw...... 69 3.12 Derivation of anaphors with object control verbs, Noah and Emma persuaded themselves/each other to be happy...... 70 3.13 Derivation of both ditransitive subject coindexation word orders, Noahi showed himselfi Liam./Noahi showed Liam himselfi...... 74 3.14 Comparison of derivations of ditransitive subject vs. object coindexation, Noahi showed Liam himselfi./Noah showed Liam j himself j...... 75 3.15 Derivation of ditransitive object coindexation, Noah showed Liami himselfi...... 76 3.16 Derivation of anaphors in picture-DPs using delayed tree-locality, Noah and Emma saw the pictures/every picture of themselves/each other...... 78 3.17 Alternate elementary semantic tree to ensure proper variable ...... 79 3.18 Derivation of anaphors in adjuncts, Noah and Emma sang to themselves/each other. . . . . 80 3.19 Derivation of anaphors with raising verbs, Noah and Emma seem to themselves/each other to be happy...... 82 3.20 Derivation of anaphors with ECM verbs, Noah and Emma want themselves/each other to be happy...... 83 3.21 Derivation of anaphors with subject control verbs, Noah and Emma tried to see them- selves/each other...... 83 3.22 Derivation of sentence with multiple anaphors, Noah and Emma introduced themselves to each other...... 85

4.1 Graph depicting strong reciprocity, Noah, Liam, and Mason saw each other...... 88 4.2 Graph depicting weaker reciprocity, The plates are stacked on top of each other...... 88 4.3 Depictions of extended/subplurality readings ...... 90 4.4 Depiction of weakened reciprocity, The medalists stood alongside each other...... 101

x 5.1 Base morphological forms ...... 112 5.2 Derivation of do ...... 113 5.3 Unlexicalized interface tree sets ...... 114 5.4 Derivation of redo ...... 115 5.5 Derivation of doable ...... 116 5.6 Ambiguous derivational affix tree sets with underspecified feature values ...... 118 5.7 Tree sets for happy and -ness ...... 118 5.8 Derivation of unhappiness that succeeds ...... 120 5.9 Derivation of unhappiness that fails due to feature clash ...... 121 5.10 Derivation of the number inflectional suffix, dogs ...... 123 5.11 Unlexicalized interface verb tree set with tense links ...... 124 5.12 Tree sets for past tense ...... 125 5.13 Derivation of past tense, walked ...... 126 5.14 Tree sets for future tense ...... 129 5.15 Derivation of future tense, will walk ...... 130 5.16 Morphological tree sets with INFL feature ...... 131 5.17 Elementary trees for comparative suffix and comparative with COMP and DEG features ...... 134 5.18 Derivation of comparatives, happier and more apt ...... 136 5.19 Derivation of unhappier ...... 137 5.20 Word level and unlexicalized interface tree sets for the English reflexive, herself ...... 143 5.21 Derived reflexive tree set, herself ...... 144

6.1 Derivation of , Noè ed Emma lo vedono...... 149 6.2 Derivations of reflexive/reciprocal clitics, Noè ed Emma si vedono./Noè ed Emma vogliono vedersi...... 151 6.3 Tree set for + , Noè ed Emma si vedono l’un l’altro...... 151

xi List of Tables

2.1 Reflexive anaphor syntactic environments found in corpus ...... 32 2.2 Contingency table for distribution of reflexive anaphors vs. intensifiers for itself vs. non-itself 37 2.3 P-values for distribution of reflexive anaphors and intensifiers ...... 38 2.4 P-values for distribution of reflexive anaphors and non-adnominal intensifiers ...... 38 2.5 P-values for distribution of intensifiers and override reflexives ...... 39 2.6 Contingency table for distribution of override vs. non-override reflexives for 3rd person vs. non-3rd person ...... 40

4.1 The six reciprocal meanings according to Dalrymple et al. (1998) ...... 93 4.2 Eight possible combinations of three relation properties for reciprocals ...... 105 4.3 The various forms of RECP4 with example sentences ...... 106

5.1 binary verbal and features ...... 115

xii 1 The Landscape: Presenting the Challenge

1.1G OALSANDCONTRIBUTIONS

The of this dissertation is modeling reflexives (himself, themselves) and reciprocals (each other, one another) in a unified way using the formalism of Synchronous Tree Adjoining Grammar (STAG). Reflexives and reciprocals, collectively called anaphors, form an unusual class of across languages that syntactically function like other , but differ due to their varied meanings and lexical composition. Early linguistic theories (Lees and Klima, 1963; Dougherty, 1970; Jackendoff, 1972; Chomsky, 1981) claimed that both obeyed the same set of constraints and differed only in their meaning; however, later work (Lebeaux, 1983; Everaert, 2008; Reuland, 2008) has revealed that reflexives and reciprocals are complex phenomena with several interacting and sometimes conflicting features. Much research has focused on reflexives or reciprocals individually but less has assessed both as parallel phenomena.

From the perspective of processing, reflexives and reciprocals are a relevant and challenging phenomenon because they participate in dependency relations that sometimes involve a non-local antecedent, which can render some analyses computationally intractable. An approach that preserves the antecedent-anaphor dependency without requiring extra computational power is thus desirable; an approach that can additionally generalize two separate phenomena into one mechanism is even better.

The primary goal of this dissertation is to provide one such unified analysis of reflexives and reciprocals. The analysis is unified in three main ways. First, reflexives and reciprocals are modeled in the formalism of STAG, which utilizes syntactic-semantic tree pairs that undergo synchronized operations. Second, the analysis merges these two phenomena semantically by abstracting out the notions of reflexivity and reciprocity into parallel semantic operators. Third, using reflexives as a test case, the analysis extends the formalism of STAG to encompass morphology by decomposing syntactic/semantic STAG tree pairs into morpho-syntactic/morpho-semantic tree pairs of roots, derivational affixes, and inflectional affixes. Since

1 1.2. Three sides of anaphors

English reciprocals are fixed syntactic units, and thus morphologically impoverished, they are not a good test case; however, many other languages represent both anaphors at the morphology level so even though English is not the optimal morphologically, dissecting the basic STAG elementary trees into sub-level morphological components broadens the applicability of the analysis crosslinguistically to be able to capture anaphors in languages other than English. The primary contributions of this dissertation are to provide the first STAG analysis to capture both reflexives and reciprocals, to formalize the semantic representation of reflexives and reciprocals in a way that captures their various readings, and to extend the STAG framework to incorporate the morphological composition of lexicalized elementary trees. Through a combination of corpus, computational, and theoretical work investigating the syntax, semantics, and morphology of anaphors, I provide a more comprehensive and versatile model of both reflexives and reciprocals as a unified phenomenon. In this introductory chapter, I provide a brief overview of the main components of the dissertation. I first introduce three of the sides of anaphors as a phenomenon—their syntax, their semantics, and their morphology. Then, I motivate the use of the STAG formalism for modeling these three sides of anaphors, but leave the detailed explanation of STAG itself to later in the dissertation. Lastly, I provide a more systematic overview of the dissertation by chapter.

1.2T HREESIDESOFANAPHORS

1.2.1S YNTAX

Anaphors have two main syntactic requirements. First, an anaphor must have an antecedent with which it corefers in an appropriate location, generally preceding it in the sentence (Büring, 2005). Sentence (1a) is grammatical because it obeys these constraints, whereas sentence (1b) is ungrammatical because the anaphor is in an inappropriate structural relation with the antecedent.

(1) a. Noahi saw himselfi.

b. * Himselfi saw Noahi.

Second, an anaphor must agree in gender, person, and number with its antecedent, as shown in (2).

(2) a. * Noahi saw herselfi.

b. * Youi saw myselfi.

c. * Emmai saw [each other]i.

2 Chapter 1. The Landscape: Presenting the Challenge

Dougherty (1970) was one of the first to point out the syntactic similarity between reflexives and reciprocals, observing that each other is governed by a simplex sentence condition paralleling that for reflexivization (put forth by Lees and Klima (1963)), which constrains the anaphor to occur in the same as its antecedent. Jackendoff (1972) expanded upon this idea by showing that the specific environments in which reciprocals occur seem to be almost identical to those of reflexives. According to the constraints on anaphors in general, both have the syntactic requirement of being bound by and coreferenced with a local antecedent, so it makes sense that they would occur in similar environments.

(3) a. The women see themselves/each other in the mirror.

b. The children care about themselves/each other more than their caretakers.

c. Why would he mind that to *ourselves/*each other he looked like a fool?

d. The boss looks like he wants to strangle *yourself/*each other.

However, despite these similarities, there are a few important exceptions, which can be categorized into two groups: environments that allow only reflexives and environments that allow only reciprocals. The first group, in which reflexives appear but reciprocals do not, includes two main cases. The first case is when reflexives function emphatically as intensifiers, as in (4a); reciprocals do not serve this purpose.1 I adopt the term for this kind of reflexive to highlight that it serves to intensify the antecedent and can be removed from the sentence without losing any information (other than emphasis).

(4) a. ...the performers themselves also should be considered as important factors in teaching expression. (COCA)2

b. *...the performers each other also should be considered as important factors in teaching expression.

The second case is when reflexives appear in positions prescriptively occupied by , which does not usually occur for reciprocals, as shown in (5). There have been a variety of terms in the literature for this kind of reflexive, including but not limited to untriggered, exempt, and logophoric, but each of these terms describes a different subset of the instances of reflexive encompassed by this category. I adopt the term

OVERRIDE for this kind of reflexive to highlight the fact that the use of a reflexive in these environments overrides the default use of a pronoun.

1In this dissertation, I only consider the contiguous lexical reciprocals each other and one another, and exclude variations such as each...the other, which can appear in different environments and take on additional meanings. 2This example and others labeled similarly are taken from the Corpus of Contemporary American English (COCA).

3 1.2. Three sides of anaphors

(5) a. The first move came as a collaboration between Einstein and myself. (COCA) The first move came as a collaboration between Einstein and me/*each other.

b. Many participants, including us/ourselves/*each other, saw fantastic results from using the product.

c. After a long trial, the jury convicted the security guard, the nightclub owner, and us/ourselves/*each other, the runners, of drug trafficking.

For the second group, Lebeaux (1983) pointed out three apparent exceptions in which reciprocals are rated “considerably better” than reflexives: as the subject of a tensed clause (6a), as the subject of an NP (6b), and as the subject of a “for-to” clause (6c). He claims that the difference in distribution lies in the requirement of reflexives to occur in properly governed positions, whereas reciprocals can occur in non-properly governed positions, as shown in (6).3

(6) a. John and Mary think that ?each other/*themselves will win.

b. John and Mary like each other’s/*themselves’ parents.

c. It would please the boys very much for each other/ ?themselves to win.

Chapter 2 is dedicated to not only clarifying the terminology in the literature, especially for the first group, but also presenting an empirical approach to determining the similarities and differences in the syntactic distributions of reflexives and reciprocals.

1.2.2S EMANTICS

Although reflexives and reciprocals overlap in their syntactic distributions, they consistently differ in their relation with the antecedent: reflexives indicate a relation between the antecedent parts and themselves, while reciprocals indicate a relation among the antecedent parts. As a result, reciprocals must have a antecedent over which to distribute, whereas reflexives can have either a plural or singular antecedent. By way of example, consider the sentences in (7), identical except for the alternation between reflexive and reciprocal. The canonical reflexive reading—DISTRIBUTIVE REFLEXIVITY—of the sentence in (7a) is that the relation (here, saw) holds between each atom in the plural antecedent and itself: Noah saw Noah and Emma saw Emma. In other words, the action is distributed among the atomic parts of the antecedent.

3Lebeaux (1983) uses plural reciprocal sentences and singular reflexive sentences, which does not set up a clear , so the sentences have been converted into minimal pairs in which the only difference is whether a reflexive or reciprocal appears.

4 Chapter 1. The Landscape: Presenting the Challenge

(a) (b)

Figure 1.1: Schematic depictions of subplurality readings in the scenario of boys collectively lifting. (a) Inter- mediate (subplurality) reflexive reading of The boys lifted each other. (b) Corresponding across-group reading of The boys lifted themselves.

Similarly, the canonical reciprocal reading—STRONGRECIPROCITY—of (7b) is one in which the relation holds between each atom in the antecedent and each other distinct atom: Noah saw Emma and Emma saw Noah.

(7) a. Noah and Emma saw themselves.

b. Noah and Emma saw each other.

Other anaphoric readings exist as well. Reflexives can have two additional readings—cumulative and, for antecedents of cardinality greater than two, intermediate (subplurality). CUMULATIVE REFLEXIVITY occurs when the relation expressed by the verb holds of the entire plurality and itself—the action is true of the cumulative group. For the sentence in (8), consider an (admittedly artificial) scenario in which a group of boys is standing on a platform attached to a pulley system. The cumulative reading holds when the group of boys cumulatively work together to lift their platform and thereby themselves as a whole.

(8) The boys lifted themselves.

The SUBPLURALITY reading occurs when a relation holds of contextually salient subpluralities within the whole antecedent. Using the same example, now consider several subpluralities of boys, each of which is standing on its own platform. Each platform is attached to its own pulley system and each subplurality of boys must (collectively) pull a rope to lift its own platform and thereby the group. The subplurality reading, depicted in Figure 1.1(a), then indicates that the lifting relation holds of each subplurality of boys because each group raises its own platform to lift themselves. (A distributive reading would also be possible in the scenario in which each boy is on his own platform and individually lifts himself.) Reciprocals can have even more readings, including multiple subplurality readings and various weakened readings. One reciprocal subplurality reading, referred to as an ACROSS-GROUP reading (Gennaro

5 1.2. Three sides of anaphors

Chierchia, p.c.), occurs when the reciprocal relation holds across subsets of the domain of reciprocity. In the sentence in (9), which is simply the reflexive version of (8), imagine once again that there are two subpluralities of boys, each standing on a platform. This time, though, using the pulley system causes the other platform (and the boys thereon) to be lifted, as depicted in Figure 4.3(b).

(9) The boys lifted each other.

A second subplurality reading occurs when the reciprocal relation holds over elements of some partition of the antecedent. Fiengo and Lasnik (1973) identified this WITHIN-GROUP reading of reciprocals, using the example (10a). Imagine a scenario in which there are many men, can be partitioned into groups of two, with reciprocal hitting between the members of each group. In this scenario, Fiengo and Lasnik (1973) claim that (10a) is still true even if no hitting occurs between members of different groups. In such cases, the antecedent is divided into subdomains, determined by context, and strong reciprocity holds within every subdomain, as shown in (10b). (There are also cases in which both of these subplurality readings are available for the same sentence.)

(10) a. The men are hitting each other.

b.

Many (Langendoen, 1978; Dalrymple et al., 1998; Beck, 2001, among others) have additionally pointed out various weakened readings (separate from the subplurality readings), when strong reciprocity is relaxed to varying degrees, so that not every element of the reciprocal domain must stand in the reciprocal relation with every other element. Dalrymple et al. (1998) provide one account of these weakened readings. Drawing on the work of Langendoen (1978) and Kánski (1987), Dalrymple et al. (1998) provide a taxonomy of six possible meanings for reciprocals, ranging from strong to weak, as shown in (11).

(11) a. Strong reciprocity: The teammates refer to each other using nicknames.

b. Strong alternative reciprocity: The people buried in the cemetery are ancestors of each other.

c. Intermediate reciprocity: The pitchers sat alongside each other.

d. Intermediate alternative reciprocity: The students gave each other measles.

e. One-way weak reciprocity: The pirates stared at each other.

f. Inclusive alternative ordering: The planks are stacked on top of each other.

Chapter 4 focuses on providing appropriate semantic to model the reflexive and reciprocal relations and capture all of these possible readings.

6 Chapter 1. The Landscape: Presenting the Challenge

1.2.3M ORPHOLOGY

In English, reflexives are morphologically complex, while reciprocals are morphologically impoverished. English reflexives are superficially comprised of two : a pronoun and -self /-selves. In first and second person, the pronoun resembles a pronoun (my, your, our), and in third person the pronoun takes the form of a (him, them).4 The origin, history, and current status of these two morphological components are often contested, as described in detail in Chapter 5, but I adopt the following explanation, as summarized by Sinar (2006).

The first of the English reflexive is a personal pronoun that syntactically agrees with its antecedent in φ features and semantically plays the role of a . This pronoun is not possessive because it originated across persons and number as a (dative) personal pronoun, and the appearance of the first and second person pronouns as having a possessive surface form is due to extraneous (phonological) circumstances. The second morpheme is self /selves, which originated as an intensifier in , but was reanalyzed as and now serves as a two-place predicate denoting the identity relation.

Reciprocals, on the other hand, I assume (for the present purposes) are a fixed syntactic form in English and are not decomposable into individually meaningful morphemes. Thus, I consider their meaning to derive solely from the phrase level so for morphology, I focus on reflexives instead. However, many other languages rely on morphological representations of both reflexives and reciprocals to convey their meaning so examining anaphors from this angle is still worthwhile for future crosslinguistic work.

Chapter 5 presents a historical account of the morphology of English reflexives and then shows how reflexives can be used as a test case for morphological STAG, after building up the morphological STAG framework.

1.3S YNCHRONOUSTREEADJOININGGRAMMAR

Any comprehensive account of reflexives and reciprocals should be able to capture the aforementioned syntactic and semantic properties, ideally on both a syntax-semantics level and a morphology level. However, the variety of syntactic environments in which anaphors can be found as well as the diverse range of semantic interpretations they yield make anaphors a challenging test for any model.

One approach that has successfully handled linguistic phenomena whose syntactic and semantic

4Her has the same form as both a personal and a possessive pronoun, so is superficially ambiguous between the two.

7 1.4. Dissertation outline derivations seem to diverge, and done so in a tractable way, is STAG. STAG utilizes syntactic-semantic tree pairs, each containing one lexical head, that undergo synchronized operations to produce a unified syntactic and semantic analysis of linguistic phenomena. Since anaphors require a referential lexical item, or antecedent, to supply their semantic value, they depend on both syntax, in the form of distributional constraints, and semantics, in the form of specific relations with the antecedent. Thus, STAG has the potential to be an effective way of modeling both reflexives and reciprocals.

However, many languages represent reflexivity and reciprocity with morphemes, which requires finer-grained flexibility than that provided by lexicalized STAG. Storoshenko (2010) provided the first crosslinguistic analysis of reflexives in STAG, using Korean, Shona, and Plains Cree as representative languages of different reflexive uses, and recognized the utility of representing a word’s morphological components. Surprisingly, capturing the morphological makeup of STAG lexicalized elementary trees is an unexplored aspect of STAG, but is necessary for modeling both reflexivity and reciprocity crosslinguistically.

Chapter 3 provides an in-depth description of STAG, incrementally building up the framework through examples, and then presents a novel analysis that shows how STAG can not only capture the syntactic distribution and semantic representation of both reflexives and reciprocals, but also do so in a unified way through the use of semantic operators. Chapter 5 then extends this analysis down to a word level, specifically using English reflexives as a test case.

1.4D ISSERTATION OUTLINE

The rest of the dissertation is laid out as follows. Chapter 2 describes and defines all of the various kinds of reflexives and reciprocals in English. Reciprocals are fairly straightforward, so I focus on reflexives and only briefly present reciprocals at the end. First, I provide an in-depth assessment of reflexives, including a review of previous reflexive classifications and terminology. Then I propose a new taxonomy based on an empirical examination of reflexives in the Corpus of Contemporary American English and highlight particularly interesting insights from the data.

Based on this comprehensive understanding of the various kinds of reflexives and reciprocals, Chapter 3 presents a unified STAG analysis of both anaphors by employing interchangeable semantic operators, REFL for reflexives and RECP for reciprocals. I start by building up the formalism from scratch. Then I present an analysis of the canonical reflexive (distributive reflexivity), based on an extension of a previous preliminary analysis of reflexives by Frank (2008), which is shown to immediately extend to capture the canonical reciprocal (strong reciprocity). With this foundation, I test the analysis on a variety of syntactic

8 Chapter 1. The Landscape: Presenting the Challenge configurations.

Chapter 4 refines the semantic definitions of the operators, REFL and RECP, in order to capture readings beyond the core notions of distributive reflexivity and strong reciprocity. First I present the various possible readings for reciprocals and review a previous attempt at systematically identifying their interpretation, namely that of Dalrymple et al. (1998). Using their account as a foundation, I build up RECP into a form that captures all possible reciprocal readings then show how it straightforwardly extends to also capture the reflexive readings in REFL. Chapter 5 extends the current STAG framework by decomposing phrase level elementary syntactic and semantic trees into a lower word level, namely morpho-syntactic and morpho-semantic elementary trees. Since no one to my knowledge has extended STAG down to the word level, I build up the framework by first modeling derivational and inflectional morphemes as well as how they interact with each other. Then, I discuss morphological and attribute phrase bracketing paradoxes. Lastly, I present reflexives as a test case, since I assume that reciprocals in English are morphologically impoverished. Reflexives are broken down into their morphological components that are shown to build up to form the phrase level analysis of anaphors presented in Chapter 3. Chapter 6 presents some preliminary investigations into future work, including extending the STAG analysis to reflexives and reciprocals in other languages and using machine learning to glean more insights into differences between reflexive and pronoun distributions. I conclude by summarizing the findings from the previous chapters, building up to a coherent and unified view of the syntax, semantics, and morphology of reflexives and reciprocals.

9 2 The Forest: Understanding the Data

Anaphors as a type of has been a popular topic in linguistics since early . Reflexives and reciprocals have often been grouped under the umbrella term of anaphor to simplify descriptions and analyses; however, there are clear instances in which their distributions differ, as discussed in Chapter 1. This chapter aims to provide an overview of the distribution of each anaphor in English.

For reflexives, the correct constraints on their distribution, and even the exact definition of a reflexive itself, are still open questions. On the one hand, reflexives for the most part seem to be restricted to certain environments and seem to share properties with reflexives in other languages. On the other hand, they also seem to appear in unexpected places that the coverage of the constraining theory. Reflexives are further complicated by the possibility of differences across person and number. Moreover, the literature on reflexives has become so expansive and diverse that it is often difficult to understand the differences among theories and the exact definitions of the terminology used. Reciprocals, in contrast, are syntactically fairly straightforward since they are restricted to plural antecedents, do not differ by person, and seem to appear in predictable places overall. The challenge for reciprocals comes in the semantics, which I discuss in Chapter 4.

Since the early Generative Grammar days, there have been a variety of attempts to describe the distribution of both anaphors, but surprisingly few of these have approached the task from an empirical angle. This chapter seeks to fill this void. Using the Corpus of Contemporary American English, I present empirical findings on the distribution of reflexives and reciprocals. Since reflexives are more contentious and diverse than reciprocals, this chapter focuses primarily on reflexives while reciprocals are only briefly discussed at the end in Section 2.3.3.

The layout of this chapter is as follows. To begin, I define the terminology I use throughout the chapter and mention the contributions provided. Section 2.1 provides a survey of the entire range of reflexives, amalgamating previous theories and taxonomies and clarifying terminology often used loosely throughout the literature. Interwoven into this survey is the motivation behind the terminology I choose to use. To test

10 Chapter 2. The Forest: Understanding the Data these findings, I conducted a corpus analysis using the (currently) largest corpus of American English, the Corpus of Contemporary American English (COCA). Section 2.2 describes the corpus data, the method used to extract and statistically test differences across reflexives, and the annotation scheme for those reflexives.

Section 2.3 presents the results of combining the literature review with the attested data from the corpus. First, I present a novel all-encompassing taxonomy of reflexives that not only incorporates many separate research ventures but also categorizes reflexives in a different way from previous attempts in order to provide an exhaustive and disjoint classification. The main motivation for mutually exclusive categories is that reflexives can be clearly grouped according to their features, which enables more precise annotation labels and statistical analyses of those categories to reveal insights on their behavior. Using this proposed classification, I present some statistical findings on differences among reflexives themselves. Finally, Section 2.3.3 turns to the distribution of reciprocals and Section 2.4 concludes by highlighting the contributions of this chapter and suggesting areas for future work. Before going further, though, due to the variety of terminology used throughout the field, it is worth defining some of the specific terms I use.

2.0.1T ERMINOLOGY

The terminology for describing reflexives and their uses varies widely in the literature. Not only do the terms themselves vary, but the definitions of those terms across authors also vary, sometimes only subtly and often not explicitly. Throughout this chapter, I provide analogous (or nearly analogous) terms, along with a few authors who use those terms when possible, and I highlight the slight differences between the terms.

For the present purposes, I use the underspecified term REFLEXIVE (instead of, for instance, reflexive pronoun) in its morphological sense to refer to all kinds of self -forms in English (myself, yourself, etc.), regardless of their function or position in a sentence. I do not use reflexive pronoun to avoid an association with or implicit relation to personal pronouns. Although I focus strictly on reflexives in English, I also do not use the term self -form to avoid a bias toward considering strictly English aspects of reflexivity.

I distinguish three main kinds of reflexives, which also have a multitude of names in the literature, and use the terms reflexive anaphor, intensifier, and override reflexive. Reflexive KIND refers to this high level classification of reflexives, while reflexive TYPE refers to the next level of differentiation, the various types of reflexives within those kinds (e.g. adnominal, biclausal, within a PP ). REFLEXIVE ANAPHOR refers to the most common reflexive that appears in a local configuration with its antecedent.1 An example

1The use of “anaphor” here requires these reflexives to be in an anaphoric dependency and coreferential with an antecedent, but does not exclude reflexives categorized as another kind from also being anaphoric.

11 of this kind is in (12a).2 INTENSIFIER describes emphatic reflexives that can be removed from the sentence without losing any information (other than emphasis), as in (12b). Emphatic is not used here since reflexive anaphors and override reflexives can also be used emphatically. Lastly, OVERRIDE REFLEXIVE is used in lieu of the plethora of other terms, such “exempt”, “untriggered”, and “logophor”, because it seems to best capture the distribution for this kind of reflexive. An example is in (12c). Evidence in support of these terminology decisions as well as clarification of previous term definitions are provided in Section 2.1.

(12) a. The participants engaged themselves in the discussion and shared their opinions.

b. We are a little nervous because this is a lot of money, and it would really hurt us if we had to do it ourselves.

c. ...the performing artists, such as yourselves, say this song is for someone I know who died of AIDS.3

2.0.2C ONTRIBUTIONS

This chapter has three main contributions. The primary contribution is a novel comprehensive taxonomy that categorizes reflexives according to a different metric than previously used in order to provide a disjoint and exhaustive classification. Previous taxonomies have not succeeded in being both exhaustive and disjoint: not exhaustive because the classification did not account for all appearances of reflexives, and not disjoint because classes of reflexives overlapped in often unaccounted for ways. A taxonomy that is both exhaustive and disjoint provides a descriptively adequate account of English reflexives that could reveal other identifying features of each reflexive kind that went previously unnoticed, and could allow automated labeling of reflexive data to expedite annotation. This taxonomy, which is explained in detail in Section 2.3, comes from a combination of a survey of previous work and a corpus study, which are the other two contributions. Specifically, this chapter goes beyond other work because it does not simply list the environments in which reflexives appear or discuss theoretical constraints on these environments; instead, it provides a broad survey of the previous literature across the full range of reflexives and highlights the differences among the theories’ coverage. In addition, through a corpus study, this chapter provides the first examination (to my knowledge) of differences across individual reflexives (myself, yourself, etc.) and the first empirical test (to my knowledge)

2All examples throughout this chapter are taken from COCA, unless otherwise noted. 3The reflexive here does not fall under reflexive anaphor because even though it is local to its antecedent, it is not in a direct anaphoric, co-referent relation with its antecedent.

12 Chapter 2. The Forest: Understanding the Data of the claim in the literature that override reflexives occur more frequently in first and second persons.

2.1S URVEY OF THE RANGE OF REFLEXIVES

For the most part, there is a general consensus that reflexives in English can be divided into three main kinds, or uses: reflexive anaphors, intensifiers, and override reflexives. This section first reviews each reflexive kind in detail based on major works that have contributed to an understanding of that kind. Then, I summarize four previous taxonomies of reflexives, all of which help build the foundation of the taxonomy presented in Figure 2.4 in Section 2.3.1. The features discussed and the included in this section are by no means exhaustive.

2.1.1R EFLEXIVE ANAPHORS

The first category of reflexives is the reflexive anaphor, which tends to occur most frequently (reinforced by the corpus findings in Section 2.3). Again, the term anaphor is used here, rather than the more general term pronoun for instance, to highlight that these reflexives occur in an anaphoric dependency and thus must be coreferential with an antecedent, but this does not prevent other reflexive kinds from also being anaphoric. All previous literature tends to agree that this kind of reflexive, at the least, consists of local reflexives appearing in position, usually as a coargument of the same verb as its antecedent. Following Stern

(2004) (who follows Kemmer and Barlow (1996) and Cresswell (1997)), the term ARGUMENT refers both to entities selected by the verb, such as subjects and objects, and to any entity carrying its own semantic role, such as objects of prepositions. In (13a), the reflexive is an argument because it is the object of the verb. In (13b), the reflexive is also considered an argument, rather than considering the entire PP as the argument, since the verb and preposition form a complex thematic unit that together select for a DP argument, which here is the reflexive (Marantz, 1984). Reflexive anaphors can also appear in slightly less local positions, such as in biclausal control configurations (13c), or depending on the theory, within PP adjuncts of the verb (13d), as long as they are coreferential with their antecedent. The perspective I adopt aligns more closely with the looser distribution in that reflexive anaphors occur in a variety of argument and non-argument positions, but I postpone discussion of their full distribution until describing the new taxonomy in Section 2.3.1.

(13) a. object of : Meanwhile, John dragged himself from the river.

b. object of verb + preposition: For his own enjoyment, however, Prince usually relies on himself.

13 2.1. Survey of the range of reflexives

c. subject control: Shelter officials want to introduce themselves.

d. within predicate PP adjunct: A lot more people are feeling comfortable with themselves about it...

2.1.2I NTENSIFIERS

The second main kind of reflexive identified in the literature is the intensifier. Following König and Gast (2002), the term intensifier is used in lieu of emphatic since reflexive anaphors and override reflexives can also be used emphatically.4 Intensifiers occur strictly as adjuncts (to either a DP or a VP), and can be omitted without making the sentence ungrammatical. As the name suggests, their primary purpose is to intensify or emphasize their antecedent, and as a result, they generally evoke alternatives to the with which they combine.

There are two main types of intensifier: ADNOMINALS, which are modifiers within a larger DP, and

ADVERBIALS, which are modifiers of a clause. (15) shows an example of each; in depth descriptions of each follow. (The interested reader is directed to König and Gast (2002) for a review of (one perspective on) the historical development of intensifiers and how they relate to reflexive anaphors.)

(15) a. adnominal: I myself am long, thin, pale-faced and blond.

b. adverbial: If so, they can fix the damage themselves.

2.1.2.1A DNOMINAL

Adnominals, also sometimes called appositives, occur directly after their antecedent and function as a modifier within a larger DP. They generally add the meaning of no other than or no less than (Huddleston and Pullum, 2002) or evoke alternatives to the antecedent (König and Siemund, 2000b).5 The antecedent and its adnominal can occur in most structural positions, as shown in (16), but if the adnominal is separated from its antecedent, the reflexive no longer modifies the DP and instead modifies the VP, so is considered an

4 To add to the confusion, older literature (Kuno, 1987; Zribi-Hertz, 1989) refers to some instances in argument position of what I call override reflexives, such as the one in (14), as “emphatic reflexives”. Thus, I avoid using that term altogether. (14) John thinks that Mary is taller than him/himself. (Zribi-Hertz, 1989)

5The exact meaning of adnominals, especially in contrast to the two meanings of adverbials, is very subtle and is left for future work.

14 Chapter 2. The Forest: Understanding the Data adverbial.6

(16) a. subject: Artists themselves often pass on out-dated knowledge about their own art forms.

b. object of verb: I’d still have a life of luxury because I appreciate life itself.

c. object of preposition: The long walk had refreshed him but he was unsure about the decision itself.

2.1.2.2A DVERBIAL INTENSIFIERS

Adverbials are slightly more complex. Instead of modifying a DP, they are clausal adjuncts and thus crucially do not appear immediately after a DP but more freely appear throughout the clause. Generally, adverbials can occur in central position, in between an auxiliary and a verb, or in final position, at the end of a clause, as shown respectively in (18).7

(18) a. central: The harsh reality is that most are eaten by their unabashedly cannibalistic relatives before they get big enough to themselves eat the smaller ones.

b. final: I guess I’m thinking about it myself.

Additionally, adverbials can have two different meanings. The usual distinction is that INCLUSIVE adverbials can be paraphrased by “too” or “as well”, while EXCLUSIVE adverbials are paraphrased by “alone”. Other sometimes clearer paraphrases include “either” or “as for (reflexive)” for inclusive adverbials, as shown in (19a). For exclusive adverbials, a good test is to check if an optional by is allowed before the reflexive, as in (19b). (See Storoshenko (2011) for a more fine-grained distribution and more in-depth analysis of inclusive and exclusive adverbials.)

(19) a. inclusive: ...he does not directly have any intelligence experience himself. paraphrase: As for himself, he does not directly have any intelligence experience.

6An opposing view is by Bickerton (1987), who claimed that a sentence-final intensifier was simply extraposed from its original position next to the antecedent because otherwise the reflexive would not have a theta role. Choosing between the two analyses is not relevant for the purposes of this dissertation, so I adopt the more recent conclusion in which intensifying reflexives immediately following the DP they modify are adnominals and all others are adverbials. (See Storoshenko (2011) for more details on the two approaches and arguments in favor of the approach adopted here.) 7Huddleston and Pullum (2002) also include an “initial” case, in which the reflexive occurs at the beginning of the sentence, as in (17). However, these reflexives seem more cataphoric and thus may be better categorized as override reflexives according to the diagnostics presented here; future work will determine their exact classification. (17) Myself, I slid on out of there grinning like a jackass at how grateful the cowboy would be.

15 2.1. Survey of the range of reflexives

b. exclusive: He had edited every word himself. optional by: He had edited every word by himself.

However, the real difference seems to hinge on the adverbial’s relation to alternatives: inclusive adverbials are agnostic about alternatives to the denotation to which the reflexive refers, while exclusive adverbials exclude any possible alternatives. For instance, in (19a), the adverbial only indicates that the male under discussion (he) lacks intelligence experience, but does not provide any information about anyone else’s credentials. In contrast, in (19b), the adverbial (under the exclusive reading) indicates that he edited every word and specifically implies that no one else did any editing. The version of (19b) including by is sometimes classified separately as a predicate PP adjunct. However, it seems logical to classify these particular manner adjuncts as intensifiers since they alternate with exclusive adverbials in structure (including or omitting by) yet maintain the same meaning.8 Additional motivation is discussed in Section 2.3.1. Since inclusive and exclusive adverbials can appear in the same positions, the corpus study revealed that a sentence can ambiguously have both an inclusive and an exclusive reading:

(20) You didn’t have the stomach to do it yourself. inclusive: You didn’t have the stomach to do it either/too. exclusive: You didn’t have the stomach to do it by yourself.

The definition of intensifiers I adopt follows the literature as described above. Intensifiers consist of both adnominals, which are adjuncts occurring immediately after a DP, and adverbials, which are adjuncts to a VP. Adverbials can further be divided into inclusive and exclusive, the latter of which alternates between a manner adjunct version and a plain adverbial form. Intensifiers clearly differ from reflexive anaphors because intensifiers cannot occur in argument position, but are restricted to adjunct positions instead. As a result, intensifiers can be omitted from the sentence without altering the sentence’s , while reflexive anaphors cannot. Finally, intensifiers strictly serve as emphatics, generally to evoke a contrast, whereas reflexive anaphors can be emphatic but are not required to be.

2.1.3O VERRIDE REFLEXIVES

The final main kind of reflexive is the least understood despite the vast amount of literature devoted to trying to define it. I refer to this kind as an override reflexive (Huddleston and Pullum, 2002), although a variety of

8This idea comes from Storoshenko (2008), who suggests that manner adjuncts have a “canonical” form, using by, and a “derived” form, in which by is omitted.

16 Chapter 2. The Forest: Understanding the Data other names are often used, including “exempt reflexive” (Pollard and Sag, 1992a), “untriggered reflexive” (Parker et al., 1990), “locally free reflexive” (Baker, 1995), “long-distance-bound reflexive” (Zribi-Hertz, 1989), and “logophoric reflexive” or “logophor” (Cantrall, 1974; Kuno, 1987; Charnavel and Sportiche, 2016, among many others). Each of these names caters to a different aspect of this kind of reflexive yet none seems to capture the entire distributional range. The remainder of this section is devoted to defining each reflexive name above and the distribution captured, as defined by the authors cited.

2.1.3.1E XEMPT REFLEXIVES

“Exempt” has been commonly used as an umbrella term for any reflexive appearances that are not expected under Chomsky’s (1981) Binding Theory. Sometimes exempt reflexives are generalized to be all those that appear in non-argument position (Pollard and Sag, 1992a). These reflexives are thus declared “exempt” from the theory’s constraints on reflexives. However, neither of these descriptions is adequate to account for the difference between reflexive anaphors and override reflexives (let alone distinguish these from intensifiers). A key problem with the Binding Theory approach is that reflexives and pronouns are assumed to be in complementary distribution (according to Conditions A and B). However, the acceptability of both a pronoun and reflexive in (21a) shows that pronouns and reflexives do not always contrast. A problem with considering exempt reflexives to be only those in non-argument position is that sometimes override reflexives occur in argument position even if they are not bound by a local antecedent, as in (21b). Also, intensifiers clearly appear only in non-argument position.

(21) a. In the darkness of the house, the woman could not make out any object or human form but sensed its presence near herself (/her).

b. The fact that Paul had nominated myself for the position didn’t please Frank. (Huddleston and Pullum, 2002)

2.1.3.2U NTRIGGERED REFLEXIVES

“Untriggered” relates to the subset of override reflexives that are not coreferential with another DP, such as those in (22), which are quoted in Parker et al. (1990). These sentences crucially do not contain an antecedent for the reflexive. As a result, they tend to be most acceptable in first and second person since the speaker or hearer can serve as a salient but covert antecedent. Untriggered reflexives do not describe the same distribution as exempt reflexives because exempt allow the possibility of a sentence-internal

17 2.1. Survey of the range of reflexives antecedent, as in (21a), while untriggered do not. Additionally, the definition of untriggered reflexives appropriately does not exclude those in argument position.

(22) a. Several of the employees and myself wrote to the chairman.

b. There are groups for people like yourself.

c. This is a photo of myself about five years ago.

2.1.3.3L OCALLY FREE REFLEXIVES

“Locally free reflexives”, as defined by Baker (1995), refer to reflexives that do not have a syntactically prominent local antecedent. In all of the sentences in (23), the reflexive is in a separate clause from its antecedent, and thus the reflexive is locally free. Since the reflexive is still within the sentence, though, these reflexives are not “untriggered”. Since the reflexive in each sentence can grammatically be replaced with a pronoun and since the reflexive is sometimes in argument position, locally free reflexives do not define the same distribution as exempt reflexives.

(23) a. Tom believed that [ the paper had been written by Ann and himself ]. (Ross, 1970)

b. John thinks that [ Mary is taller than himself ]. (Zribi-Hertz, 1989)

c. Mary complained that [ the teacher gave extra help to everyone but herself ]. (Keenan, 1988)

Baker (1995) additionally claims that locally free reflexives have a contrastiveness requirement, which fits with his classification of this kind of reflexive as an intensified non-nominative pronoun. However, as König and Siemund (2000a) point out, not all reflexives that are locally free exhibit contrastiveness:

(24) Bill said that the rain had damaged the pictures of himself. (adapted from Pollard and Sag (1992a); quoted in Charnavel and Zlogar (2015))

2.1.3.4L ONG-DISTANCE-BOUND REFLEXIVES

“Long-distance-bound (LDB) reflexives”, as described by Zribi-Hertz (1989), are similar to “locally free reflexives” in that they comprise those reflexives that are not locally bound; however, they differ by appealing to (which is discussed in detail in the next section), rather than intensification, and considering different persons separately. In other words, a distinction is made between first and second persons on the one hand, and third person on the other hand: although a reflexive must always have an

18 Chapter 2. The Forest: Understanding the Data antecedent within its , only first and second persons can have an implicit antecedent whereas third person reflexives must have an explicit antecedent. This contrast is exemplified in (25), in which (a) myself lacks a lexical antecedent within the sentence and (b) himself is bound by he (or by a null subject for single false step). (The corpus study probes further into differences among reflexives by person in Section 2.3.2.2.)

(25) a. Mary thought that [ a picture of myself ] would be nice on the wall. (Zribi-Hertz, 1989)

b. Watched as he was by countless enemies at home and abroad, [ a single false step would have brought ruin and disgrace on himself ]. (Encyclopaedia Britannica, 11th ed.; quoted in Zribi-Hertz (1989))

2.1.3.5L OGOPHORIC REFLEXIVES

Lastly, “logophoric reflexives” encode thought, speech, or perception from a subject of consciousness9 (Cantrall, 1974; Kuno, 1987; Zribi-Hertz, 1989; Reinhart and Reuland, 1993).10 In other words, if a reflexive is bound by a conscious entity within the discourse, then it is a logophor. Logophors usually occur in the subject position of a clause embedded under verbs of communication, cognition, psychological states, or perception, as in (26a) (König and Siemund, 2000a); however, they can also appear in object position, as in (23). Additionally, they can have an antecedent in a previous sentence, as in (26b), or no antecedent at all (in first and second person) as long as they express some salient entity’s perspective, as shown in (25a).

(26) a. John said to Mary that physicists like himself were a godsend. (Kuno, 1987)

b. John was furious. The picture of himself in the museum had been mutilated. (Pollard and Sag, 1992a)

Due to the restriction of logophors to express a perspective, Zribi-Hertz (1989) states that the subject of consciousness must be “human”, or in the case of itself as in (27), semantically human.

(27) But, aside from this, the familyi was keenly conscious of the way in which such an estrangement

would react on itselfi. (Zribi-Hertz, 1989)

9The term “subject of consciousness” is from Banfield (1979) and was adopted (and made popular) by Zribi-Hertz (1989). 10Reinhart and Reuland (1993) use the term “logophor” differently from the others cited, as a for “exempt”, representing both “emphatic” (in Zribi-Hertz’s (1989) sense of the term as an argument position discourse focus reflexive; see footnote 14) and point-of-view non-argument position reflexives (in the logophoric sense as defined here). Due to the origin of the term logophor by Hagège (1974) to describe certain pronouns in West African and Central African languages that express point of view, I use logophor to refer only to reflexives under the influence of someone’s perspective.

19 2.1. Survey of the range of reflexives

Similarly, but in a more general sense, Charnavel and Sportiche (2016) claim that all logophors must be “animate”.11 Although Charnavel and Sportiche (2016, footnote 16) do not explicitly define their use of the word “animate”, they do admit that the distinction of animate versus inanimate is not precise enough since non-animate terms can be used as a proxy for people. Indeed, taking animate to mean semantically alive, conscious being is not enough, as (28) exemplifies. Here, the environment is exempt and the antecedent is a company (clearly inanimate), so a reflexive should not be allowed under this definition. The acceptability of the reflexive thus supports an extension of the concept of beyond humans to also include entities that express animate-like qualities. In (28), the inanimate antecedent AOL most likely represents the group of people who work for the company, and those employees are the ones who will build the new business.

(28) AOL will even build a new business selling software tools to businesses like itself that want to rack up sales on-line. (adapted from COCA)

However, there certainly does seem to be a contrast between the acceptability of animate (or human) and inanimate logophors, evidenced by the sentences in (29) provided by Charnavel and Zlogar (2015):

(29) a. Anonymous posts about herself on the internet hurt Lucy’s feelings.

b. * Anonymous posts about itself on the internet hurt the camera’s sales.

But this is not always the case, especially for sentences explaining mathematical concepts, as exemplified in (30). Here, the author is discussing the sigmoid function, claiming that there is a simple polynomial relationship between the derivative of sig(t) and sig(t) itself. The antecedent of the reflexive is sig(t), but it is not explicitly stated in the sentence. This reflexive is clearly exempt and inanimate, in any sense of the word. Although these examples are rare, they do exist, providing more evidence that animacy might not be sufficient to account for this third kind of reflexive (at least in English).

(30) This simple polynomial relationship between the derivative and itself is computationally easy to perform. (Wikipedia entry (since changed); quoted in Zwicky (2007)) meaning: This simple polynomial relationship between the derivative of sig(t) and sig(t) itself is computationally easy to perform.

There are two more reasons that the term logophoric reflexive does not seem appropriate for describing the disjoint set of reflexives not captured under the terms reflexive anaphor and intensifier (as defined

11Charnavel and Sportiche (2016) in fact go further, claiming that animacy is a necessary condition for all exempt reflexives and thus all exempt are in fact logophoric.

20 Chapter 2. The Forest: Understanding the Data here).12 First, any local, argument position reflexive anaphor can also be logophoric if it expresses someone’s point of view. In (31a), the sentence is expressing the viewpoint of Noah, and himself refers to Noah, so the reflexive is a logophor; however, since the reflexive is locally bound by its antecedent, this reflexive is in fact a reflexive anaphor, not an override reflexive. Second, not all override reflexives are in fact logophoric. In (31b), the reflexive is not in a local configuration with its antecedent and the statement containing the reflexive comes from the perspective of a third party—the solicitors—who are not the referent of the reflexive. The sentence is not logophoric since the reflexive does not refer to the one presenting a perspective.

(31) a. logophoric reflexive anaphor: Noahi thinks that hei should introduce himselfi. (constructed)

b. non-logophoric override: He goes because of ‘an irretrievable breakdown’ between the board of the company and himself, according to the official announcement issued by Irwin Mitchell, the company’s solicitors. (; quoted in König and Siemund (2000a): 22c)

Therefore, a logophor differs from an exempt reflexive because a logophor can be in an argument or adjunct position, while an exempt reflexive is generally considered to only be in an argument position. A logophor differs from an untriggered reflexive because a logophor can have a local (or non-local) antecedent, whereas untriggered refers only to reflexives lacking an antecedent. A logophor differs from a locally free reflexive because a logophor does not have to have an antecedent in the sentence and it does not have to evoke a contrast. Finally, even though long-distance-bound reflexives are fundamentally the same as logophors since both rely on point of view (according to the definition used here), long-distance-bound reflexives are separated here since they cannot be locally bound, while logophors can be free, non-locally bound, or locally bound.

In sum, despite the variety of names, none of these terms describe the same distribution of reflexives and none succeed in describing all reflexives that fall outside the of reflexive anaphors and intensifiers (as defined here). Having reviewed the subtle differences among the other names, I now present the motivation for using the term override reflexive.

12Zribi-Hertz (1989) may not in fact have intended long-distance-bound reflexives to be an all-inclusive account of this category of reflexive; later, Zribi-Hertz (1995) states that “logophoricity should not be regarded as a necessary property of locally-free himself ”.

21 2.1. Survey of the range of reflexives

2.1.3.6O VERRIDE REFLEXIVES

The term override reflexive, as used in Huddleston and Pullum (2002), was coined to represent cases in which a reflexive overrides the default pronoun to appear in a position in which it otherwise would not. This explains why this category of reflexives allows (with minor exceptions to be discussed in Section 2.3.1) a pronoun to also appear without a change in meaning. In fact, the acceptability of replacing a reflexive with a pronoun is the primary test I use for categorizing this kind of reflexive: if a pronoun is also acceptable in this position and does not change the meaning, the reflexive is an override reflexive. Huddleston and Pullum (2002) list the following environments and corresponding examples for override reflexives:

(32) a. coordination: Ann suggested that the reporter pay both the victim and herself for their time.

b. comparatives: They were all much better qualified than myself.

c. inclusion/exclusion: Everybody, including yourself, will benefit from these changes. Liz couldn’t understand why nobody except herself had complained.

d. as for: As for myself, it doesn’t worry me which one they choose.

e. how about: I enjoyed it—how about yourself?

f. of be: The only one they didn’t invite was myself.

g. complement of a preposition in predicative complement function: All Ann’s novels are really about herself.

h. nominative complements (pic-DPs): The Lord Mayor sighed. The portrait of himself newly presented to the gallery had been hung in an obscure alcove.

The benefit of the term override reflexive over the other terms is that override reflexives only depend on whether or not a pronoun can equally appear in lieu of the reflexive without a change in meaning. By not relying on syntactic configurations, contrastiveness, or logophoricity, reflexives can be cleanly divided into disjoint but exhaustive kinds, as I show in Section 2.3.1. With a clearer understanding of the terminology for the three kinds of reflexives, the next section reviews previous attempts to create a taxonomy of reflexives.

2.1.4P REVIOUS TAXONOMIES

The original classification of reflexives (and reciprocals) was Chomsky’s (1981) Binding Theory. Since then, others have defined finer-grained classifications, particularly focusing on reflexives since they are more

22 Chapter 2. The Forest: Understanding the Data

Reflexives

Abide by Cond. A Exempt from Cond. A

Reflexive Anaphor Intensifier Override

Figure 2.1: One version of the traditional taxonomy of reflexive kinds

complex. In this section, I first present the traditional Binding Theory view and then discuss three of the other reflexive taxonomies—that of Huddleston and Pullum (2002), König and Gast (2002), and Storoshenko (2008).

2.1.4.1T RADITIONALVIEW

Much of the early work on reflexives focused on whether or not a reflexive was captured under (some version of) Binding Theory. If the reflexive fell within the scope of the appropriate domain, it was considered a “true” reflexive; if it did not abide by the binding constraints, it either motivated an adjustment to the binding conditions (picture-DPs), or was considered “exempt” from Binding Theory and disregarded. One version of this traditional taxonomy, based on Chomsky’s (1981) Binding Theory, is shown in Figure 2.1. At the higher level (boxed labels), reflexives are split between those that abide by Condition A and those that are exempt from Condition A (by being grammatical but not abiding by the constraints of Condition A). A reflexive abides by Condition A if it is bound (c-commanded) in its binding domain, which (for the present purposes) is the smallest clause containing the reflexive, its case assigner, and a higher subject. The lower level of classification has more variation across sources depending on the aspect of reflexivity being investigated. Here, the reflexives that abide by Condition A are divided into reflexive anaphors, which are required to be an argument that is in an anaphoric, co-referent relation with its antecedent, and intensifiers, which appear in adjunct position but are still local and thus bound. Those exempt from Condition A are a collection of any reflexives that do not fit the right constraints and are referred to as override reflexives or logophors, among many other terms.

2.1.4.2H UDDLESTONAND PULLUM (2002)

Huddleston and Pullum (2002) categorize reflexives primarily according to structural position. Figure 2.2 displays a hierarchical representation of their reflexive kind classification. Reflexives are first divided into

23 2.1. Survey of the range of reflexives

Reflexives

Complement use Emphatic use

Basic Override

Mandatory Inadmissable Optional

Figure 2.2: High-level representation of Huddleston and Pullum’s (2002) classification of reflexives

either complement use (complement of a verb or complement of a preposition) or emphatic use (adjunct in clause structure or modifier in DP structure). Examples of the former are in (33) and of the latter are in (34).13

(33) a. complement of verb: Rhiana feeds herself now.

b. complement of preposition: Liz talks to herself.

(34) a. adjunct in clause structure: Rhiana wrote the report herself.

b. modifier in DP structure: Liz herself presented the prize.

Complement use reflexives can be further divided into basic reflexives and override reflexives. Basic reflexives comprise mandatory reflexives (35a), inadmissable reflexives (35b), and optional reflexives (35c).

(35) a. mandatory: Anni blames herselfi/*heri for the accident.

b. inadmissable: Anni realizes that they blame *herselfi/heri for the accident.

c. optional: Anni tied a rope around herselfi/heri.

As seen in Figure 2.2, optional reflexives can also be classified as override reflexives (same meaning as my use of the word, as defined in Section 2.1.3.6). The authors’ classification system is thus not disjoint across categories. Basic optional reflexives require a “close structural link” between the reflexive and antecedent, manifested through being related to the same verb (36a), being related to the same noun (36b), or being related through a verb and a noun (36c).

(36) a. verb domain: Sue defended herself.

b. noun domain: They rejected Ed’s representation of himself as a victim.

13All examples in this subsection are taken from Huddleston and Pullum (2002).

24 Chapter 2. The Forest: Understanding the Data

c. verb-noun domain: Max found a photograph of himself in Jill’s wallet.

Override reflexives, always optional, do not have this same close link with their antecedent. One test the authors propose for distinguishing between basic reflexives and override reflexives is that only override reflexives can occur purely deictically (with no anaphoric link to the antecedent). Another test is that reciprocals can occur in only basic reflexive environments, not in environments that allow override reflexives. For the other reflexive use—the emphatic use (the equivalent of intensifiers)—reflexives occur in four positions, as shown in (37), either as a modifier in DP structure (first position) or as a clausal adjunct (other three positions).

(37) a. modifier in DP structure: I myself do not regard it as important.

b. clause adjunct - front: Myself, I do not regard it as important.

c. clause adjunct - central: I do not myself regard it as important.

d. clause adjunct - end: I do not regard it as important myself.

Huddleston and Pullum (2002) go on to discuss two meanings of clausal adjuncts, referred to as inclusive and exclusive adverbials in other literature. The authors relate the exclusive meaning to the overt by manner adjunct version, but do not explain further. This reflexive kind has an important effect on the taxonomy, though. One possible categorization is that manner adjuncts fall under complement use reflexives since the reflexive is the complement of the preposition by; however, since the by is optional, the overt by version would then be classified in a completely different type from the omitted by version, which does not seem ideal considering they have the same meaning and the use of the preposition is usually stylistic preference. The other possible classification is that these manner adjuncts fall under emphatic use reflexives since their meaning is the same and the only difference is the inclusion or exclusion of the preposition. This scenario, though, means that emphatic use reflexives can appear in complement position, which dissolves the neat separation between reflexive kinds.

2.1.4.3K ÖNIGAND GAST (2002)

König and Gast (2002) distinguish three kinds of reflexives: “reflexive pronouns (anaphors)”, “intensifiers”, and “untriggered self -forms”. Reflexive pronouns (anaphors) occur in argument positions of transitive verbs and are co-referent with an antecedent. In contrast, intensifiers occur in adjunct position to a DP and are not

25 2.1. Survey of the range of reflexives

Figure 2.3: Taxonomy from König and Gast (2002) (Figure D3 in the paper) showing a tertiary split for the three main kinds of reflexives; double arrows represent shared features between two kinds.

co-referential with their antecedent. A further distinguishing factor between these two kinds is that they can have different translations in other languages, such as si/sé (reflexive pronoun (anaphor)) versus stesso (intensifier) in Italian. Untriggered self -forms occur in argument positions, can be replaced by a pronoun, and do not have an antecedent in the same clause. The authors claim that this kind of reflexive falls in between reflexive pronouns (anaphors) and intensifiers in the taxonomy because it shares properties with both. As a result, their taxonomy of reflexives branches three ways equally, as in Figure 2.3.

2.1.4.4S TOROSHENKO (2008)

Storoshenko (2008) conducted a corpus study comparing the coverage of Chomsky’s (1981) approach (syntactic structure manifested in Condition A) with Reinhart and Reuland’s (1993) approach (predicate structure manifested in Principles A and B) of naturally occurring reflexives. In the process, he found frequencies for ten different categories of reflexives, all based on syntactic position, in both spoken (Switchboard) and written (Wall Street Journal) data. The categories included positions such as the canonical (in argument position and co-referential with a coargument of its verb), biclausal (including raising and control), picture noun phrase, exempt (replaceable by a pronoun), appositive, and manner adjunct, among a few others. The study concluded that both syntactic structure and predicate structure play a role in accounting for the variety of naturally occurring reflexives. The study was a useful preliminary investigation into empirical reflexive behavior and determined a need for further research into intensifiers, specifically adverbials. With this survey of the various kinds and taxonomies of reflexives as a foundation, the next section

26 Chapter 2. The Forest: Understanding the Data introduces my empirical study, the data I consulted, and the methods I used to test these theories.

2.2C ORPUS OVERVIEW

The reflexive corpus analysis sought to satisfy three main goals: (i) to test the descriptive adequacy of research on reflexives and identify any cases that do not seem to fit with previous descriptions, (ii) to create a disjoint and exhaustive taxonomy of attested English reflexives, and (iii) to examine finer-grained distinctions that have either not been thoroughly discussed (to my knowledge) or do not have a consensus in the literature.

2.2.1D ATA

This project used the full text of the Corpus of Contemporary American English due to its size, genre breadth, and represented years in order to obtain the most comprehensive and accurate assessment of the distribution of reflexives. COCA is currently the largest available balanced corpus of American English. The version I used (obtained early December 2017) encompassed the years 1990 through 2015 and contained 440 million words14 spread across the genres of spoken, fiction, magazines, newspapers, and academic sources (Davies, 2008). The spoken genre contains transcripts of unscripted conversation on over 150 television and radio programs. The fiction genre comprises short stories and plays from magazines, books, and movie and televisions scripts. The magazine genre (100 total) ranges across topics in news, health, finance, religion, and beyond. The newspaper genre includes eighteen newspapers, such as USA Today and the New York Times, and lastly, the academic genre consists of 100 journals with balanced coverage of each topic, such as education and technology. I did not annotate reflexives for genre or time period in this study since the focus was on the descriptive use of reflexives in general across all the available genres and time periods.

2.2.2M ETHOD

In order to focus exclusively on reflexives, I wrote a Python script to automatically extract sentences containing each reflexive (myself, yourself, etc.) from the corpus. Each such reflexive was exported to a separate Excel spreadsheet and the sentences were automatically randomized. In order to annotate the reflexives, I consulted, compared, and conflated previous literature. The first round of annotation made use of the classifications of Huddleston and Pullum (2002), König and Gast (2002), and Storoshenko (2008) (as

14As of late December 2017, COCA expanded to include data from 2016 and 2017, which boosted the word count to over 560 million.

27 2.3. Survey and corpus results described in Section 2.1.4). After annotating sentences of a few different reflexives according to these three classifications, I developed a hybrid classification system of reflexive kind and type that also incorporated categories motivated from the data. The results presented in this chapter are from the final classification system, which is described in Section 2.3. Seventy-five sentences of each reflexive were annotated for the hybrid classification of kind (reflexive anaphor, intensifier, override reflexive) and type (e.g. argument of verb, argument of noun, adnominal, adverbial), as well as for aspects such as function (e.g. argument of a transitive/intransitive/, inclusive/exclusive adverbial), more detailed contextual information (e.g. within a /appositive/cleft construction), antecedent (overt/covert), and other features specific to the φ features of the reflexive. If a sentence contained more than one reflexive, only one reflexive token was assessed.15

Next, I counted the occurrences of reflexive anaphors, intensifiers, and override reflexives. (The distribution of reflexive kind for each reflexive is displayed in Figure 2.5 and discussed in the next section.) I conducted a Fisher’s exact test on relevant reflexive comparisons using R to determine the significance of the differences. Due to the small numbers of intensifiers and override reflexives, I chose a Fisher’s exact test, instead of a chi-square test for instance, to maintain consistency across all significance tests. I used a post-hoc pairwise Fisher’s exact test with a significance threshold of 0.05 to compare each reflexive to every other. Since this comparison was decided after viewing the results, I used a Bonferroni correction to adjust for the number of all possible pairs to reduce type I error.

2.3S URVEY AND CORPUS RESULTS

In this section, I present the findings of intersecting the literature survey with the empirical corpus search. First, I explain the new taxonomy and motivate the reasoning behind this classification. Then, I discuss the distribution of reflexive kinds for each reflexive, highlighting any statistically significant differences. Finally, I turn to the distribution of reciprocals.

2.3.1A NEW REFLEXIVE TAXONOMY

As mentioned in Section 2.1.4.1 and shown in Figure 2.1, traditionally Binding Theory classified reflexives as those that obey Condition A and everything else was classified as exempt. However, based on the literature review, previous taxonomies, and corpus examination, it seems more effective to categorize

15Only one reflexive token was analyzed since often sentences with multiple reflexives repeated the same kind of reflexive in a list, which would skew the overall count of that particular kind of reflexive.

28 Chapter 2. The Forest: Understanding the Data reflexives according to a different metric.

The literature review revealed that there are three main features of reflexives discussed: the distance between a reflexive and its antecedent (locality), the reflexive’s structural position (syntactic constraints), and some kind of relation between reflexives and pronouns (distribution). For the first feature, this comes down to whether or not the antecedent is local to, or binds (in some way), the reflexive. For the second, the structural position can refer broadly to whether the reflexive is an argument or adjunct, or more specifically to syntactic configuration such as biclausal, copular complement, or adverbial. For the third feature, the discussion primarily focuses on the complementarity of the distribution of pronouns and reflexives (or lack thereof).

The corpus study distinguished the three main kinds of reflexives and examined the relations among them. Out of the three main features, the only one that seems to cleanly separate the reflexive kinds into disjoint categories is the relation between the reflexive and a pronoun. (Again, a disjoint classification is desirable because it affords an unambiguous labeling of reflexives and the ability to run statistical tests on any patterns in the data.) The locality feature is not sufficient for distinguishing the three kinds because reflexive anaphors, intensifiers, and override reflexives can all be local to their antecedent. Intensifiers and reflexive anaphors (according to most definitions) are required to be local. Previous work has often claimed that override reflexives are only non-local to their antecedent; however, local cases of override reflexives do exist, examples of which I found in COCA:

(38) He kept the clay and the button and when he’d added water the clay could be made into things, into a ball or round and flat and when he pressed the button there it left another button like itself.

The antecedent it is clearly local to the reflexive, but the environment of the reflexive is a common override environment, as mentioned by Huddleston and Pullum (2002), and confirmed by the grammaticality of the pronoun it in the reflexive’s place. Thus, locality does not differentiate the three reflexive kinds.

Similarly, syntactic configurations, such as whether the reflexive is an argument or adjunct, are also not sufficient for distinguishing reflexive kinds. Intensifiers strictly occur as adjuncts, and depending on the theory, reflexive anaphors may occur only as arguments or as both arguments and adjuncts. Override reflexives, though, can be both arguments and adjuncts, as discussed in Section 2.1.3, so basing the taxonomy on syntactic position is not sufficient. If using a finer-grained classification, such as whether the reflexive occurs as the argument of a transitive/raising/control verb or within a PP adjunct, the classification becomes even hazier.

Fortunately, pronouns can play the needed role. Figure 2.4 shows how the interaction of reflexives and

29 2.3. Survey and corpus results

Reflexives

pronouns ungrammatical pronouns grammatical

Intensifier different meaning same meaning

Adnominal Adverbial Reflexive anaphor Override Reflexive

Inclusive Exclusive

Figure 2.4: New taxonomy of the kinds of reflexives (in boxes) and the types of reflexives (below the boxed kinds)

pronouns is in fact quite informative for distinguishing the three main kinds of reflexives. Looking first at the reflexive kinds (boxed), this taxonomy branches in a completely different way from the original Binding Theory taxonomies, first separating out intensifiers, and then distinguishing between reflexive anaphors and override reflexives. The taxonomy should be read similarly to a decision tree in which an italicized label indicates a distinguishing feature of all items on that branch. This taxonomy differs from others in the literature because it is based on the relationship (grammatical interaction) between reflexives and pronouns16, while other taxonomies focus on the syntactic distribution of reflexives (or sometimes the semantics of reflexives).

2.3.1.1I NTENSIFIERS

Starting from the root of the hierarchical tree, the first distinguishing characteristic is whether or not replacing the reflexive with a pronoun leads to grammaticality or ungrammaticality. To judge grammaticality, it is assumed that the analysis of the syntactic structure under investigation is preserved; in other words, each specific analysis or structure (e.g. intensifier, reflexive anaphor, or override) is tested for grammaticality individually, rather than testing the raw grammaticality of the sentence (under any analysis and structure) overall. For instance, if testing the reflexive in (39a) for pronoun replacement, each possible reflexive kind must be analyzed separately. First, testing himself used as an intensifier (thus hug here is intransitive), as paraphrased in (39b), replacing the reflexive with a pronoun leads to ungrammaticality under the intensifier analysis since intransitive hug now has a direct object. In contrast, testing himself used as an argumental reflexive anaphor (thus hug here is transitive), as paraphrased in (39c), results in

16I am not making any claims here about the distribution of pronouns.

30 Chapter 2. The Forest: Understanding the Data grammaticality (although the meaning changes, which I will return to shortly).

(39) a. intensifier: Noah doesn’t like to hug himself. (constructed) test: Noah doesn’t like to hug him.

b. intensifier paraphrase: Noah himself doesn’t like to hug.

c. reflexive anaphor paraphrase: Noah doesn’t like to give himself a hug.

Intensifiers are thus differentiated in the left branch of the taxonomy by their inability to be replaced by pronouns, which seems logical given that intensifiers are not referential anaphors but are focus constructions (König and Gast, 2002). Continuing along this left branch yields the different types of intensifiers, as defined in Section 2.1.2. The first split is based on syntactic position: adnominals occur immediately after the antecedent they emphasize, while adverbials occur elsewhere in relation to their antecedent. Adverbials can then be further divided based on meaning into inclusive or exclusive.

2.3.1.2R EFLEXIVE ANAPHORS

Turning to the right branch of the tree, all reflexives on this side are replaceable by pronouns, but are further split into whether the pronoun changes the meaning of the sentence. As seen in (39a), replacing a reflexive anaphor with a pronoun necessarily results in a completely different meaning: instead of Noah not liking to hug himself, Noah doesn’t like to hug some other male individual. Reflexive anaphors thus exhibit the complementary distribution with pronouns that the original Binding Theory attempted to capture. A few examples of reflexive anaphors were provided in (13), but Table 2.1 contains a list of the final categorization of reflexive anaphor by type and function.17 This selection is inspired by the taxonomies discussed in Section 2.1.4 but adjusted based on empirical findings from the corpus study described in Section 2.2. As mentioned previously, since reflexive type does not divide reflexives into disjoint kinds (since both reflexive anaphors and overrides can have these types), they are not included in the taxonomy. The table is divided into three main sections based on reflexive type. The first type is when reflexives appear in the argument position of the verb. The syntactic function of the reflexive was labeled transitive only if the reflexive served as the direct argument of the verb of which the antecedent was the subject.18 The

17Every example of reflexive anaphor found in the corpus is categorized as one of these types; unclear or borderline cases reflect more of an indecision on behalf of the annotator rather than a missing category among this list. 18Following König and Gast (2002), I separate inherent, or obligatory, reflexive verbs, as in (40), from my taxonomy because the only possible object of these verbs is a reflexive and they seem to be fixed expressions, and thus somewhat idiomatic. (40) ...and some people availed themselves of the opportunity to get up, pick up their gear and leave.

31 2.3. Survey and corpus results

Type Syntactic Function Example Sentence argument of transitive They throw themselves behind parked cars. a verb I cried myself to sleep.

within an argument First and foremost, you have to believe in yourself.

ditransitive (DO/IO) Through blind trusts he would ultimately give him- self 85,000 acres of public land...

argument of I am myself around you.

argument of nominal complement snapped a picture of herself. (constructed) a noun (uses of)

adjunct PP adjunct (of V/N) When you do things kinda worthwhile...it makes you (uses prepo- feel good about yourself. sitions other than of)

Table 2.1: Exhaustive list of syntactic environments of reflexive anaphors represented in the corpus search

32 Chapter 2. The Forest: Understanding the Data second function is a resultative, a reflexive functioning as the argument of an . The within an argument label applied to reflexives appearing as the object of a verb and preposition that function as a unit, as described in Section 2.1.1. For ditransitives, the reflexive appeared as either the direct object or indirect object. Finally, the argument of the copula category, following Storoshenko (2008), contained reflexives appearing as a complement to the copula. The second type contains any reflexive that appears in a nominal complement, which I defined specifically based on the presence of the preposition of. This type includes only those reflexives that could not be replaced by a pronoun and maintain the same meaning. The final type contains reflexives within PP adjuncts that crucially had any preposition other than of. These also had to pass the pronoun replacement test. I discuss the types in both of these sections in more detail in the next subsection.

2.3.1.3O VERRIDE REFLEXIVES

The final kind of reflexive is the one that when replaced by a pronoun maintains the original meaning. Override reflexives thus share properties with pronouns. For example, both reflexives and pronouns can be an argument or adjunct (or within an argument or adjunct). In addition, the antecedent can be non-local (in one sense or another) to the pronoun or override reflexive and there may not even be an antecedent (other than deictically or from discourse). As a result, override reflexives nicely encompass all of the distributions described by the various terms for this reflexive kind. They do not discriminate against reflexives in certain , which allows override reflexives to appear in any configuration, and do not rely on the presence or absence of a local or non-local antecedent. Two of the syntactic cases that are most problematic for reflexive theories are reflexives appearing in nominal complement (picture-DPs) position and those in PP adjuncts: in some instances, only a reflexive is grammatical while in others both a reflexive and a pronoun are allowed. For instance, in (41a), both a reflexive and a pronoun are grammatical within the nominal complement construction, while in (41b), only the reflexive is allowed. The syntactic configuration is nearly equivalent (and could be made equivalent without changing the effect), yet the acceptability of the pronoun differs between the two.19

(41) a. They’re seeing part of themselves/them in her.

19A preliminary explanation for the difference in grammaticality between the two is that if the picture-DP means some kind of representation of the antecedent, such as picture of, photo of, version of, or even a subset of the representation, such as part of, then the reflexive is optional and a pronoun could also appear. If the nominal complement expresses a different relation between the reflexive and the antecedent, though, such as sense of or opinion of, then the reflexive seems to be mandatory. However, a much more exhaustive search through the corpus is needed to determine how robust this observation is.

33 2.3. Survey and corpus results

b. As infants begin to gain a sense of themselves/*them as bounded entities, they begin to experience the care of the adults around them...

The same is true for reflexives in PP adjuncts, such as in (42b). Relying on a syntactic-based theory would thus have to appeal to another constraint in order to account for these differences. Classifying reflexives only according to pronouns avoids these problems, while still providing a descriptive categorization.

(42) a. To seek health in a sick world we can not just build a wall around ourselves/us.

b. Noah told a story about himself/*him. (constructed)

More motivation for grouping reflexives according to their interaction with pronouns comes from the classification of by manner adjuncts. These manner adjuncts do not pass the pronoun replacement test, exemplified by the contrast in (43). Therefore, they should be classified as intensifiers and cannot be reflexive anaphors or override reflexives. Based on their shared meaning with exclusive adverbials and the only difference between the two being the presence or absence of by according to stylistic choice, they do seem to best be classified as intensifiers.

(43) He had edited every word (by) *him/himself.

As a side note, by myself is not always an exclusive adverbial manner adjunct intensifier, though; it can also appear as a copular complement, such as in (44). Although by myself in these cases means “alone” and cannot grammatically be replaced by a pronoun (thus indicating it is an intensifier), upon closer examination it does not share other features with intensifiers. For instance, if the word by is omitted (the test for exclusive adverbials), the sentence is no longer grammatical (at least under this particular meaning). In addition, the reflexive functions as an argument (object of the preposition), not an adjunct, which indicates it might be a reflexive anaphor or override reflexive instead. However, it cannot be a reflexive anaphor because, as seen in (44b), the reflexive does not always have an antecedent in the sentence. It also cannot be an override reflexive because the reflexive cannot be replaced by a pronoun. As a result, this kind of by myself does not seem to fall into any category of reflexive kind, regardless of criteria for classification; instead, it seems to function as an idiom, a fixed phrase indicating not the manner in which something is done, but the non-reflexive meaning “alone”. This reasoning is supported by other copular complements containing reflexives, such as (44c). Since even in other examples the copular complement seems more like an idiomatic fixed expression, these cases can be considered a separate phenomenon.

(44) a. I was by myself.

34 Chapter 2. The Forest: Understanding the Data

b. It was about five months with audio tapes and videotapes, and just trial and error by myself in a room.

c. Sasha was beside herself with excitement...

One exception to the pronoun replacement test for determining override reflexives, though, involves the third person reflexive itself and its corresponding pronoun it. As seen in the sentences in (45), the reflexive appears in typical override environments (as listed in Section 2.1.3.6), but the pronoun does not sound nearly as acceptable (if acceptable at all) as pronouns in other override examples. An interesting observation, though, is that if it/itself is replaced with a different pronoun/reflexive (such as me/myself or him/himself ), and the sentence altered slightly for semantic continuity, the sentences sound much better and seem to conform to the typical override category.

(45) a. Your future is empty—there is nobody in it, nothing—nothing except it/itself!

b. The World Bank shifted its lending to keep creditors, including it/itself, at bay.

c. This is one way—perhaps the only way—for a lowly being such as it/itself to be in touch with the supreme power.

A likely reason for this is that the word it is phonologically light, both in general and specifically in comparison to itself. Therefore, it avoids nuclear stress; however, in these sentences, stress falls on the position of the pronoun. As a means of avoiding stress on a light particle, the reflexive itself appears instead as a phonologically heavier and more qualified option. Other pronouns such as me and him are heavier than it, so sound better in these positions and do not create as much of a dissonance. As a result, the preference for itself over it does not seem to pose a problem for the classification system.

2.3.1.4C OMPARISON WITH OTHER TAXONOMIES

This proposed taxonomy differs from the three main taxonomies presented in Section 2.1.4—those of Huddleston and Pullum (2002), König and Gast (2002), and Storoshenko (2008)—in a few crucial ways. First, it differs from all three by classifying reflexive kind purely based on the reflexive’s relation to a pronoun, both syntactically and semantically. König and Gast (2002) do not mention pronouns whatsoever, purely describing reflexives in regards to their syntactic environment, which does not create a disjoint and exhaustive classification. Storoshenko (2008) does mention that override (what he calls exempt) reflexives are replaceable with a pronoun, but does not distinguish between intensifiers and reflexive anaphors and

35 2.3. Survey and corpus results

80

60

40 % Occurrences

20

0 myself yourself himself herself itself oneself ourselves yourselves themselves

Reflexive Anaphor Intensifier Override Reflexives

Figure 2.5: Distribution of reflexive kinds for each reflexive

simply provides a list of reflexive environments found in his corpus search. Huddleston and Pullum (2002) do mention a complementarity with pronouns, specifically that pronouns compete with complement use reflexives, but do not have a comparable emphatic use so do not compete with emphatic use reflexives.

The taxonomy I propose most closely aligns with Huddleston and Pullum’s (2002) categorization, but the main difference is that Huddleston and Pullum’s (2002) is not disjoint, involving overlap across reflexive kind for mandatory and optional reflexives as well as for reflexive type across complement and emphatic use. While a disjoint taxonomy is not needed for observational adequacy, if descriptive adequacy or an application beyond theory, such as automating reflexive annotation, is desired, a disjoint classification is imperative.

In sum, this chapter’s taxonomy improves upon previous ones by providing a comprehensive, exhaustive, and disjoint taxonomy across all instances of reflexives found in the literature and corpus search. The next subsections present the significant statistical findings from the reflexive corpus study.

2.3.2R EFLEXIVE CORPUS FINDINGS

Based on the results of the reflexive corpus annotation, Figure 2.5 shows the percentage of each reflexive kind per reflexive. Two main research questions guided the investigation to determine any significant differences across the data: (i) Does the distribution of reflexive kind differ across reflexives? and (ii) Is there a significant effect of person on override reflexives versus non-override reflexives, as the literature claims? The next subsections describe the results found in response to these questions.

36 Chapter 2. The Forest: Understanding the Data

# of Reflexive Anaphors # of Intensifiers Itself 36 39 Non-itself 492 82

Table 2.2: A 2x2 contingency table of the count data for the distribution of reflexive anaphors and intensifiers for itself versus all other reflexives combined

2.3.2.1D IFFERENCES ACROSS REFLEXIVE KIND DISTRIBUTION

An immediate observation from the graph is that the distribution of reflexive kinds for itself, in particular reflexive anaphors versus intensifiers, clearly differs from that for the other reflexives. The results of a Fisher’s exact test determined that the distribution of reflexive anaphors and intensifiers for itself significantly differs from the distribution of reflexive anaphors and intensifiers for all non-itself reflexives (p < .001; odds ratio = 0.154). The odds ratio indicates that the magnitude of the effect is quite large: the ratio of reflexive anaphors to intensifiers for non-itself reflexives is over six times as large as the same ratio for itself.20 The count data for this test is displayed in the 2x2 contingency table in Table 2.2.

In order to determine which reflexives in particular differed, I conducted a post-hoc pairwise Fisher’s exact test with a Bonferroni correction across the distributions of reflexive anaphors and intensifiers for each reflexive. The resulting p-values of these comparisons are displayed in Table 2.3.

There are three interesting findings from this table. First, the distribution of reflexive anaphors versus intensifiers for itself differs significantly (p < .001) from that for all other reflexives except himself. One reason that itself seems to have more intensifiers than the other reflexives could be due to the vague and varied nature of a third person gender neutral pronoun. It is the most multi-functional pronoun, ranging from expletive use to weather/time use to idiomatic use. Its reflexive counterpart thus seems more likely to appear as an intensifier in order to help clarify and emphasize its exact referent. Looking specifically at the types of intensifiers, 72% of itself intensifiers are adnominals, used primarily for abstract or important entities such as identity, democracy, and life. Comparing this to another reflexive for , ourselves only has 25% of its intensifiers as adnominals. This suggests that itself may be more commonly used to emphasize a DP directly preceding, possibly to evoke a contrast. Since reflexives like ourselves already have a salient referent (the speaker and associated entities), emphasis or contrast might be unnecessary.

Turning to the intensifier types of himself, there is not a significant difference in this regard from itself, possibly because himself also has a higher number of adnominals (57%). Looking at the individual

20This was found by taking the inverse of the odds ratio.

37 2.3. Survey and corpus results

Table 2.3: The p-values for a post-hoc pairwise Fisher’s exact test with Bonferroni correction for the distribu- tion of reflexive anaphors and intensifiers across reflexives

Table 2.4: The p-values for a post-hoc pairwise Fisher’s exact test with Bonferroni correction for the distribu- tion of reflexive anaphors and non-adnominal intensifiers across reflexives adnominal intensifier sentences, many of the antecedents of himself refer to important or well-known people, such as God, the president, or other prominent leaders. One hypothesis is that itself and himself emphasize important entities so use adnominals, and thus intensifiers, more than other reflexives. To test this hypothesis, I conducted another pairwise Fisher’s test, this time comparing reflexive anaphors to non-adnominal intensifiers. The results are in Table 2.4: there are no longer any significant differences across reflexives when adnominals are excluded. Therefore, the higher use of adnominals by itself and himself seems to help account for their increased intensifier use overall. In fact, König and Siemund (2000b) propose an analysis of adnominal intensifiers in which an adnominal relates a center (its antecedent) to a periphery of alternative values to its antecedent. As a result, adnominals are more likely to occur with prominent or high rank figures (the Pope, the Queen) than with less specific and everyday characters (the waiter, the dog). Returning to Table 2.3, the second interesting finding is that the distribution for oneself significantly differs from that for himself (p < .001). The graph indicates that the rate of reflexive anaphors to intensifiers for oneself is much higher than that for himself. Looking more closely at the data, oneself almost always appears as a reflexive anaphor and is typically used to describe situations applying to a general group of

38 Chapter 2. The Forest: Understanding the Data

Table 2.5: The p-values for a post-hoc pairwise Fisher’s exact test with Bonferroni correction for the distribu- tion of intensifiers and override reflexives across reflexives

people or abstract concepts to which everyone can relate. Since oneself is usually vague, it makes sense that using intensifiers to emphasize something in particular would be rare. Himself and oneself thus serve the opposite purpose, which could help explain the statistical significance between them.

The third finding is that there is a significant difference between the distribution for yourselves and that for himself (p = .009). Similar to oneself, the graph shows that the rate of reflexive anaphors to intensifiers for yourselves is much higher than that for himself. One possible explanation is that many of the reflexive anaphors for yourselves were imperatives, which inherently carry emphasis. It could be that yourselves expresses emphasis using imperatives, which are classified as reflexive anaphors, whereas himself was more likely to be used as an intensifier for its emphatic uses. However, the statistical difference between the two is not as significant as the others, so there may not be an immediate explanation.

Turning specifically to the distribution of intensifiers versus override reflexives, I used a post-hoc pairwise Fisher’s exact test with a Bonferroni correction to identify any significant differences in distribution across reflexives. Table 2.5 contains the resulting p-values of these comparisons. The only significant differences occur with the reflexive itself, specifically in contrast to myself, ourselves, and yourselves. Referring once more to the graph in Figure 2.5, the reason for significance is due to the higher rate of intensifiers to override reflexives for itself, while that rate for myself, ourselves, and yourselves is much lower. As seen in the last test, itself has a high rate of intensifiers in general so one would expect the difference between intensifiers and override to be significant, especially in comparison to first and second person reflexives that are known to have a higher number of override reflexives. The number of overrides for itself is particularly low, because as discussed previously, most override reflexives seem to be animate, and itself generally refers to inanimates. This result segues into the next research question: Are there any significant differences in reflexive kind across reflexive person?

39 2.3. Survey and corpus results

# of Override # of Non-override Third person 5 370 Non-third person 21 279

Table 2.6: A 2x2 contingency table of the count data for the distribution of override reflexives versus non- override reflexive (reflexive anaphors and intensifiers) for third person and non-third person (first and second persons)

2.3.2.2D IFFERENCES ACROSS PERSON

Several sources (Huddleston and Pullum, 2002; Zribi-Hertz, 1989) have noted that override reflexives tend to occur more frequently in first and second person than in third person, but (to my knowledge) this hypothesis has not been tested empirically. The 2x2 contingency table in Table 2.6 shows the count data for override reflexives versus non-override reflexives (reflexive anaphors and intensifiers) for third person and non-third person (first and second persons). A Fisher’s exact test showed that the distribution of override and non-override reflexives is significantly different in third person than in first and second persons (p < .001; odds ratio: 0.1799).21 The odds ratio indicates a large effect size: the ratio of override to non-override reflexives for first and second persons is 5.5 times that ratio for third person. In order to determine specifically if override reflexives are more common in first and second person than in third person, though, a two proportion z test was performed, using the null hypothesis that the proportion of third person override reflexives is the same as the proportion of non-third person override reflexives. The result was significant (z = 4.03, which is greater than the table z-score for a 95% confidence interval, 1.96), so the null hypothesis is rejected. As a result, there is indeed a significant difference in the proportion of override reflexives between third and non-third person, with there being significantly more non-third person overrides than third person overrides. There are a variety of directions to pursue to further understand reflexives, which I discuss in Section 2.4. This concludes the preliminary investigation of reflexives, and I now finally return to reciprocals.

2.3.3R ECIPROCALS

Based on the literature and my preliminary corpus examination, reciprocals have a fairly straightforward distribution. There are only two versions of the English reciprocal: each other and one another.22 The

21I ran the test both including oneself and excluding oneself (the former of which is shown here); the result was significant in both cases. 22Once again, I only consider each other and one another, and exclude variations such as each...the other, which behave differently.

40 Chapter 2. The Forest: Understanding the Data prescriptive rule requires that each other be used when referring to two entities, while one another be used when referring to three or more. However, my preliminary corpus investigation into their distribution, as well as other previous investigations (Quirk et al., 1985; Swan, 1980, among others), reveal that this rule is largely ignored in practice. I also did not find any apparent differences between each other and one another in regards to the kinds of predicates with which they occur. Applying a similar schema as for reflexives—annotating for type and syntactic position—did not reveal any immediate interesting insights either, so I did not pursue reciprocals further.

2.4S UMMARY AND FUTURE WORK

The study presented in this chapter expands upon previous work by conducting a more comprehensive investigation of attested reflexive types and creating a subsequent reflexive classification based on the complementary (or non-complementary) relationship between reflexives and pronouns (both syntactically and semantically), rather than on syntactic structure or locality. This taxonomy improves upon previous ones by being exhaustive across all reflexives and creating disjoint kinds, which provides descriptive adequacy of reflexives in general and the possibility of more accurate reflexive classification and annotation.

Additionally, this study looked at individual reflexives and determined that the primary significant difference across reflexive kind distribution is between itself and the other reflexives, except himself. However, this contrast seems to at least partially rely on a higher use of adnominal intensifiers by itself and himself since there were no significant differences across reflexives when adnominals were excluded. The study also confirmed that override reflexives do seem to appear more in first and second person than in third person.

As mentioned in Section 2.1.2, further work is needed on examining adnominal and adverbial intensifiers, particularly in regards to their syntactic structure and semantic meaning. An opposing view to the one presented in this chapter is that intensifiers only comprise adverbials, and adnominals are simply a variant position of an adverbial (Storoshenko, 2011). Under this view, both adnominals and adverbials allow inclusive and exclusive readings, and specific features, such as predicate agentivity and interaction with scopal elements, determine when each reading is permitted. Examining the instances of adnominals and adverbials in the corpus in more detail could help determine which classification is most descriptively accurate. Since the writing of this chapter, more data has been annotated, which should be incorporated into the results here to help identify more robust patterns.

Another possible future direction for research is investigating the properties of the predicates with which

41 2.4. Summary and future work both reflexives and reciprocals occur. Since many aspects of reflexivity and reciprocity seem to depend on predicate structure and properties, a computational approach into whether there is a way to predict the kind, type, or meaning of an anaphor based on predicate features may be insightful. Lastly, using a computational approach to the pronoun replacement test, in which a model must predict whether a reflexive or pronoun occurs in the sentence, could be informative for the viability of automatic annotation of reflexive kind. I discuss a preliminary attempt at testing this idea in Chapter 6. In the next chapter, I narrow the scope from assessing the forest—the data—to introducing the individual trees that comprise the model, and then test the analysis on a variety of anaphor examples.

42 3 The Trees: Introducing the Model

In this chapter, I show how both reflexives and reciprocals can be captured in a unified way through the framework of STAG. First, I present an STAG analysis of the canonical reflexive (distributive reflexivity), based on a revision and simplification of Frank’s (2008) previous STAG analysis of reflexives. Then I show how the analysis immediately extends to capture the canonical reciprocal (strong reciprocity). Using this foundation, I test the analysis on a variety of examples, and with the extension of delayed tree-locality apply it to more complex cases. For the purpose of demonstrating the analysis, I focus on environments in which both reflexives and reciprocals appear.

3.0.1W HY STAG?

An attractive feature of the formalism of STAG is its potential to handle linguistic phenomena whose syntactic and semantic derivations seem to diverge. STAG utilizes syntactic-semantic tree pairs that undergo synchronized operations to produce a unified syntactic and semantic analysis of linguistic phenomena. Since anaphors require a referential antecedent to supply their semantic value, they depend on both syntax, in the form of distributional constraints, and semantics, in the form of specific relations with the antecedent. Thus, STAG has the potential to be an effective way of modeling both reflexives and reciprocals; yet STAG’s tight integration of syntax and semantics places strong constraints on the syntax-semantics interface, making anaphors a challenging and illuminating test case for the formalism. Previous attempts to model anaphors in STAG have focused specifically on reflexives and have not expanded to incorporate reciprocals. The variant of STAG assumed, following other recent work on STAG for natural-language semantics, is based on set-local multicomponent TAG (MCTAG). In synchronous set-local MCTAG (henceforth, simply “STAG”), a lexical item is represented by a set of syntactic and semantic elementary trees, all of which substitute or adjoin at the same time into another tree set (thus “set-locally”) (Weir, 1988). This formalism has been shown to handle a range of phenomena at the syntax-semantics interface, including nested quantifiers (Nesson and Shieber, 2006), extraction phenomena

43 (Nesson and Shieber, 2007), prepositions (Nesson, 2009), it-clefts (Han and Hedberg, 2006), pied-piping in relative (Han, 2006), and clitic climbing (Bleam, 2000).

Previous applications of TAG to anaphors have either appealed to extra facilities, such as recursive semantic features (Kallmeyer and Romero, 2007; Ryant and Scheffler, 2006; Champollion, 2008), or used the more constrained STAG plus adjustments, such as using de Bruijn indices in the semantics (Nesson, 2009), creating multiple reflexive trees (Storoshenko et al., 2008), or operating at multiple links in the derivation (Frank, 2008). No STAG approach to my knowledge has captured both reflexives and reciprocals. The present analysis seeks to fill this void by showing that both kinds of anaphors can be captured uniformly in STAG.

To achieve this, I simplify and generalize one previous analysis of reflexives in STAG, namely that of Frank (2008), so it can apply to reciprocals and a variety of reflexive cases. Frank uses STAG augmented with c-command and dominance constraints to ensure the antecedent precedes the reflexive and the variables are properly bound. He successfully captures simple reflexive cases, but does not conduct a comprehensive analysis extending to complex reflexives or to reciprocals. A notable aspect of Frank’s approach is the allowance for the trees of a single multicomponent set to operate not just at a single link but at multiple links. This “multiple link TAG” extension is in fact a novel and enabling aspect of Frank’s analysis, but has not to my knowledge been explored further. In Section 3.2, I argue that this extension is weakly equivalent to MCTAG without multiple links.

I simplify Frank’s (2008) analysis, eliminating the c-command and dominance relations used for proper variable binding by appealing to fundamental syntactic and semantic constraints. I also generalize his analysis to apply to both reflexives and reciprocals. Motivated by their almost identical syntactic distribution and similar semantic representation, I propose a novel unified analysis of reflexives and reciprocals that paramaterizes the analysis of anaphors by a semantic operator, REFL for reflexives and RECP for reciprocals. The new full analysis is described in Section 3.3.

I demonstrate the power of this approach in Section 3.4 by testing it against a variety of anaphor contexts, including cataphoric constructions, object control verbs, and ditransitive verbs in which the reflexive can be coindexed with the subject or object. To handle non-local cases, I avail myself of a version of delayed tree-locality, originally proposed by Chiang and Scheffler (2008) and in Section 3.5, I show how delayed tree-locality accounts for syntactic constructions such as anaphors in picture-DPs and quantificational picture-DPs, anaphors in adjuncts, and anaphors as arguments of raising, Exceptional Case Marking (ECM), and subject control verbs, as well as sentences with multiple anaphors.

44 Chapter 3. The Trees: Introducing the Model

3.0.2N OTATION AND TERMINOLOGY

Before providing more background on STAG and anaphors, I briefly review the notation and terminology used throughout this chapter.1 The basic units of a TAG are INITIALTREES and AUXILIARY TREES

(together comprising the ELEMENTARY TREES) with nodes labeled by appropriate categories. These combine via the operations of SUBSTITUTION (replacing a leaf node with a tree) and ADJUNCTION (inserting a tree at an interior node). An initial tree substitutes into a host tree at a leaf node that can accept substitution (indicated by the diacritic ↓) if the category of the initial tree’s root matches the category of the leaf node. An auxiliary tree contains a unique foot node (indicated by the diacritic ∗) that matches the tree’s root in category, and adjoins into another tree at a node that matches the category of the foot node (and root node). (For examples of a substitution node and foot node, refer to Figure 3.4 (c) and (a), respectively.)

Nodes that can undergo operations are designated by links, shown in the trees with numbered boxes ( 1 ). (Multiple boxes marked with the same numbered link specify the sites of operation of a set of trees.) The

final structural representation of the input sentence after all operations have been performed is the DERIVED

TREE; the steps of operator application can be summarized in a DERIVATION TREE.

For syntactic trees, the categories labeling tree nodes are syntactic categories: S2, DP3, VP, V, PP and so forth. For semantic trees, I use type-theoretic categories: e for entities and t for truth values and higher-order functions over these. Traditionally in linguistics, function types are represented using angle brackets as hσ,τi, where σ and τ are arbitrary types. I use a shortened form στ, interpreted with right-associativity, where it does not result in . Thus, one-place predicates are et, two-place predicates eet, and an operator that takes a binary predicate (eet) and returns a unary predicate (et) would be notated heet,eti.

Reciprocals reciprocate over plural entities. I do not require a sophisticated notion of plurality (such as Scha (1981), van Bentham (1989), or Westerståhl (1989)) for the semantics. I notate the type of sets of entities of type σ as σ and the plural entity combining a and b as a + b; I further optionally identify singular entities a with singleton plural entities {a}. Plural DPs will sometimes denote plural entities (like Noah and Emma of type e), and certain verbs (of type et, like meet) will require plural entities. Certain quantified DPs (like everyone) may have both interpretations—the quantifier meaning (as in everyone left) of type het,ti

1I assume familiarity with TAGs; for an introduction, see the presentation by Joshi (1987). 2The approach shown here uses S as the sentential root and recursive VP trees for auxiliaries and verbs, à la GPSG, rather than a tense projection (TP) with a T0 level, as used by Storoshenko and Han (2013) for instance. Representing all auxiliaries (and modals) as VP auxiliary trees that adjoin into the verb simplifies the analysis by reducing the number of different trees needed and their composition is elegantly controlled via the VP nodes’ feature structures. However, both VP and TP strategies are feasible, which I show in Section 3.1.1.1. 3I use a Phrase (DP) to refer to the maximal projection of nominals, except when referring to sources that use a different label, namely a Noun Phrase (NP).

45 3.1. Background and the plural interpretation (as in everyone met) of type e. Finally, I allow type variables in type-labeled nodes in semantic trees to indicate schematically the set of ground instances. This can be thought of as operating under a notion of type unification. With this notational basis, I now describe how STAG can capture basic syntax-semantics relationships to build up the framework for capturing anaphors.

3.1B ACKGROUND

3.1.1S YNCHRONOUS TREE ADJOINING GRAMMAR

I use set-local feature-structure-based synchronous MCTAG, supplemented with a version of delayed tree-locality for non-local anaphoric cases. In the elementary units of an STAG, a syntactic tree expressing a linguistic structure is paired with a corresponding semantic tree expressing its interpretation as captured in a formal logic (Shieber and Schabes, 1990). The derivation tree is identical for the syntax and semantics, since substitution and adjunction apply synchronously to linked nodes in syntactic-semantic tree pairs. In order to capture more complex syntactic and semantic relationships, such as quantifiers and reflexives, I appeal to MCTAG, in which the elementary units pair sets of trees (in my case, sets of syntactic plus semantic trees). I typically constrain these tree sets to operate set-locally since non-local MCTAG (MCTAG with no locality requirements) is computationally intractable (Rambow and Satta, 1992).

Following Vijay-Shanker and Joshi (1988), each node in a tree (including foot nodes) have both an associated top feature structure, how the tree is seen from above, and bottom feature structure, how the tree is seen from below, containing finite feature values. (Substitution nodes, however, only carry a top feature structure.) Each node’s feature structures must unify with the feature structures of any substituting or adjoining node in order for the operation to take place. Top and bottom feature structures must then unify at the end of the derivation; if they do not unify, the derivation crashes, implying that the attempted derived configuration is ungrammatical. If a node has only one feature structure, then its top and bottom feature structures have already unified and the node is closed for adjunction so no other trees can adjoin there. For reasons of readability and succinctness, I only show feature structures when relevant to the discussion.

In the ensuing subsections, I will incrementally build up the analysis through examples of simple transitive sentences, then by incorporating pronouns, quantifiers, and topicalization. These analyses, necessary for the further development of the anaphor analysis, rehearse similar versions given by Shieber (1986), Williford (1993), and Nesson and Shieber (2007).

46 Chapter 3. The Trees: Introducing the Model

3.1.1.1T RANSITIVEVERBS

Figure 3.1 provides an example of an STAG account of the simple transitive sentence

(46) Noah saw Emma.4

Figure 3.1(a) contains the elementary syntactic and semantic trees for the subject (Noah) and the object (Emma), respectively. These will substitute into the elementary verb trees in (b) at their corresponding links.

Both the syntactic and semantic trees for saw contain two substitution nodes, one for the subject ( 1 ) and one for the object ( 2 ). The matching diacritics across the syntactic and semantic trees indicate that these nodes must both undergo operations synchronously at that location. The derivation tree in Figure 3.1(c) shows the steps involved in substituting the two arguments into the predicate trees, namely substituting noah at link 1 and emma at link 2 . The final derived tree pair after both substitutions have been made is shown in (d). I point out in passing that if the more traditional linguistic structure using TP (rather than S) is desired, the elementary predicate trees can easily be encoded using TP and T0, as shown in Figure 3.2, without a loss in generative capacity.

3.1.1.2P RONOUNSANDCASE

Morphological case on restricts their distribution. To encode the restrictions, I make use of feature-structure-based TAG (Vijay-Shanker and Joshi, 1988), a standard variant of TAG. In this constraint-based variant of TAG, feature structures consisting of features and their values are associated with a node and must unify with the feature structure of any substituting or adjoining node in order for the operation to take place; if any features conflict, the unification fails (Vijay-Shanker and Joshi, 1988). Under the restriction (which I obey) that the domain of feature values is finite, feature-structure-based TAG is equivalent to TAG without features. In particular, I can mark DP substitution nodes in their feature structure with their case requirements (which can be thought of as a manifestation of their being assigned abstract Case (Polinsky and Preminger, 2014)), while lexical item trees rooted at DP that exhibit morphological case will have that case depicted in the root feature structure as well.5 Figure 3.3 demonstrates for the sentence in (47). Here, the feature structure associated with the root node for the Noah tree does not inherently have case in English so the case is unmarked, but the features of third person, singular, and masculine are specified, as shown in Figure 3.3(a). The pronoun her

4In these examples, I choose names from the Social Security Administration list of top baby names for 2015. 5This analysis essentially follows Polinsky and Preminger (2014) in the view that all English DPs are assigned abstract Case, a primitive feature expressing the relationship between an argument and its syntactic content, and that English pronouns additionally have overt morphological case.

47 3.1. Background

(a) Elementary Argument Trees: DP e DP e

Noah noah Emma emma

(b) Elementary Predicate Trees: S t

DP↓ 1 VP et e↓ 1

V DP↓ 2 eet e↓ 2

saw saw

(c) Derivation Tree: saw 1 2

noah emma

(d) Derived Trees: S t

DP VP et e

Noah V DP eet e noah

saw Emma saw emma

Figure 3.1: STAG trees for the simple transitive sentence Noah saw Emma.

TP t

0 DP↓ 1 T et e↓ 1

T VP eet e↓ 2

V DP↓ 2 saw

saw

Figure 3.2: Equivalent elementary predicate trees using TP rather than S and recursive VPs

(overtly) carries and third person, singular, and feminine features, as shown in Figure 3.3(b).

In the verb trees in (c), the node corresponding to the subject, indicated by 1 , is assigned so

48 Chapter 3. The Trees: Introducing the Model can only accept a DP with nominative or unspecified case; a DP carrying a different specified case could not substitute here because the case features would conflict and unification would fail. Therefore, Noah can substitute at 1 , and through a similar logic, only her, or another DP with accusative or unspecified case, can substitute into the accusative object position at 2 .

(47) Noah saw her.

This built-in feature checking system will play a role in several aspects of my STAG framework, including matching phi-features (number, person, gender) of anaphors and antecedents, making c-command and dominance constraints unnecessary, accounting for cataphoric constructions, and modeling morphology. Having explained the utility and effectiveness of feature structure constraints for manifesting case and agreement in STAG analyses, I will assume them implicitly henceforth, but for reasons of readability and succinctness, I do not show feature structures explicitly in subsequent examples unless relevant to the discussion.

    DP DP (a)   e (b)   e φ 3sgM φ 3sgF CASE CASE acc noah her Noah her

(c) SX t  XXX "  # XX DP VP P et e↓ 1  PPP CASE nom " # ↓ 1 V DP eet e↓ 2 CASE acc saw ↓ 2 saw

(d) saw (e) S t 1 2

noah her DP VP et e

Noah V DP eet e noah

saw her saw her

Figure 3.3: Elementary STAG trees and feature structures for (a) DPs, (b) pronouns, and (c) transitive verbs; (d) is the derivation tree and (e) the derived trees for the simple transitive sentence Noah saw her.

49 3.1. Background

(a) DP t e (b) DP t∗ e

no one ¬∃z t t∗ z Emma emma

et e

person z

(c) S t 1 2 (d) saw 1 2

DP↓ 1 VP et e↓ 1 no one emma

V DP↓ 2 eet e↓ 2

saw saw (e) S t

DP VP ¬∃z t t

No one V DP et e et e

saw Emma person z eet e z

saw emma

Figure 3.4: Elementary STAG trees for (a) quantifiers, (b) DPs (revised), and (c) transitive verbs (revised); (d) is the derivation tree and (e) the derived trees for the quantifier subject sentence No one saw Emma.

3.1.1.3Q UANTIFIERS

The examples so far have been straightforward, with one syntactic and one semantic tree for each word in the sentence. Many words, however, manifest multiple trees in their lexical makeup. I utilize MCTAG and for the time being constrain the tree sets to operate set-locally. Figure 3.4 contains an example of set-local synchronous MCTAG for the simple transitive sentence with a quantifier antecedent in (48).

(48) No one saw Emma.

Figure 3.4(a) contains the elementary trees for the generalized quantifier no one. Following Williford (1993), I alter the analysis of DPs so that instead of having only one semantic tree, there are two semantic trees that form a tree set: the SCOPETREE and the REFERENCETREE. The scope tree manifests binding by

50 Chapter 3. The Trees: Introducing the Model the quantifier of the variable in the reference tree. I maintain this parallel structure among all DPs by adding to non-quantificational DPs like Emma a degenerate scope tree t∗, shown in (b). This degenerate scope tree does not visibly change the derived tree, so merely serves as a placeholder to maintain consistency across quantificational and non-quantificational DP tree sets. From here on, every argument tree set will have both a scope and a reference tree in the semantics. The elementary verb trees in (c) are the same, except now the semantic tree has two link diacritics at its root to reflect where the two arguments’ scope trees can adjoin. They adjoin to the root so they outscope the reference trees that substitute into the two slots below. The derivation tree in (d) maintains the same structure as in the previous example. The derived tree pair in (e) shows how on the syntax side, the structure is identical to that in the previous example with noah simply replaced by no one. On the semantics side, though, the scope tree of no one has adjoined at the root of the verb tree; the scope tree of emma has also adjoined at the same place, but since it is simply a t-headed placeholder tree, there is no change to the derived tree. The reference tree of no one has substituted into the subject position of the verb tree at 1 and the reference tree of emma has substituted into the object position at 2 . The analysis thus manifests the pairing of the sentence No one saw Emma with the logical form

¬∃z : personz . sawemmaz .

As a salutary side effect of the multiple adjunction options at the root of the semantic tree, it follows that sentences with multiple quantifiers will exhibit ambiguous quantifier scope (Williford, 1993). Synchronous MCTAG, which permits one lexical item to be represented by a tree set instead of by a single tree, thus provides the flexibility needed for semantically representing quantifiers. Next, I show that multicomponent tree sets are also useful on the syntax side, for phenomena such as topicalization.

3.1.1.4T OPICALIZATION

Nesson and Shieber (2007) show how topicalization can be modeled with a multicomponent tree set comprised of an S-rooted tree containing the topicalized lexical item and an NP (or DP) tree containing the empty string, as shown in Figure 3.5(b). The topicalized Emma thus has two syntactic trees and two semantic trees. Again for consistency, I adjust all DP tree sets to have an equal number of trees on each side, even if they are not syntactically topicalized or do not semantically require scope, but adding the extra placeholder trees is not essential to the analysis. Correspondingly, I adjust all of the links where DPs are to operate to have four nodes rather than the three as before. For example, I have added a placeholder S∗ to the tree set in (a) for Noah. The elementary verb trees in (c) take their final form with two diacritics at the root

51 3.1. Background

" # (a) S∗ DP t∗ e (b) S DP t∗ e ¨¨HH " ¨ # H CASE x DP S Noah noah ∗ emma CASE x ε

Emma (c) S 1 2 t 1 2

DP↓ 1 VP et e↓ 1

V DP↓ 2 eet e↓ 2

saw saw (d) saw (e) S t 1 2

noah emma DP S et e

Emma DP VP eet e noah

Noah V DP saw emma

saw ε

Figure 3.5: Elementary STAG trees for (a) DPs (final), (b) topicalized DPs, and (c) transitive verbs (final); (d) is the derivation tree and (e) the derived trees for the simple topicalized sentence Emma, Noah saw.

on both the syntax and semantics sides. The topicalized tree set for Emma can be thought of as the result of a lexical process that applies to all DP tree sets of untopicalized form transforming them into the topicalized form. Note also that the DP feature structures on the two topicalized syntactic trees both have a variable x as the case feature value. Having matching feature values ensures that both components obtain the appropriate case as determined upon composition into the verb tree. There is now a complete STAG framework on which to build the account of reflexives and reciprocals. In the next section, I discuss the previous attempts at capturing anaphors in TAG.

3.1.2P REVIOUS WORK ON REFLEXIVES IN TAG

In the literature, there are six main applications of TAG to capture anaphors: three are non-synchronous, building a semantic representation using recursive feature structures (Ryant and Scheffler, 2006; Kallmeyer

52 Chapter 3. The Trees: Introducing the Model and Romero, 2007; Champollion, 2008),6 and three are synchronous using TAG for both the syntax and semantics (Nesson, 2009; Storoshenko et al., 2008; Frank, 2008). Although the non-synchronous approaches account for both reflexives and reciprocals, they appeal to recursive feature structures, which can be more powerful than TAG (indeed Turing-equivalent under some usages). The three previous synchronous approaches have only looked at reflexives but do so in the more restrictive STAG framework. Before looking at an extension of an STAG approach to reciprocals, I will briefly review the previous six analyses.

3.1.2.1N ON-SYNCHRONOUS TAG APPROACHES

For the non-synchronous TAG approaches, Ryant and Scheffler (2006) employ tree-local multicomponent lexicalized TAG (LTAG) with semantic feature structures and a flat compositional semantics for each elementary tree. The multicomponent tree set for reflexives and reciprocals contains two trees: an NP tree with the lexical anaphor that is c-commanded by a degenerate NP tree that composes with its antecedent through flexible composition (FC) (Joshi et al., 2003), an extension of LTAG. This approach captures reflexives and reciprocals but requires extra subject intervention and c-command constraints to prevent overgeneration and would need to adopt the formal definition of tree-local MCTAG-FC of Chiang and Scheffler (2008) in order to account for ECM verbs in a weakly TAG equivalent way. Kallmeyer and Romero (2007) use a similar approach, but replace Ryant and Scheffler’s degenerate anaphor NP tree with a degenerate VP tree. This change does not require the FC extension (except for adjuncts) or stronger c-command constraints, but does require a dominance relation between the degenerate VP and the lexical anaphor as well as a procedure for passing antecedent features. Only with both of these additions do the locality and c-command restrictions of classic binding theory (Chomsky, 1981) then follow. Instead of compositional semantics, Champollion (2008) uses the feature-based LTAG formalism of Vijay-Shanker (1987) extended by the use of lists as values of features, as in HPSG (Pollard and Sag, 1992a), and list operations, such as appending lists together. Champollion (2008) improves upon the previous non-synchronous approaches in several ways, such as by capturing ECM verbs, adjuncts, and all conditions in binding theory with no further additions to the framework; however, the analysis requires recursive features and does not include reciprocals. Despite the advantages of these non-synchronous approaches, all three use a semantics built up separately from the syntax and appeal to recursive features, which provides a more powerful approach than TAG. I thus turn now to approaches that have used the more constrained STAG system, and build a case for why I

6Steedman (2000) also provides an account for binding but uses a combination of LTAG and combinatory categorical grammar (CCG).

53 3.1. Background

Figure 3.6: Figure from Nesson (2009) showing de Bruijn notation and its implementation in STAG for the simple reflexive sentence John likes himself.

ultimately choose to extend Frank’s (2008) analysis.

3.1.2.2S YNCHRONOUS TAG APPROACHES

For the STAG approaches, Nesson (2009) uses MCTAG but extends the notation for semantic representation with de Bruijn indices. The de Bruijn notation uses integer indices—instead of explicitly-named free variables—to indicate how many enclosing λ terms away the variable’s binding λ is. (49) compares de Bruijn notation to standard notation.

(49) a. λ.λ.1 ≡ λx.λy.y

b. λ.λ.2 ≡ λx.λy.x

Figure 3.6 shows how de Bruijn indices apply to reflexives in STAG. In the derived semantic tree, a λ abstraction has been inserted above each node bearing an entity argument (here, subject and object) as a potential binder of de Bruijn indices that may occur within those arguments. Here, the indices are both 1, meaning each λ must bind the closest entity argument: The lower 1 binds the object entity argument and the upper 1 binds the subject entity. The elementary tree of himself, which has substituted into the verb tree, also contains an index of 1: This ensures the subject entity (john) is equated with the object entity during β-reduction, thus creating reflexivity. Although this approach provides more flexibility for locality constraints and can successfully account for a variety of reflexive sentences, it does not allow the differentiation needed for reciprocals because the

54 Chapter 3. The Trees: Introducing the Model indices allow specification only of coindexation.

Storoshenko et al. (2008) take a different MCTAG approach by positing three separate reflexive syntactic trees, whose use depends on the reflexive’s binding option as a verbal argument, as shown in Figure 3.7. Each multicomponent reflexive tree set has two syntactic trees and one semantic tree. One syntactic tree is the reflexive lexical tree; the other is a degenerate auxiliary tree that carries the appropriate feature structure for agreement with the antecedent. The category of this degenerate tree determines with which argument feature unification, and thus coreference, will occur, and is what syntactically differentiates the possible reflexive tree options.

0 T version 1 Jim4 introduces himself4 to Bill5.

0 T version 2 Jim4 introduces Bill5 to himself4.

0 V version Jim4 introduces Bill5 to himself5.

TP version Julian4 believes himself4 to be intelligent. (ECM verb)

Figure 3.7: Storoshenko et al.’s (2008) multiple forms of the English reflexive

The semantics relies on dynamically varying what is a function and what is an argument. For a sentence containing a reflexive, the reflexive plays the function role, taking its sister node as its argument; however, if

55 3.1. Background an entity fills that position in the sentence instead of a reflexive, the entity would be an argument and its sister node the function. Although the analysis captures ditransitives, raising verbs, and ECM verbs, why these three reflexive tree sets are the (only) possible options and why each reflexive has its specific semantic type is not well-motivated. It may be possible to extend this analysis to reciprocals: following reflexives, the semantics could be separately defined for each case as needed and agreement could be handled in the syntax through a clever use of features. However, this approach seems to lack a unifying story behind the choice of tree set configuration. I thus turn to the final application of STAG to reflexives, which I show can be extended to both reflexives and reciprocals in a more straightforward way.

3.1.3T HE ANALYSIS OF FRANK (2008)

Frank (2008) uses tree-local MCTAG to capture simple reflexive cases but does not definitively attempt to capture reciprocals and does not extend the analysis to more complicated cases, such as raising and ECM verbs. The analysis, illustrated in Figure 3.8 for the sentence in (50), follows similarly from the STAG examples presented in Section 3.1.1, with the addition of the reflexive tree set.

(50) John sees himself.

The reflexive tree set in (c) contains two trees on the syntax side: an NP-rooted tree with the reflexive lexical item7 and a degenerate NP tree that accepts the antecedent by substitution, which ensures coreference and preserves locality. On the semantics side, there are three trees: the first contains a lambda term that binds the subsequent two variable trees to ensure a reflexive relation. Frank enforces antecedence through c-command and dominance relations. On the syntax side, the antecedent tree c-commands (CC) the reflexive tree so they substitute into the verb tree at the correct nodes. On the semantics side, the reflexive t-headed elementary tree dominates (DOM) both reflexive e-headed variable trees to guarantee that one does not substitute higher up in the derived tree beyond the scope of lambda abstraction. Frank also includes a c-command relation between the two identical variable trees to express binding constraints.

ORIGINALASPECTSOF FRANK’S ANALYSIS Frank’s (2008) analysis is novel in two ways: the structure of the derivation and the use of multiple links. First, derivations of reflexive sentences (Figure 3.8(d)) diverge from derivations of non-reflexive sentences (Figure 3.1(c)). The derivation tree in Figure 3.8(d) has the antecedent (subject) first substitute into the reflexive (object), which then as a whole

7 The 2 link here is relevant for the derivation of reflexives in picture-NPs.

56 Chapter 3. The Trees: Introducing the Model

(a) TP t 1 2 (b) NP e

0 1 e 1 et NP↓ T ↓ John john

T VP eet e↓ 2

V NP↓ 2 see

sees

CC CC

(c) NP↓ 1 NP 2 t 1 e e 2

DOM e↓ 1 et x x himself DOM

λx t∗ (d) sees (e) TP t

1 2 NP T0 e et himself john x t 1 John T VP λ john V NP e et sees himself x eet e sees x Figure 3.8: Frank’s elementary trees for (a) transitive verbs, (b) type e NPs, and (c) reflexives; (d) is the derivation tree and (e) the derived trees for John sees himself. Extra constraints are indicated with labeled arrows: CC for c-command, DOM for dominance.

57 3.1. Background composes into the verb tree at the respective links.8 The structure of this derivation is unusual in the TAG literature in not paralleling the non-reflexive derivation tree, in which the subject and object separately substitute directly into the verb tree. However, there may be cross-linguistic evidence for this type of derivation. In languages such as Finnish, which represent reflexivization with a verbal affix that detransitivizes the verb into an intransitive verb, Büring (2005) explains that this verbal reflexive marker is not a syntactic argument or clitic, providing support for a derivation tree in which the verb accepts just one argument, the subject. An analysis of clitics along these lines may be apposite as well, as I discuss in Chapter 6.1.1. Second, Frank’s analysis crucially relies on allowing a tree set to operate at multiple links. The reflex of this innovation is the multiple links decorating edges in the derivation tree, where in standard STAG, only a single link would appear. In particular, Frank’s derivation tree in (d) portrays the reflexive himself going into the verb tree at both links 1 and 2 . Implicitly, Frank is appealing to a novel generalization of MCTAG, in which multiple components of a tree set can apply at multiple links. Storoshenko and Han (2013) actually also make use of multiple links in their analysis of bound variable pronouns, but require an even further extension. For the sentence

(51) Every girli loves heri father. they represent the bound her with two syntactic trees—one degenerate DP tree carrying the appropriate φ features that composes into the every girl tree for agreement matching at link 3 and one lexical DP tree with her that composes into the father-of tree at link 1 —and two corresponding semantic trees—one function recursive on type he,ti that composes into the every girl tree at link 3 and one bound e variable tree that composes into the father-of tree at link 1 . These two separate composed trees, her + every girl and her + father-of, then compose into the verb tree at links 1 and 2 , respectively. The difference between Storoshenko and Han’s (2013) use of multiple links and Frank’s (2008) use of multiple links is that Storoshenko and Han (2013) require a multicomponent tree set to compose into multiple links across more than one tree set (every girl and father-of ), while Frank (2008) requires a multicomponent tree set to compose into multiple links within one tree set (sees). I only require the latter flexibility for my analysis of reflexives so focus on multiple links within one tree set.9 I know of no previous analysis of the nature of this extension, so I provide a discussion in Section 3.2,

8Ryant and Scheffler (2006) use a similar derivation tree in that the antecedent composes with the anaphor before both compose into the verb tree, but their use of flexible composition allows composition of trees in either direction, so the derivation tree is not actually equivalent. 9I do not know of any other cases requiring multiple links, but idioms or nominal and adverbial quantifiers could potentially make use of them. Future work should investigate these and other use cases.

58 Chapter 3. The Trees: Introducing the Model including an informal proof by reduction that MCTAG with multiple links within one tree set (MCTAG-ML) is no more expressive than standard MCTAG.

INABILITYTOCAPTURERECIPROCALS Frank’s (2008) approach accounts for simple reflexive antecedents, quantifier-bound reflexives, reflexives embedded in a picture-DP, and reflexives occurring as the argument of a ditransitive predicate. However, the approach does not directly extend to reciprocals.

Unlike reflexives, reciprocals are not simply inherently coindexed with their antecedent since the antecedent must be distributed into its atomic parts. Frank’s approach as it stands cannot account for this. The semantic trees contain only one binder of two instantiations of the same variable and are thus inherently detransitivizing. By maintaining separate binders of the two argument positions, my modifications below not only account for both reflexives and reciprocals, but also do so in a unified and simplified way.

3.2M ULTIPLE LINK MCTAG

As mentioned previously, Frank’s (2008) analysis, and thus also my analysis of anaphors, involves a slight extension of the MCTAG framework by allowing a multicomponent tree set to compose into a tree at multiple sets of links ( 1 and 2 ), instead of at only one set of links ( 1 ). In this section, I demonstrate informally via reduction that MCTAG-ML is no more powerful than standard MCTAG.

Given a MCTAG, suppose there is an initial tree α that contains two nodes, labeled with types x and y.

Node x has a link 1 and node y has a link 2 , indicating that both nodes are operable sites. Now suppose there is a multicomponent tree set β, containing two elementary trees, one rooted with label x and the other rooted with label y. The derivation involves the β tree set composing into the α tree at links 1 and 2 , respectively. Under which constraints can a multicomponent tree set go into multiple links?

First, consider the case in which any two links in a tree can accept any multicomponent tree set, as long as the features unify, per the rules of composition under MCTAG. Therefore, β could compose into α at any pair of links in which the nodes’ features unify. This multiple link freedom does not extend the power of MCTAG because MCTAG-ML can be converted to MCTAG by simply adding a single “super” link to every pair of nodes. For instance, x and y in α would each have their 1 and 2 links respectively as well as a 3 link, indicating that a multicomponent tree set could compose at both x and y at the single 3 link. Adding these additional pairs of links would increase the size of the grammar, but would not increase the grammar’s expressive power beyond standard MCTAG.

An alternative is to enforce some kind of constraint on the sets of distinct links in α that accept a

59 3.3. A new analysis multicomponent tree set. In this case, a super link could be added only to those nodes in α that allow composition at multiple links. For the present purposes, multiple links are only needed for anaphors, which exclusively compose into DP nodes in subject and object (direct object, indirect object, object of the preposition) positions. Thus, a super 3 link can be added specifically to pairs of DPs in those positions in a tree (if they exist). Since anaphors are the only multicomponent tree set (to my knowledge) that can compose at multiple links, the pairs of nodes with a super link only accept the anaphor tree set, exactly as desired. Once more, MCTAG-ML has not extended the expressive power of standard MCTAG. An additional constraint could also be enforced on the trees in the β multicomponent tree set. For example, x and y in β could carry a feature indicating they can compose at multiple links. If this feature unified with the feature of the receiving nodes in α, then the derivation proceeds. I defer the details of this reduction to future work because simply constricting the links in α is sufficient for allowing anaphors to compose at multiple links without adding power beyond standard MCTAG.

3.3A NEW ANALYSIS

In this section, I explain how my analysis builds directly on Frank’s (2008) and I adjust the analysis to be in line with the STAG framework outlined in Section 3.1.1.

3.3.1F RANK’S ANALYSIS REVISED

In Section 3.1.1, I proposed elementary tree sets for DPs that contained multiple syntactic trees and semantic trees, two of each, independently motivated for handling quantification and topicalization. The syntax has an S auxiliary tree (allowing for topicalization) in addition to the “in situ” DP tree; the synchronous semantics has a t auxiliary tree (used for quantifier scope) and an e-rooted reference tree. The argument links in the verb trees, designated by diacritics, were adjusted accordingly, ensuring that the syntactic and semantic trees accept synchronous operations at corresponding nodes. As in Frank’s analysis, the reflexives will use both subject and object links, and thus will be composed of four syntactic and four semantic trees. The tree set follows Frank’s approach with only minor changes, as shown in Figure 3.9(c). In the syntactic tree set are two S∗ placeholder trees, one for each of the DP trees, following the framework as presented previously. The first DP tree is degenerate, accepting the antecedent by substitution, and the second contains the reflexive. Both DP nodes are understood to have a matching variable as their φ feature value to ensure that the φ feature values of the incoming antecedent match those of the reflexive. The semantic tree set contains a t auxiliary scope tree for each of the e-rooted variables. In

60 Chapter 3. The Trees: Introducing the Model

the first scope tree, a reflexive operator REFL (described shortly) has been added as another binary branch in the elementary reflexive tree, along with two binding λ terms (instead of just one). The e-rooted variable trees correspondingly contain two distinct variables.

My framework already makes use of case and feature unification for pronouns, but case checking can additionally ensure the correct configuration of lexical substitution of the antecedent and reflexive, thus making the notions of c-command and dominance constraints redundant. Eliminating these extra constraints greatly simplifies the analysis by relying on the inherent features of the formalism instead of on externally-added restrictions. For English, the DP tree that accepts the antecedent is underspecified for case since it can be nominative (in subject position) or accusative (in object position, such as for ditransitives); the DP tree containing the reflexive appropriately has accusative case, the only possible case for English reflexives, which ensures that the reflexive substitutes into object position. I will discuss this concept more for each example in Section 3.4.10 As shown in (d), I use the same derivation tree as Frank, meaning I also take advantage of the multi-link extension of STAG discussed in Section 3.2.

Returning to the reflexive operator, REFL serves as a formalization of the reflexive relation. For the purposes of this chapter, in which I focus on the distributive reflexive reading, the REFL operator is given as in (52), but I discuss extensions to the operator to capture other readings in Chapter 4. Abstracting out the reflexive operator allows flexibility in its semantic definition and comparison to alternatives (such as the

RECP operator I introduce shortly).

(52) REFL ≡ λR . λZ . ∀x : x ∈ Z . ∀y : y ∈ Z ∧ y = x . Ryx

Informally speaking, the operator holds of a binary relation R and an antecedent set Z just in case every pair x and y in the set Z, where x and y are not distinct, are in the relation R.11 (The benefit of the apparent redundancy of the two universal quantifiers will become evident shortly.)

For the sentence (53a) with a singular antecedent, REFL provides the (only possible) reading—the

DISTRIBUTIVE reading—that Noah saw Noah. For plural antecedents (plural DP, plural pronoun, or conjoined noun phrase), as in (53b), the distributive reading yields that Noah saw himself (and not Emma) and Emma saw herself (and not Noah)—the relation holds between each atom in the plurality and itself, that is the action is distributed among the atomic parts of the antecedent. However, there is also an additional reading for plural antecedents—the CUMULATIVE reading—which yields that Noah and Emma both saw the

10For languages that allow reflexives to take on more cases than accusative, such as Icelandic and Korean, the case feature values could be disjunctive, à la Karttunen (1984), with alternative value options depending on context and the case of the node into which it composes; however, I leave the details of reflexives in other languages to future work. 11This definition of REFL also accounts for singular antecedents by interpreting them as singleton plural entities.

61 3.3. A new analysis pair containing both of them (as, perhaps, in a mirror). Under the cumulative reading, the relation holds of the entire plurality and itself, that is the action is true of the cumulative group.

(53) a. Noah saw himself.

b. Noah and Emma saw themselves.

In order to extend to reciprocals in a parallel fashion, and since the plural version is more general, I demonstrate the analysis using sentence (53b), instead of Frank’s (2008) example sentence (50), but the analysis is equivalent. The resulting logical form can be simplified as shown in (54b), demonstrating that the distributive reading is appropriately captured. The corresponding STAG derivation proceeds as in Figure 3.9. In order to capture the idea that reflexives can range over entities (e) or plural entities (e), the

REFL semantic tree uses the type variable τ, as shown in Figure 3.9(c), which adopts the appropriate type value based on the antecedent’s type.

(54) a. Noah and Emma saw themselves.

b. i. (REFL (λa . λb . sawab)) noah + emma ii. ≡ ((λR . λZ . ∀x : x ∈ Z . ∀y : y ∈ Z ∧ y = x . Ryx)(λa . λb . sawab)) noah + emma iii. ≡ (λZ . ∀x : x ∈ Z . ∀y : y ∈ Z ∧ y = x .(λa . λb . sawab)yx) noah + emma iv. ≡ (λZ . ∀x : x ∈ Z . ∀y : y ∈ Z ∧ y = x . sawyx) noah + emma v. ≡ ∀x : x ∈ noah + emma . ∀y : y ∈ noah + emma ∧ y = x . sawyx vi. ≡ sawnn ∧ sawee

3.3.2C OMPARISON OF ANALYSES

There are four differences between my reflexive analysis and Frank’s. First, I use extra placeholder trees to maintain a parallel structure among all DPs. The extra trees are necessitated on the syntax side by the DP tree used in the Nesson and Shieber’s (2007) fronting analysis and on the semantics side by the quantifier scope tree. This modification is not essential to my reflexive analysis as it arises solely from my incorporation of the independent fronting and quantifier analyses. Second, I eliminate binding constraints like c-command and dominance, which permits the flexibility needed for cataphora, since these relations are already captured through case checking. Third, I employ two bindings of distinct variables instead of one binding of a single variable twice, as this allows the appropriate grain needed for reciprocals. Finally, I abstract away the reflexivity notion from Frank’s trees with an operator REFL, which generalizes to also be compatible with reciprocals using a parallel operator RECP, as described in the next section.

62 Chapter 3. The Trees: Introducing the Model

(a) S∗ DP t∗ e (b) S 1 2 t 1 2

Noah&Emma noah + emma DP↓ 1 VP et e↓ 1

V DP↓ 2 eet e↓ 2

saw saw

(c) S∗ 1 DP↓ 1 S∗ DP t 1 e t∗ e

t 1 b a themselves τ τ↓

heet,τti eet

REFL λa et

λb t∗

(d) saw (e) S t

1 2 DP VP et e themselves heet,eti eet n + e 1 Noah&Emma V DP

noah+emma saw themselves REFL λa et λb t et e

eet e b saw a

Figure 3.9: Elementary trees for (a) plural DPs and (b) transitive verbs (as before); (c) is the elementary re- flexive tree set with type variable τ, standing for either an entity (e) or a plural entity (e) in the refl tree; (d) is the derivation tree and (e) the derived trees for Noah and Emma saw themselves.

63 3.3. A new analysis

3.3.3A DDINGRECIPROCALS

Using an operator for both reflexives and reciprocals captures their underlying similarities, creating a unified account of both. It seems logical to group reflexives and reciprocals together syntactically, as structurally interchangeable constructions, and distinguish between them semantically, as differing with respect solely to distribution over the antecedent. This is the motivation behind my proposed approach. An attractive property of this analysis is that simply by replacing the = in the semantic representation of

REFL with 6=, I get the formalization of the reciprocal relation RECP:

(55) RECP ≡ λR . λZ . ∀x : x ∈ Z . ∀y : y ∈ Z ∧ y 6= x . Ryx

Similarly to REFL, the RECP operator holds of a binary relation R and an antecedent set Z just in case every pair x and y in the set Z, where x and y are distinct, are in the relation R. For the reciprocal version of sentence (53b), in (56a), RECP provides the correct (and only) reading—the strong reciprocity reading—that Noah saw Emma and Emma saw Noah. The reduction in (56b) proceeds in parallel fashion to that of reflexives.

(56) a. Noah and Emma saw each other.

b. i. (RECP (λa . λb . sawab)) noah + emma ii. ≡ ((λR . λZ . ∀x : x ∈ Z . ∀y : y ∈ Z ∧ y 6= x . Ryx)(λa . λb . sawab)) noah + emma iii. ≡ (λZ . ∀x : x ∈ Z . ∀y : y ∈ Z ∧ y 6= x .(λa . λb . sawab)yx) noah + emma iv. ≡ (λZ . ∀x : x ∈ Z . ∀y : y ∈ Z ∧ y 6= x . sawyx) noah + emma v. ≡ ∀x : x ∈ noah + emma . ∀y : y ∈ noah + emma ∧ y 6= x . sawyx

In order to incorporate reciprocals into the STAG framework, I simply add the reciprocal counterparts in the same place as reflexives in the multicomponent tree set for reflexives from Figure 3.9(c). On the syntax side, I replace the lexical item themselves with each other and on the semantics side, I replace the reflexive operator (REFL) with the reciprocal operator (RECP). The only difference between the two anaphors is that reciprocals can take on additional cases, namely genitive and nominative. Thus, the DP case feature value for reciprocals can be disjunctive (Karttunen, 1984) with three alternative values: accusative, genitive, or nominative. I return to this point briefly in Section 3.3.4. For the purposes of modeling anaphors in STAG, I focus on accusative environments in which both can equally appear, so I indicate the shared structure by placing corresponding components of reflexives and reciprocals in the same node as interchangeable options, as illustrated in Figure 3.10(a).

64 Chapter 3. The Trees: Introducing the Model

(a) S∗ 1 DP↓ 1 S∗ DP t 1 e t∗ e themselves/ t 1 b a each other τ τ↓

heet,τti eet

REFL/RECP λa et

λb t∗ (b) saw (c) S t 1 2 et e themselves/each other DP VP heet,eti eet n + e 1 Noah&Emma V DP noah+emma themselves/ REFL/RECP λa et saw each other λb t et e

eet e b saw a Figure 3.10: (a) Elementary tree set for a reflexive/reciprocal; (b) is the derivation tree and (c) the derived trees for Noah and Emma saw themselves/each other.

The derived semantic tree instantiates τ as e, appropriate for the reciprocal and distributive reflexive readings. (The verb trees and antecedent trees remain the same as in Figure 3.9.) Comparing these trees to Frank’s (2008) trees in Figure 3.8, the reader can confirm that the derivation tree is identical and both methods produce the same result (up to the modification in the logical form). With this example as a foundation, I now show the utility of this representation for a range of increasingly complex reflexive and reciprocal phenomena.

3.3.4A NAPHOR PROPERTIES IN THE ANALYSIS

In Chapter 1.2, I noted distributional properties of reflexives and reciprocals that any analysis should provide for: proper antecedence, agreement with the antecedent, and syntactic and semantic divergences between reflexives and reciprocals. The present analysis provides for all of these properties. With respect to antecedence, the analysis provides for the appropriate distribution of anaphors without appealing to extra governing restrictions, by virtue of the case constraints otherwise required for capturing pronoun distribution in English as described in Section 3.1.1.2. Sentence (57a) is not generable since the feature constraint on the subject of saw (case:

65 3.3. A new analysis nominative) conflicts with the constraint on the lexical item himself (case: accusative), as depicted in Figure 3.3. Similarly, the sentence in (57b) violates the φ feature agreement constraints.

(57) a. * Herselfi saw Emmai.

b. * Noahi saw herselfi.

The same approach can be used to capture the divergences between reflexive and reciprocal distributions, cited by Lebeaux (1983), by virtue of a lexical gap in English for nominative reflexives. For instance, in the example (58a), the reciprocal each other can have nominative case, and can thus appear in subject position, whereas themselves is given a feature constraint of “case: accusative” reflecting its morphological case. As a result, themselves conflicts with the “case: nominative” position into which it must substitute and unification fails.

(58) a. John and Mary think that ?each other/*themselves will win.

b. John and Mary like each other’s/*themselves’ parents.

c. It would please the boys very much for each other/ ?themselves to win.

There happens to be no nominative reflexive in English (“theyselves” or “sheself”, say), but as mentioned previously, crosslinguistically some languages provide for overt nominative reflexives, as seen in Korean (Storoshenko and Han, 2013):

(59) a. Motun sonyei-nun cakii-ka ttokttokha-tako sayngkakha-n-ta. every girl-TOP self-NOM intelligent-COMP think-PRES-DECL ‘Every girl thinks that she is intelligent.’

b. Motwui-ka cakii-uy apeci-lul salangha-n-ta. everyone-NOM self-GEN father-ACC love-PRES-DECL ‘Everyone loves his father.’

In these cases, the case feature value on the anaphor can be adjusted as needed, potentially becoming disjunctive, but I leave capturing the nuances of anaphors in other languages for future work. The same logic applies when anaphors are the (possessive) subject of DP, as in (58b). In these cases, the anaphors are assigned . Again, reciprocals can have genitive case, whereas reflexives cannot, so the alternative possessive pronoun forms, such as my, your, and their, replace the reflexive. Thus, each other’s is grammatical, but their (or their own for emphasis) is strongly preferred over themselves’. Lebeaux (1983) alludes to a suggestion that the grammatical surface pronoun in this prenominal position could

66 Chapter 3. The Trees: Introducing the Model simply be a reflexive in a suppletive pronominal form; however, he rejects this idea claiming it does not explain why this is the only case of and why the reflexive takes the particular form of a pronoun. Appealing to case and the rationale that reflexives already have viable alternative case-matching forms while reciprocals do not, helps address these concerns and explain the distribution for (58a) and (58b).

Finally, for anaphors in the subject of a “for-to” clause as in (58c), reflexives in fact seem to be acceptable, especially in different examples (also adapted from Lebeaux (1983)):

(60) John and Mary bought books for each other/themselves to read.

Here, case can account for the grammaticality of the reciprocal and the reflexive because both can receive accusative (or oblique) case from the preposition for. It may be that the slight preference for the reciprocal version over the reflexive version is simply because the reflexive in these sentences is redundant, so is usually dropped. In (60), for instance, the salient reading is that John and Mary bought the books for themselves and that they will be the ones to read them; therefore, for themselves need not be included, unless the context requires the explicit reflexive to clarify meaning.

Environments in which reflexives appear but reciprocals do not, the intensifier and override uses of reflexives, may also be straightforwardly captured by the analysis but are left for future work. In summary, the present analysis is consistent with the distribution of reflexives and reciprocals, both their shared and divergent traits.

3.4A PPLICATIONS

In this section, I demonstrate how the analysis essentially unchanged accounts for various reflexive and reciprocal phenomena, including cataphora, anaphors with object control verbs, and anaphors as arguments of ditransitive verbs. I focus on the core anaphoric cases common to both reflexives and reciprocals, excluding the cases discussed in the previous section that are unique to each kind of anaphor, which I leave for future work.

3.4.1C ATAPHORA

Cataphora, such as in (61a), would appear to present a problem for analyses requiring c-command constraints, as the required c-command relation does not appear to hold overtly in the derived tree. My approach however is completely consistent with the account of topicalization of Nesson and Shieber (2007),

67 3.4. Applications by treating the anaphor as a topicalized item.12 I illustrate this derivation in Figure 3.11 for the simplified cataphoric reciprocal sentence in (61b).13

(61) a. (Noah and Emma like many people, but) each other, they can’t stand.

b. Each other, Noah and Emma saw.

The syntactic tree set for the reciprocal, shown in Figure 3.11(a), simply reflects topicalization of the reciprocal following directly the topicalization analysis of Nesson and Shieber (2007). The S auxiliary tree now contains the lexical reciprocal and the corresponding DP tree contains the empty string. Using a feature-checking system instead of binding principles provides the flexibility needed to capture cataphora because the topicalized anaphor carries accusative case on its DP node. Since the empty string DP node has a variable for its case feature value that matches the value of the topicalized anaphor DP, the empty string appropriately also has accusative case. Thus, the S auxiliary tree adjoins at the root of the verb tree and the empty string DP substitutes into the object position with no feature conflicts. The semantics side remains unchanged.14 The derivation proceeds as usual according to the derivation tree in (b) to produce the derived trees in (c).

3.4.2A NAPHORSWITHOBJECTCONTROLVERBS

Syntactic constructions with object control verbs, such as persuade in (62a), follow directly from my analysis as put forth so far.

(62) a. Noah and Emma persuaded themselves/each other to be happy.

b. * Noah and Emma persuaded themselves/each other Liam to be happy.

Object control verbs have three arguments: an (Noah and Emma), a theme (themselves/each other), and an open (to be happy). This configuration is represented in the elementary object control verb tree set in Figure 3.12(a). The lower predicate, to be happy, cannot have its own subject, as evidenced by (62b), so the persuaded tree set contains a DP tree with PRO in the syntax. Following linguistic control theory, this PRO is caseless so carries the case feature value “none” in its feature structure. The semantics has a corresponding variable tree so both PRO and the variable substitute into the subject position of the to

12I only consider examples in which the anaphor stands alone as a topicalized item, and leave anaphors embedded in topicalized adjuncts and adverbial phrases for future work. 13Cataphoric reflexives follow similarly so are not shown. 14For the present purpose of modeling cataphora in STAG, I assume that cataphoric anaphors are a syntactic phe- nomenon, although the semantics could also be changed to account for the different that can result from cataphoric constructions.

68 Chapter 3. The Trees: Introducing the Model

" # " # (a) S 1 DP S DP t 1 e t e ∗ !a ∗ !! aa CASE " # CASE acc S ↓ 1 DP ∗ τt τ↓ 1 b a CASE acc ε heet,τti eet each other RECP λa et

λb t∗ (b) saw (c) S t

1 2 DP S et e each other 1 each other DP VP heet,eti eet n + e noah+emma Noah&Emma V DP RECP λa et

saw ε λb t

et e

eet e b

saw a

Figure 3.11: (a) Elementary trees for a cataphoric (topicalized) reciprocal; (b) is the derivation tree and (c) the derived trees for the cataphoric (topicalized) sentence Each other, Noah and Emma saw.

be happy trees. Since non-finite verbs do not assign case, the subject DP substitution slot in the to be happy syntactic tree remains underspecified for case. Instead, the root S node, the subject DP node, and the higher

VP node have matching variable z values in their feature structures, indicating that once a DP substitutes in, the subject DP node will adopt the case of the incoming DP and this case feature will be copied over to the higher VP node and the root S node. (The rationale for having matching case on the S and VP nodes will become clear in subsequent examples.)

The derivation proceeds according to the derivation tree in (c), in which the antecedent composes into the anaphor tree set, which then as a whole composes into the object control persuade tree set in a tree-local fashion at links 1 and 2 . This tree set then composes into the non-finite verb to be happy tree set at link 1 to produce the fully derived trees in (d). The to be happy DP node feature structure unifies with that of the substituted caseless PRO by adopting the “none” feature value as its z variable value. Since the higher VP and root S nodes also have the variable z as their case feature value, they adopt the value “none” as well.

69 3.4. Applications

" # DP (a) S 1 2 t 1 2 e CASE none DP↓ 1 VP et e↓ 1 z PRO V DP↓ 2 S∗ λz t

persuaded et e↓ 2

eet e

ht,eeti t∗ z " # S persuaded CASE (b) 1 t 1 (c) to-be-happy " # S 1 CASE z et e↓ 1 persuaded XXX  XX 1 2 " # " # DP VP to-be-happy themselves/each other CASE z 1 CASE z ↓ 1 " # VP noah+emma CASE Q  Q V VP t ##cc to V AdjP et e (d) S be happy heet,eti eet n + e

DP VP REFL/RECP λa et λb t Noah&Emma V DP S et e themselves/ persuaded each other DP VP λz t b et e

PRO V VP eet e a

ht,eeti t z to V AdjP persuaded et e

be happy to-be-happy z

Figure 3.12: Elementary trees for (a) object control verbs and (b) non-finite predicates with appropriate links; (c) is the derivation tree and (d) the derived trees for the object control verb sentence Noah and Emma per- suaded themselves/each other to be happy.

70 Chapter 3. The Trees: Introducing the Model

3.4.3A NAPHORICARGUMENTSOFDITRANSITIVEVERBS

In ditransitive sentences, such as in (63), the reflexive can ambiguously have two antecedents, Noah or Liam.15 My analysis as it stands predicts only the reading in which the reflexive refers to the subject.

(63) Noahi showed Liam j himselfi/ j.

The subject coindexation version of the sentence additionally has a ditransitive alternation, as in (64b), which results in a different meaning. The first word order in (64a) can be paraphrased as Noahi showed himselfi to Liam, whereas the second word order in (64b) is paraphrased as Noahi showed Liam to himselfi.

(64) a. Noahi showed Liam himselfi.

b. Noahi showed himselfi Liam.

Even though the sentence’s meaning changes, my analysis can still account for this alternative word order. Figure 3.13 contains the relevant trees for both word orders of this indexation. The derivation tree in

(b) corresponds to (64a), in which the reflexive + antecedent composes into showed at links 1 (nominative case) and 3 (accusative case) and liam composes at link 2 (also accusative case). Since proper are not specified for case in English, noah unifies its underspecified case feature value with the accepting subject nominative DP node; liam does similary except with accusative case. In the derivation tree in (c) for (64b), the link options are reversed: the reflexive + antecedent composes into showed at links 1 and 2 and liam composes at link 3 . The alternative links, and the fact that the accusative reflexive must unify in case feature so has to go into object position, account for the syntactic order and semantic meaning of both versions of the subject coindexation, as shown by the derived trees for each reading in (d) and (e), respectively. The second coindexation, in which the reflexive corefers with the object, can be captured with an alternative semantic REFL tree.16 The reflexive operator tree simply adds a λ abstraction over a variable for the subject and takes scope at et (instead of at t), as illustrated in (e) on the right side of Figure 3.14. (The left side of the figure repeats the subject coindexation trees with this word order for easier comparison.)

Since this tree will now adjoin at the et node of the verb tree (instead of at its t root), I add a 20 link at the et node and at the daughter substitution e node in the verb tree, as shown in (a). The 20 link can be considered an alternative option into which the REFL tree set can compose, depending on whether the

15Once again, ditransitive sentences involving a reciprocal (Noah and Emma showed Liam and Olivia each other) follow directly, so I leave out the details. 16The use of a separate, but related, reflexive tree set for object coindexation could provide evidence for a distinction between subject-bound anaphors and object-bound anaphors; a thorough crosslinguistic investigation into the appearance of each kind of bound anaphor across languages is needed to determine the viability of this idea.

71 3.4. Applications

reflexive is coindexed with the subject (uses link 2 ) or with the object (uses link 20 ). In order to have parallel link placement in the syntactic verb tree, I can replace one S∗ placeholder tree in the syntactic reflexive tree set with a VP∗ placeholder tree. This change can indicate that the REFL tree set will use the 20 links rather than the 2 links. Adding this alternative link option thus does not significantly alter my model.

The derivation tree for object coindexation in (f) differs from that for subject coindexation in (c) only because noah now composes directly into the verb tree (still at link 1 ), while liam composes into the REFL tree (still at link 1 ), then the result composes into the verb tree at links 20 and 3 . The step-by-step derivation of the ditransitive object coindexation example is shown in Figure 3.15. The composition of liam with the reflexive is in (a) and the composition of this tree set as a whole into showed is in (b). The addition of composing noah also into the showed tree results in the derived tree shown in Figure 3.14(g). The reader can compare this object coindexation derived tree to the subject coindexation derived tree in (d).

Unlike the first coindexation linking the subject Noah with the reflexive, the object coindexation can only have one word order. If the object and reflexive are swapped, as in (65b), the correct reading is unavailable and appealing to case is not sufficient to account for this ungrammaticality.

(65) a. Noah showed Liam j himself j.

b. * Noah showed himself j Liam j.

However, a more nuanced case analysis, in which the equational constraint on case (that the antecedent’s case is nominative and the anaphor’s case is accusative) is replaced by an inequational constraint over a set of cases ordered by obliqueness (that the antecedent’s case is less oblique than the anaphor’s case) suffices to cover these cases. This approach is based on Pollard and Sag’s (1992b) obliqueness hierarchy, which requires an anaphor to be coindexed with a less oblique coargument, if there is one. Arguments are ranked according to their obliqueness in the following order from least to most oblique: Subject < Primary Object < Second Object < Other Complements. Pollard and Sag (1992b) claim that in double object constructions, such as (65b, the closest object to the verb is the primary object (here, himself ) and the outer object is the secondary object (here, Liam). In this case, the anaphor is less oblique (instead of more oblique) than its antecedent, and thus the sentence is correctly predicted to be ungrammatical. Applying this approach to the other ditransitive sentences correctly predicts that they should be grammatical. The obliqueness hierarchy is also useful in predicting grammaticality patterns in other configurations, such as adjuncts, ECM verbs, and anaphors in embedded clauses.17 I show how for each of these examples in the next section.

17The exact differences between appealing to obliqueness and using (some version of) c-command are left for future work.

72 Chapter 3. The Trees: Introducing the Model

In sum, even though ditransitive sentences require a separate operator tree for when the anaphor refers to the object, the derivation trees for the two coindexations are parallel to each other and may even be justified given anaphors in other languages, but that is left for future research. Therefore, this example demonstrates the ability of the analysis to accommodate complex cases through new derivations but nearly the same elementary trees.

73 3.4. Applications

(a) S 1 2 3 t 1 2 3

DP↓ 1 VP et e↓ 1

V DP↓ 2 DP↓ 3 eet e↓ 2

showed eeet e↓ 3

showed (b) Noahi showed Liam himselfi. (c) Noahi showed himselfi Liam. showed showed 1 3 2 1 2 3

himself liam himself liam

1 1 noah noah t (d) Noahi showed Liam himselfi. et e S heet,eti eet noah DP VP REFL λa et

Noah V DP DP λb t

showed Liam himself et e

eet e b

eeet e liam

showed a (e) Noahi showed himselfi Liam. t

et e

S heet,eti eet noah

DP VP REFL λa et b t Noah V DP DP λ et e showed himself Liam eet e b

eeet e a

showed liam Figure 3.13: (a) Elementary trees for a ditransitive verb; (b) is the derivation tree and (d) the derived trees for Noahi showed Liam himselfi; (c) is the derivation tree and (e) the derived trees for Noahi showed himselfi Liam.

74 Chapter 3. The Trees: Introducing the Model

(a) S 1 2 3 t 1 2 3

DP↓ 1 VP 20 et 20 e↓ 1

V DP↓ 2 20 DP↓ 3 eet e↓ 2 20

showed eeet e↓ 3

showed (b) t 1 e t∗ e (e) et t∗ e

τt τ↓ 1 b a λz t 1 ba

heet,τti eet τt τ↓ 1

REFL λa et heet,τti eet

λb t∗ REFL λa et λb t

et∗ e z (c) showed (f) showed 1 3 2 1 20 3

himself liam noah himself

1 1 noah liam (d) t (g) t et e et e

heet,eti eet noah λz t noah

REFL λa et et e λb t heet,eti eet liam

et e REFL λa et eet e b λb t eeet e liam et e

showed a eet e z

eeet e b

showed a

Figure 3.14: (a) Elementary trees for a ditransitive verb with alternative object coindexation 20 link added; Left: (b) is the reflexive tree set (as before), (c) the derivation tree, and (d) the derived semantic tree for Noahi showed Liam himselfi. Right: (e) is the adjusted reflexive tree set for object coreference, (f) the deriva- tion tree, and (g) the derived semantic tree for Noah showed Liam j himself j.

75 3.4. Applications

(a) S∗ DP S∗ DP et t∗ e e λz t a b Liam himself et e

heet,eti eet liam

REFL λa et λb t

et∗ e z

(b) S 1 t 1

et e↓ 1 DP↓ 1 VP λz t V DP DP et e

showed Liam himself heet,eti eet liam

REFL λa et

λb t et e

eet e z

eeet e b showed a Figure 3.15: (a) First step in the ditransitive object coindexation derivation: object liam composes with the reflexive; (b) second step in the derivation: liam + himself composes into the verb showed tree set

76 Chapter 3. The Trees: Introducing the Model

3.5E XTENSIONSWITHDELAYEDTREE-LOCALITY

Although a wide variety of interactions between anaphors and other constructions are captured by this analysis, there is an entire class of cases that are not expressible under the set-local view of STAG derivation I have been presupposing. In this section, I use reflexives within picture-DPs to motivate an extension of the derivation notion to allow for DELAYED TREE-LOCALITY, first proposed by Chiang and Scheffler (2008). I then demonstrate that this extension also allows for anaphors in a variety of syntactic constructions, including adjuncts, raising verbs, ECM verbs, and multiple anaphors in the same sentence.

3.5.1A NAPHORSIN picture-DPS

The canonical non-local anaphor case is anaphors embedded one level deep in a picture-DP, as in (66).

(66) Noah and Emma saw the pictures of themselves/each other.

The derivation violates set-locality because the reflexive/reciprocal tree set composes into two separate trees: the anaphor part (shown in bold in Figure 3.16(c)) composes into the object position of the picture-DP tree set, shown in (a), before composing into the verb tree, while the antecedent part (not in bold in (c)) composes directly into the subject position of the verb tree. Delayed locality resolves this issue by relaxing the set-locality constraint to allow a delay in composition. I adopt the definition of delayed tree-locality proposed by Chiang and Scheffler (2008): trees in a multicomponent tree set may compose into (any number of) other trees before eventually composing into the same (destination) elementary tree.18 The number of delays is the union of the tree sets that participate in the delay, minus the destination tree set. Delayed tree-local MCTAG differs from the more expressive non-local MCTAG in requiring that the members eventually compose into the same elementary tree, but remains weakly equivalent to standard TAG (Chiang and Scheffler, 2008). Delayed tree-locality has permitted analyses of non-local right-node raising (Han et al., 2010), bound variable pronouns (Storoshenko and Han, 2010), and clitic climbing (Chen-Main et al., 2012). Applying delayed tree-locality to (66), the derivation proceeds as shown in Figure 3.16(d). Two of the anaphor trees in Figure 3.16(c) are delayed (shown with bold font), first composing into the object of the

18Storoshenko and Han (2013) propose a slightly different definition of delayed tree-locality tailored specifically to bound variable pronouns. Deciding between these two proposals, or developing a new definition specifically for anaphors, is left for future work, but I recognize that overgeneration is a concern, since without further constraint my analysis could allow, for instance,

(67) * Noahi thinks that Emma likes himselfi. Appealing to the obliqueness hierarchy, though, ensures these cases are ungrammatical because the anaphor is the primary object but does not have a less oblique coargument (since its antecedent is in another clause) so the sentence is correctly predicted to be ungrammatical.

77 3.5. Extensions with delayed tree-locality

picture-DP set at link 2 before ultimately composing into the verb tree (at link 2 ), which also receives the antecedent trees (at link 1 ).

(a) S∗ 2 DP t∗ 2 e

D NP ız t

the N PP et e

pictures P DP↓ 2 eet e↓ 2 z

of pics-o f

(b) S∗ 2 DP t 2 e

D NP ∀z t t∗ z

every N PP et e

picture P DP↓ 2 eet e↓ 2 z

of pic-o f

(c) S∗ 1 DP↓ 1 S∗ DP t 1 e t∗ e themselves/ t 1 b a each other τ τ↓

heet,τti eet

REFL/RECP λa et

λb t∗ (d) saw (e) saw

2 2 1 the-pics-of 1 every-pic-of

2 2 themselves/each other themselves/each other

1 1 noah+emma noah+emma

Figure 3.16: Elementary trees for (a) a picture-DP, (b) a quantificational picture-DP, and (c) a reflex- ive/reciprocal with delayed trees in bold; (d) is the derivation tree with delayed tree-locality for Noah and Emma saw the pictures of themselves/each other. and (e) the derivation tree with delayed tree-locality for Noah and Emma saw every picture of themselves/each other.

Quantificational picture-DPs, as in (68), have a parallel derivation, shown in (e), differing only in the tree set for every picture of, shown in Figure 3.16(b).

78 Chapter 3. The Trees: Introducing the Model

(68) Noah and Emma saw every picture of themselves/each other.

In order to ensure that all variables are properly bound, I can rewrite the semantic verb tree as in Figure 3.17.

The root node of the verb tree is split into an upper t 1 node and a lower t 2 node to ensure proper variable binding. The link designation on each t node ensures that the REFL/RECP tree adjoins at the top t node and the quantificational picture-DP scope tree adjoins at the bottom t node, whereby REFL can bind the a variable that composed into the every picture of tree.19 This verb tree configuration is additionally needed for raising and subject control verbs, discussed in Section 3.5.3 and Section 3.5.5.

(a) t 1

t 2

et e↓ 1

eet e↓ 2

saw

Figure 3.17: Alternate elementary semantic verb tree to ensure proper variable binding

3.5.2A NAPHORSINADJUNCTS

Anaphors embedded in a prepositional phrase that functions as an adjunct to the verb, as in (69), also violate set-locality. Using delayed tree-locality, though, the derivation proceeds as for picture-DPs, as shown in Figure 3.18(c). First, the antecedent composes into the anaphor tree set and then the anaphor half of that tree set composes into the adjunct tree and ultimately into the verb tree, while the antecedent half composes directly into the verb tree.

(69) Noah and Emma sang to themselves/each other.

More complicated adjunct examples, such as in (70), are handled similarly through the use of delay as well as appealing to an inequational obliqueness constraint. For the grammatical sentence in (70a), Noah first composes into the reflexive tree set. Then the reflexive component composes into an adjunct about tree at the accusative object position, and then as a whole adjoins into the verb talk-to tree at the VP node. The antecedent component is not delayed and composes directly into the accusative object position of to in the verb tree. Case is not enough to rule out the ungrammatical version of the sentence in (70b); however, as is standard in frameworks such as Relational Grammar, to-phrases are considered less oblique than

19Storoshenko and Han (2010) encounter a similar problem for bound variable pronouns, but instead of the approach adopted here, they assume that there is a semantic constraint against derivations resulting in unbound variables.

79 3.5. Extensions with delayed tree-locality

(a) VP 2 et 2 (b) S 1 2 t 1 2 (c) sang

2 VP∗ PP et∗ et DP 1 VP 2 et 2 e 1 ↓ ↓ 1 to

2 P DP↓ 2 eet e↓ 2 V sang themselves/each other to to sang 1 noah+emma

Figure 3.18: Elementary trees for (a) PP adjuncts and (b) intransitive verbs with appropriate links; (c) is the derivation tree with delayed tree-locality for the sentence containing an anaphor embedded in a PP adjunct, Noah and Emma sang to themselves/each other. about-phrases, meaning that the anaphor is less oblique than its antecedent and the sentence is correctly predicted to be ungrammatical.

(70) a. Emma talked to Noahi about himselfi.

b. * Emma talked to himselfi about Noahi.

3.5.3A NAPHORSWITHRAISINGVERBS

In contrast to object control verbs, raising verbs, such as seem in (71), do not have an inherent subject argument; instead, even though the subject of the sentence appears in the subject position of the raising verb, the lower clause verb provides the subject argument position, shown in Figure 3.19(a) with a 1 link. Therefore, the usual representation of seem in the TAG literature (with minor variations) does not contain a DP subject node, as shown in (b). However, seem does assign nominative case to its subject. Thus, the root VP of the seem tree has the value nom for its CASE feature, as shown in (b). The DP object of the preposition receives accusative case from the preposition to, so this feature structure is also shown.

(71) Noah and Emma seem to themselves/each other to be happy.

Once again, this configuration violates set-locality because the anaphor composes into the raising verb

20 tree at link 2 , but there is no position for the antecedent to also compose. However, the relaxation provided by delayed tree-locality allows the lexical anaphor part of the tree set to compose into the raising

21 verb at link 2 through delay (and both accusative features unify), which then composes into the lower

20An alternative local derivation would be to simply include a subject position in the elementary raising verb tree. Although this solution solves the locality issue, it has implications for the treatment of raising constructions in gen- eral, namely positing that raising verbs can have an external subject even though they only assign one theta role—to a proposition, not a subject—so I do not pursue this line of reasoning here. 21One addition change is needed for this derivation but it does not overtly the tree sets: the placeholder S auxiliary scope tree for the anaphor needs to be converted into a VP auxiliary scope tree so it can compose into the seem tree along with its lexicalized DP tree at the 2 links.

80 Chapter 3. The Trees: Introducing the Model

clause verb trees at link 3 . As previously foreshadowed, the nominative case feature on the root VP node of the raising verb tree then propagates to the subject DP node and root S node of the to be happy tree. When the antecedent component composes into the to be happy tree at link 1 , its underspecified case feature value adopts the nominative case value of the subject DP node during feature unification and thus properly obtains case. (d) contains the syntactic derived tree after feature unification and the derivation tree in (c) outlines this process. On the semantics side, as with quantificational picture-DPs, the predicate to-be-happy tree in

(a) can be drawn with a top t 1 2 node and a bottom t 3 node to ensure that the anaphor tree binds the a variable in the raising verb tree.

3.5.4A NAPHORSWITH ECM VERBS

ECM verbs, also known as subject-to-object raising verbs, as in (72), have two arguments: a subject (Noah and Emma) and a proposition (themselves/each other to be happy). Based on these structural properties, the elementary tree for an ECM verb contains a subject position, which has nominative case, and its foot S node has an accusative case feature value since it assigns case to its object, which is the subject of the predicate it adjoins into to fill its proposition argument. Figure 3.20(a) shows the relevant nodes with case features.

(72) Noah and Emma want themselves/each other to be happy.

In contrast to the previous examples, for ECM verbs the antecedent part of the anaphor tree set is the delayed part (shown in bold in (b)) by first composing into the subject of the ECM verb tree, where it receives nominative case, and then composing into the root of the non-finite verb tree. The derivation tree in (c) reflects this difference through the links shown. Since the lower predicate tree has its root S node, subject DP node, and higher VP node all with matching variables for case feature value, once the ECM verb tree adjoins, all of these nodes adopt accusative case. When the anaphor composes into the to be happy tree, its accusative feature value unifies with that of the subject DP and the derivation succeeds.

Other ECM constructions can involve multiple (surface accusative) objects, as in (73b), in which appealing to an inequational obliqueness constraint is once more needed to predict proper grammaticality.

(73) a. Emma wants himi to love himselfi.

b. * Emma wants himselfi to love himi.

81 3.5. Extensions with delayed tree-locality

" # " # S VP CASE CASE nom (a) 1 2 t 1 2 (b) 2 t 2 " # " # S VP CASE z X t 3 CASE et e↓ 2  XX P  XXX  PPP " # V VP " # VP et e 1 ht,eti t DP ↓ ¨¨HH ∗ CASE z ¨ H CASE z 3 seem PP VP∗ ↓ 1 " # to-be-happy ,,ll seem-to VP P DP↓ 2 CASE Q  Q to V VP ##cc to V AdjP

be happy

" # (c) to-be-happy (d) S CASE nom 3 ``` ```` 1 seem-to " # " # DP VP 2 CASE nom CASE nom themselves/each other ``` ``` 1 Noah&Emma V VP` ``` noah+emma `` seem PP VP !a Q !!! aaa  Q P DP V VP ##cc to themselves/each other to V AdjP

be happy

Figure 3.19: Elementary trees for (a) non-finite predicates with appropriate links, syntactic features, and se- mantic configuration for variable binding and (b) raising verbs with an anaphor object; (c) is the derivation tree with delayed tree-locality and (d) the syntactic derived tree for Noah and Emma seem to themselves/each other to be happy.

3.5.5A NAPHORSWITHSUBJECTCONTROLVERBS

Subject control verbs, such as try, have two arguments—an agent (Noah and Emma) and a proposition (to see themselves/each other)—as shown in Figure 3.21(a) for the sentence (74).

(74) Noah and Emma tried to see themselves/each other.

As with object control verbs, the lower verb cannot have its own subject, so the tried tree set contains a DP tree with caseless PRO in the syntax and a corresponding variable tree in the semantics that substitute

82 Chapter 3. The Trees: Introducing the Model

(a) S∗ 1 DP↓ 1 S∗ DP t 1 e t∗ e themselves/ τ t τ 1 b a each other ↓ heet,τ ti eet

REFL/RECP λa et

λb t∗

(b) S 1 t 1 (c) to-be-happy ``` ``` " # 2 DP VP PP et e 1 1 want CASE nom  PP ↓ ↓ 1 " # 1 S ht,eti t∗ themselves/each other CASE V 1 " # S want noah+emma want CASE acc *

Figure 3.20: Elementary trees for (a) a reflexive/reciprocal with delayed trees in bold and (b) ECM verbs with feature passing; (c) is the derivation tree with delayed tree-locality for the ECM verb sentence, Noah and Emma want themselves/each other to be happy.

into the object position of the lower non-finite verb to see tree set (not shown but parallel to to be happy). The derivation proceeds according to the derivation tree in (b), which is similar to that of ECM verbs. The antecedent first composes into the anaphor tree set. Then, the antecedent part of the anaphor tree set delays by composing into the subject position (at link 1 ) of the subject control tree set, getting nominative case, and then into the non-finite verb tree at the 1 links. The anaphor part of the tree set is not delayed and composes directly into the non-finite verb tree at the 2 links.

(a) S 1 DP t 1 e (b) to-see

1 DP 1 VP PRO et e 1 z ↓ ↓ 2 tried

1 V S∗ λz t themselves/each other tried et e 1 noah+emma ht,eti t∗ z

tried Figure 3.21: Elementary trees for (a) subject control verbs and (b) is the derivation tree for Noah and Emma tried to see themselves/each other.

83 3.5. Extensions with delayed tree-locality

3.5.6M ULTIPLE ANAPHORS

The final application of my analysis to non-local phenomena is for sentences such as (75a) that contain multiple anaphors within the same sentence, discussed in particular by Heim et al. (1991). Figure 3.22 contains the delayed tree-locality MCTAG account of this example, which follows from the previous examples but with two instantiations of the REFL/RECP tree set. The antecedent first composes into the REFL tree set in (d). The lexical reflexive part of this REFL tree set composes immediately into the introduce verb tree in (a) at link 2 . The antecedent part (shown in bold) is delayed by first composing into the RECP tree set in (c) at link 1 and then as a whole composing into the introduce tree at links 1 and 3 . The other order of reciprocal-reflexive, as in (75b), works similarly.

(75) a. Noah and Emma introduced themselves to each other.

b. Noah and Emma told each other about themselves.

84 Chapter 3. The Trees: Introducing the Model

(a) S 1 2 3 t 1 2 3 (b) introduce

1 3 DP↓ 1 VP et e↓ 1 2 each other

V DP↓ 2 PP eet e↓ 2 1 themselves introduce P DP 3 eeet e 3 ↓ ↓ 1 to introduce noah+emma

(c) S∗ 1 DP↓ 1 S∗ DP t 1 e t∗ e

et e 1 b a each other ↓ heet,eti eet

RECP λa et

λb t∗

(d) S∗ 1 DP↓ 1 S∗ DP t 1 e t∗ e

τ t τ 1 b a themselves ↓ heet,τ ti eet

REFL λa et

λb t∗

Figure 3.22: (a) Elementary trees for the verb introduce; (b) is the derivation tree with delayed tree-locality for the multiple anaphor sentence Noah and Emma introduced themselves to each other.; (c) is the recp tree set, and (d) the refl tree set with delayed trees in bold

3.6S UMMARY AND FUTURE WORK

In this chapter, I have shown how the formalism of STAG can not only handle both reflexives and reciprocals, but also provide a unified account of both, founded on the idea that these anaphors share a syntactic distribution but differ slightly and uniformly in their semantics. To accomplish this, I provide STAG tree sets for reflexives and reciprocals that differ only in their lexical presentation and their interpretation through operators REFL and RECP that capture their parallel semantic nature. It is, to my knowledge, the first STAG analysis to provide for reciprocals as well as reflexives. The analysis is consistent with earlier STAG analyses accounting for such syntactic phenomena as topicalization and semantic phenomena as quantification, while building on the previous STAG account by Frank (2008) of reflexives alone, making anaphoric notions more explicit, eliminating the need for c-command and dominance

85 3.6. Summary and future work constraints, and generalizing the analysis to capture reciprocals as well. There are a variety of other examples on which to test this analysis next, including the two cases shown in (76) that are challenges for many theories of anaphors and thus could be a could test for this analysis. In addition, as mentioned previously, it would be useful to apply this analysis crosslinguistically, especially to languages that allow anaphors in multiple cases and to languages that use a different case system, such as ergative-absolutive. Furthermore, applying the analysis to the two other kinds of reflexives, intensifiers and overrides, could be an interesting test.

(76) a. Split antecedents: Emma collaborated with Olivia on biographies about themselves/each other.

b. VP ellipsis and strict/sloppy readings: Noah likes himself and Liam does too.

Lastly, it is important to investigate the appropriate limits on delayed tree-locality to prevent overgeneration. One useful test case might be “long distance” or “wide scope” reciprocals, as in the reading of sentence (77a) shown in (77b), for which the STAG formalism may have a unique advantage. Higginbotham (1981) claims that this reading could be considered a long-distance binding of the reciprocal. Previous analyses of these cases have primarily taken a heavy semantics, light syntax approach (Dimitriadis, 2000) or a light semantics, heavy syntax approach (Heim et al., 1991). The cooperation between syntax and semantics in STAG may strike the right balance to account for these instances and may give insights into how to constrain delayed tree-locality.

(77) a. John and Mary think they like each other.

b. John thinks “I like Mary” and Mary thinks “I like John”.

In the next chapter I drill down into the leaf nodes of the model, specifically the operators REFL and RECP, to discuss how to refine their semantic definitions to account for additional anaphoric readings beyond distributive reflexivity and strong reciprocity.

86 4 The Leaves: Refining the Model

This chapter aims to refine the semantic definitions of the operators, REFL and RECP, in order to capture readings beyond the core notions of distributive reflexivity and strong reciprocity. I focus first on reciprocals since they exhibit a wider range of readings. I review their various readings as well as two previous approaches to determining the appropriate reading of a reciprocal, namely that of Dalrymple et al. (1998) and that of Winter (2001), the latter of which builds on the former analysis. I then build up the semantic operator RECP introduced in the last chapter into a form that accounts for all possible reciprocal readings and simplifies, generalizes, and explains Dalrymple et al.’s (1998) approach. I additionally show how the operator can be straightforwardly adjusted to account for all reflexive readings as well.

4.0.1R ECIPROCITY

The is exemplified in the sentence

(78) Noah, Liam, and Mason saw each other. which provides a way of enumerating a set of pairs participating in the “seeing” relation: viz., Noah saw Liam, Noah saw Mason, Liam saw Noah, etc. In fact, in the core reading of the sentence, every pair participates in the “seeing” relation. I will call the binary relation involved in the reciprocal construction (in this case, “seeing”) the RECIPROCAL RELATION and the participants in the relation (in this case, Noah,

Liam, and Mason) the DOMAINOFRECIPROCITY. In this case (though not all cases, as discussed below), the domain of reciprocity is comprised of the elements of the antecedent of the reciprocal, the subject of the sentence.

Thinking of the elements of the domain of reciprocity as nodes in a graph, with a directional edge from node a to node b if a and b are in the reciprocal relation, the reciprocal construction conveys the idea that the induced graph is (in graph-theoretic terms) a CLIQUE, that is, that every ordered pair of nodes is connected by an edge. (See Figure 4.1 for a depiction of the induced graph for the example sentence.) This clique

87 Noah Liam

Mason

Figure 4.1: Graph depicting Sentence 78. An edge from one node to another indicates that the former saw the latter.

Figure 4.2: Graph depicting Sentence 79. An edge from one node to another indicates that the former plate is stacked (immediately) on top of the latter plate.

interpretation of reciprocals constitutes its core reading, often termed the STRONGRECIPROCITY reading. But many others have noted apparent deviations from strong reciprocity that do not form cliques, but indeed are quite natural. As a simple example, consider the sentence

(79) The plates are stacked on top of each other.

Such a sentence well describes a scene in which is found a conventional stack of dinner plates. But it is not the case that in such a scenario (depicted as the graph in Figure 4.2), every pair of plates is in the “stacked on top of” relation since the bottom plate is not on top of any other plate. One previous work that systematically identified the possible reciprocal readings is by Dalrymple et al. (1998). The authors claim that there is a fixed taxonomy of six meanings for reciprocal constructions, ranging from strong (strong reciprocity (SR)) to weak (inclusive alternative ordering (IAO)), and propose a specific process for selecting among these possible meanings to find a reciprocal sentence’s actual truth conditions. This process accurately captures a variety of reciprocal examples. In this chapter, I unify the six meanings into one by appealing to a kind of Gricean accommodation, thereby simplifying, generalizing, and explaining the Dalrymple et al. (1998) process. I simplify the process by claiming that, instead of reciprocals being multiply ambiguous, there is only one reciprocal meaning

RECP (a relation defined over the reciprocal relation R and reciprocal domain Z), viz., a form of strong reciprocity, and this relation can be accommodated to form different related relations. I generalize the

88 Chapter 4. The Leaves: Refining the Model process because the accommodations of the relation are not fixed but are applied as required by the relation, which allows flexibility for capturing related phenomena through various accommodations. Lastly, I explain the process by providing motivation for why there are six reciprocal meanings. These three tasks are realized through a single semantic operator, RECP, serving as a unified analysis of reciprocals that not only captures both strong reciprocity and its weakened forms, but also has the flexibility to extend to various other reciprocal meanings, including and partitioned readings. Finally, the analysis bears a striking connection to a simple analysis of reflexives via a parallel operator, REFL.

4.0.2N OTATION AND TERMINOLOGY

Before discussing reciprocity in more depth, I describe some notation and terminology used throughout the chapter. I use lower-case letters as variables over individuals (x, y) and functions over individuals ( f ), and upper-case letters as variables over sets of individuals (Z) or properties (P) or binary relations (R). I use calligraphic letters (P) for functions over sets.

I use a standard higher-order logic notation. As is conventional, I use adjacency for application, which I take to be left associative, and I omit parentheses where it does not result in ambiguity. Bound variables are introduced with an (optional) indication of the domain they range over, their RESTRICTION, as well as their

SCOPE. Functions are notated with lambda notation (λhvariablei : hrestrictioni . hscopei), so that, for instance, λx : x ∈ Z . f x is a function from elements of the set Z to their image under the function f . Note the restriction x ∈ Z on the bound variable x. Logical quantification is notated similarly: ∀x : x ∈ Z . Px indicates that every element of Z has property P for instance. With this notational basis, I now describe in more detail strong reciprocity and its apparent variations.

4.1T HEPHENOMENA

I claim that reciprocity is fundamentally strong reciprocity, in which the reciprocal relation forms a clique (in graph-theoretic terms) over the reciprocal domain. Strong reciprocity requires every individual in the reciprocal domain to stand in the reciprocal relation with every other individual. This interpretation serves as the core reading of reciprocals. In this section, I describe several other cases of reciprocity readings that apparently diverge from strong reciprocity, namely, extended readings and weakened readings, before turning to my unified analysis in Section 4.2.

89 4.1. The phenomena

(a) (b)

Figure 4.3: Schematic depictions of extended readings in the scenario of boys collectively lifting. (a) Across- group reciprocal reading of The boys lifted each other. (b) Corresponding subplurality reading of The boys lifted themselves.

4.1.1E XTENDEDREADINGS

When the antecedent contains more than two elements, there can be two additional variations on strong reciprocity, which I refer to as EXTENDED readings. The first variation of this notion of strong reciprocity occurs when the elements of the domain of reciprocity are not elements of the antecedent, but rather subsets of the antecedent (Gillon, 1992). The reciprocal relation holds across these subsets. For instance, consider an (admittedly artificial) scenario in which a set of boys stand on a pair of platforms, a few boys on each platform, where each platform is outfitted with a pulley system whereby the boys on a platform, by pulling a rope, cause the other platform (and hence the boys thereon) to be lifted. The scenario, depicted in Figure 1.1, and repeated here in Figure 4.3(a), could be described by the sentence

(80) The boys lifted each other.

A naive interpretation of strong reciprocity would require that every boy lift every other boy, but here that does not hold. Rather, strong reciprocity holds over a domain of reciprocity that is a set of two subgroups of boys. I refer to these cases as ACROSS-GROUP readings (Gennaro Chierchia, p.c.). A second variation on strong reciprocity occurs when the reciprocal relation holds strongly but separately over elements of some partition of the antecedent. Fiengo and Lasnik (1973) identified this WITHIN-GROUP reading of reciprocals, using the example (81a). Imagine a scenario in which there are many men, who can be partitioned into groups of two, with reciprocal hitting between the members of each group. In this scenario, Fiengo and Lasnik (1973) claim that (81a) is still true even if no hitting occurs between members of different groups. This case still exemplifies strong reciprocity because hitting occurs between every member within every subgroup. In such cases, the antecedent is divided into subdomains, determined by context, and reciprocity holds within every subdomain, as shown in (81b).

90 Chapter 4. The Leaves: Refining the Model

(81) a. The men are hitting each other.

b.

A single sentence can exhibit either within-group or across-group readings, depending on context. For instance, the sentence

(82) a. The boys and girls taught each other.

b g b. b g or b b g g b b g g has a within-group reading in which the boys (individually) taught the boys and the girls taught the girls, and an across-group reading in which the the boys (collectively) taught the girls and the girls taught the boys. These two extensions to reciprocal readings can even co-occur in a single sentence to yield a reading in which there are both within-group and across-group aspects. An example is (83a), portrayed pictorially in (83b).

(83) a. The men’s and women’s relay teams compete against each other.

m m w w b. m m w w

m m m m w w w w m m m m w w w w

Imagine that there are multiple men’s relay teams competing against each other as well as multiple women’s relay teams competing against each other, but with no competing between men’s teams and women’s teams. Thus, the antecedent is first partitioned into subdomains of reciprocity according to gender (within-group), and then these subdomains are further divided into subgroups (relay teams), each of which competes against the others (across-group). Next, I look at cases in which the notion of strong reciprocity seems to be weakened.

4.1.2W EAKENEDREADINGS

Many (Langendoen, 1978; Dalrymple et al., 1998; Beck, 2001, among others) have pointed out apparent deviations from strong reciprocity, in which the strong reciprocity requirement is relaxed to varying degrees, so that not every element of the reciprocal domain must stand in the reciprocal relation with every other element. I review two main accounts of these weakened readings that inspired and shaped my analysis: an

91 4.1. The phenomena original account by Dalrymple et al. (1998) and a later account by Winter (2001) that expands upon the original account.1

4.1.2.1D ALRYMPLE ET AL.’S (1998) ACCOUNT

Dalrymple et al. (1998) claim that reciprocals are multiply ambiguous and propose a principle they call the Strongest Meaning Hypothesis (SMH) to determine the appropriate reading of a reciprocal in a particular context. Drawing on the work of Langendoen (1978) and Kánski (1987), Dalrymple et al. (1998) provide a taxonomy of six possible meanings for reciprocals, ranging from strong to weak, as illustrated in Table 4.1.2

As shown by the table divisions, I organize their six meanings into three sets of two—strong, intermediate, and weak—for clarity. Within each set of two readings, the first meaning involves a relation holding symmetrically of every pair (holds of x and y and of y and x); the second meaning (the

ALTERNATIVE RECIPROCITY reading) involves a relation that must hold only in one of the two directions (either of x and y or of y and x). The “strong reciprocity” reading is the same as the one I have described as the core notion of reciprocity.

Given this fixed taxonomy of reciprocal meanings, Dalrymple et al. (1998) propose a process for determining reciprocal meaning. First, the six possible reciprocal meanings—SR, SAR, IR, IAR, OWR, and IAO—are conflated according to the symmetry and/or of the relation R. If the relation R is symmetric, the six meanings reduce to three: SR ≡ SAR, IR ≡ IAR, and OWR ≡ IAO. If the relation is transitive, the six reduce to five: SR ≡ IR, SAR, IAR, OWR, and IAO. Lastly, if the relation is both symmetric and transitive, the six reduce to two: SR ≡ SAR ≡ IR ≡ IAR and OWR ≡ IAO. Next, each of the remaining meanings is tested, starting with the strongest, to see if the meaning holds of the relation. Lastly, appealing to the SMH, the truth conditions of the sentence are those captured by the strongest possible meaning candidate consistent with contextually provided information.

For example, for (84), the process proceeds as follows. First, reduce the six possible reciprocal meanings to three because the relation is symmetric: SR ≡ SAR, IR ≡ IAR, OWR ≡ IAO. Second, starting with the strongest first, test each remaining reading to see if the relation can hold. Since people only have two sides

1Both of these accounts assume that reciprocity is by default strong reciprocity that is semantically weakened; how- ever, the opposite view also exists, such as by (Langendoen, 1978), in which the default is weak reciprocity that is pragmatically strengthened. Both Dalrymple et al. (1998) and Winter (2001) argue against the view that weak reciprocity can be pragmatically strengthened, via conversational implicatures for instance, since implicatures can be cancelled while the effects of the SMH cannot. Based on this argument as well as others in the literature, I also uphold that reciprocity is more likely to be strong reciprocity by default. 2I have slightly changed the notation used by Dalrymple et al. (1998) for each reciprocal reading to follow that described in Section 4.0.2.

92 Chapter 4. The Leaves: Refining the Model

Strong reciprocity (SR) ∀x : x ∈ Z . ∀y : y ∈ Z ∧ y 6= x . Rxy “The legislators refer to each other indirectly.”

Strong alternative reciprocity (SAR) ∀x : x ∈ Z . ∀y : y ∈ Z ∧ x 6= y . Rxy ∨ Ryx No example provided by Dalrymple et al. (1998)

Intermediate reciprocity (IR) ∀x : x ∈ Z . ∀y : y ∈ Z ∧ x 6= y .

∃z0,...,zm ∈ Z . x = z0 ∧ Rz0 z1 ∧ ···

∧ Rzm−1 zm ∧ zm = y “The pitchers sat alongside each other.”

Intermediate alternative reciprocity (IAR) ∀x : x ∈ Z . ∀y : y ∈ Z ∧ x 6= y .

∃z0,...,zm ∈ Z .

x = z0 ∧ (Rz0 z1 ∨ Rz1 z0) ∧ ···

∧ (Rzm−1 zm ∨ Rzm zm−1) ∧ zm = y “The students gave each other measles.”

(One-way) Weak reciprocity (OWR) ∀x : x ∈ Z . ∃y : y ∈ Z ∧ x 6= y . Rxy “The pirates stared at each other.”

Inclusive alternative ordering (IAO) ∀x : x ∈ Z . ∃y : y ∈ Z ∧ x 6= y . Rxy ∨ Ryx “The planks are stacked atop each other.”

Table 4.1: The six reciprocal meanings according to Dalrymple et al. (1998)

93 4.1. The phenomena and with more than two people, every pitcher cannot be directly sitting alongside every other pitcher, SR (≡ SAR) cannot hold. IR (≡ IAR) can hold, though, since every pitcher can sit alongside every other pitcher either directly or indirectly. (Note that OWR (≡ IAO) can also hold since every pitcher can be sitting alongside some other pitcher.) Third, appealing to the SMH, the truth conditions of (84) are captured by the strongest possible remaining meaning candidate, in this case IR (≡ IAR).

(84) The pitchers sat alongside each other. [IR]

This approach obtains the correct meaning for a wide variety of reciprocal sentences. However, it neither justifies why there are these particular six reciprocal meanings to choose from nor motivates why the strongest meaning is the appropriate one. My analysis also relies on context, but determines a reciprocal’s meaning through contextually signaled accommodations of a single core reciprocal relation. In Section 4.4, I show how all six of these reciprocal readings can be reduced to a single parameterized semantic representation that is in fact strong reciprocity, so I postpone more detailed discussion until then.

4.1.2.2W INTER’S (2001) ACCOUNT

The second account, by Winter (2001), builds directly upon Dalrymple et al.’s (1998) account, reformulating their SMH of reciprocals into an Extended SMH (ESMH) that applies more generally to plural predication. The ESMH is defined as follows:

(85) Extended Strongest Meaning Hypothesis: “A complex plural predicate with a meaning that is derived from one or more singular predicates using universal quantification is interpreted using the logically strongest truth conditions that are generated from its basic universal meaning and that are not contradicted by known properties of the singular predicate(s).”

In other words, if the semantics of a plural predicate involves universal quantification over singularities, whether the predicate involves a reciprocal, Boolean of two predicates, or atomic distributivity, the ESMH applies. In graph terms, the ESMH defines the appropriate interpretation of a reciprocal reading as the maximal graph permitted without contradicting the known lexical properties of the predicate. This approach improves upon and expands that of Dalrymple et al. (1998) by transforming the SMH from a specific principle about reciprocals to a more general process of plural predication. My approach, developed independently of Winter’s (2001), is a dual approach in the sense that both analyses seem to yield the same reciprocal reading predictions. Although my approach does not extend to pluralities more generally (yet), it does easily extend to capture all of the possible reflexive readings, which

94 Chapter 4. The Leaves: Refining the Model is the focus of this dissertation, and in addition to the weakened readings, captures the extended readings discussed in Section 3.5, which Winter (2001) excludes. In the next section, I present my analysis of reciprocity using a semantic operator, RECP, and sequentially apply it to extended readings, reflexives, and weakened readings.

4.2C APTURINGEXTENDEDREADINGS

A common means of representing the semantic conditions of reciprocals is by using an operator. Bennett (1974), in an extension of Montague’s semantics, seems to have first proposed a reciprocal operator. According to his syntactic rule S70, the reciprocal “applies to a relation and a set if and only if every pair of non-identical members of the set stand in the relation (in both orders)” (Carpenter, 1997). This reciprocal operator idea has since been adopted and made more explicit by Heim et al. (1991) and Büring (2005), among others. Heim et al. (1991) propose a compositional analysis of reciprocals in which the each of each other raises at logical form (LF) to adjoin to the antecedent of the reciprocal and serve as a distributive operator over the noun phrase. The residue of the construction after movement, e other, is a reciprocator operator that operates on the predicate VP, rather than on the subject NP, to contribute the distinctness requirement. The authors restrict their attention to two member antecedents, and thus only strong reciprocity, presuming that their results would hold under a more sophisticated analysis of antecedents of a larger cardinality. (Beck (2001) points out that their basic analysis cannot extend to capture weaker readings without modification, but presents one such modification.)3 Büring (2005) uses not only a reciprocal distributive operator, D, but also a binder prefix, β, which functions at LF to semantically bind a DP whether it is a pronoun, reflexive, or reciprocal. This approach captures strong reciprocity, but its ability to capture weaker readings is undetermined. Büring (2005) additionally observes that

“while it seems clear that more readings than just strong reciprocity are required, the questions of just which and how many readings there are, as well as how the actual reading is selected for a particular example, remain somewhat open.”

I aim to answer these questions. In the next sections, I introduce the basic reciprocal operator RECP that captures the core notion of reciprocity, so-called strong reciprocity, and then progressively modify RECP to account for the different extended and weakened readings.

3An explicit comparison of the coverage of compositional analyses of reciprocals, such as that of Heim et al. (1991) and Beck (2001), with that of the analysis presented in this chapter is left for future work.

95 4.2. Capturing extended readings

4.2.1S IMPLECASES

The core strong reciprocity reading can be formalized as an operator RECP over a binary relation (R) and an antecedent set (Z).

(86) RECP ≡ λR . λZ . ∀x : x ∈ Z . ∀y : y ∈ Z ∧ y 6= x . Ryx

Informally speaking, the operator holds of a relation R and set Z just in case every pair x and y in the set Z, where x and y are distinct, are in the relation R. The definition here just formalizes the idea that Z is a clique of R. Applying RECP to the sentence (87) yields the correct (and only) reading that Noah gazed at Emma and Emma gazed at Noah.

(87) Noah and Emma gazed at each other.

I point out in passing an attractive property of this analysis. Replacing the 6= with =,

(88) REFL ≡ λR . λZ . ∀x : x ∈ Z . ∀y : y ∈ Z ∧ y = x . Ryx yields a formalization of (one version of) the reflexive relation, as appropriate for, for example,

(89) Noah and Emma gazed at themselves. under the reading in which each of the two gazed individually (as in separate mirrors), Noah at Noah, Emma at Emma. The specification that y = x allows for a simplification to the semantically identical (and more familiar)

(90) REFL0 ≡ λR . λZ . ∀x : x ∈ Z . Rxx .

I explore this property of the analysis in detail in Section 4.3. In order to capture the extended readings of

Section 4.1.1, RECP must be modified slightly. I turn to these modifications now.

4.2.2A LLOWINGFORACROSS-GROUPREADINGS

Recall that some reciprocal cases in which the antecedent of the reciprocal has more than two elements involve a domain of reciprocity composed of subsets of the antecedent rather than elements of the antecedent. For instance, the sentence (80) can hold in a scenario in which the boys are divided into subpluralities and every subplurality of boys lifts every other subplurality of boys.

To capture this interpretation, I modify the semantic definition of RECP by introducing the notion of a

PARTITION. A partition of a set S is a set of disjoint non-empty subsets of S whose union is S. Higginbotham (1981) proposed the idea of a partition to indicate that a relation holds between a plural DP

96 Chapter 4. The Leaves: Refining the Model and its VP if there is a partition of the plural DP such that the VP holds of every element in that partition. Using his example, the sentence in (91) is false on the view that the plurality composed of Handel and Wagner has the property expressed by wrote operas since no opera was written through the combined effort of Handel and Wagner. In order to make (91) true, the plurality can be partitioned into its elements so wrote operas is separately true of Handel and of Wagner. For reciprocals (and reflexives), partitions allow the antecedent to be separated into various subgroupings, which can yield across-group readings.

(91) Handel and Wagner wrote operas.

The RECP operator can be easily modified to incorporate a partition for the purpose of allowing across-group readings. I introduce a new function P(Z) that maps a set Z onto a unique CONTEXTUALLY

SALIENT PARTITION of Z. Instead of each x and y being members of the set of individuals Z, they become members of the partition of Z, namely P(Z). This slight alteration partitions the antecedent into intermediate subpluralities, which are viewed as individuals for the purpose of the participation in the

4 reciprocal relation. The revised operator definition, renamed RECP1 to avoid confusion, is

(93) RECP1 ≡ λR . λZ . ∀x : x ∈ P(Z) . ∀y : y ∈ P(Z) ∧ y 6= x . Ryx

Returning to the example in (80), the contextually salient partition of boys is the partition into the groups on each platform. The RECP1 operator then ensures that each such group of boys x stands in the lifting relation with every other group y.

Crucially, since one of the partitions of a set is the partition into its singleton subsets (the SINGLETON

PARTITION), the RECP1 operator definition subsumes the previous RECP in cases where the singleton partition is contextually salient. That is, RECP1 still allows readings where the domain of reciprocity is just the individual elements of the antecedent.

4.2.3A LLOWINGFORWITHIN-GROUPREADINGS

For scenarios such as the one described for sentence (81a), reciprocity holds within contextually salient subpluralities. This interpretation requires a different use of partitioning in which the antecedent set is

4Partitions may in fact be too specific, and the more general notion of a cover might be preferable. A cover of a set S is a set C of non-empty subsets of S whose union is S (Schwarzschild, 1996). It thus eliminates the disjointness requirement. Support for covers over partitions comes from the following example due to Gillon (1987): (92) The men wrote musicals. in which the men denotes Rodgers, Hammerstein, and Hart. The sentence is true, despite the fact that none of the men individually wrote musicals, because Rodgers and Hammerstein wrote musicals together and Rodgers and Hart wrote musicals together. A partition approach fails since the subsets overlap—Rodgers is a part of both subsets—while a cover approach succeeds because the union of the subsets is the set of men. I hold to partitions for now and leave deciding on the exact term for future work.

97 4.3. Capturing reflexives

partitioned into multiple domains of reciprocity, as in this definition of a reciprocal operator RECP2:

0 0 0 (94) RECP2 ≡ λR . λZ . ∀Z ∈ P(Z) . ∀x : x ∈ Z . ∀y : y ∈ Z ∧ y 6= x . Ryx

For sentence (81a), the contextually salient partition would group the antecedent set of men into pairs, so that for every pair Z0 within the group of partitioned men P(Z), man x stands in the reciprocal hitting relation with his fellow fighter y. Thus, each partitioned fighting group is itself a subdomain of reciprocity.

Again, this extension RECP2 subsumes the original RECP, because one possible partition of Z is the

PARTITION OF THE WHOLE, that partition that has just a single element, the set Z itself.

4.2.4C OMBININGEXTENDEDREADINGS

As mentioned above, both within-group and across-group aspects can co-occur in a single sentence, as in (83a). Combining the two formalizations above allows for just this case:

0 0 0 (95) RECP3 ≡ λR . λZ . ∀Z ∈ P(Z) . ∀x : x ∈ P(Z ) . ∀y : y ∈ P(Z ) ∧ y 6= x . Ryx

Returning to the example (83a), RECP3 allows for partitioning Z into a two-gender partition, where each gendered subplurality Z0 is further partitioned into relay teams, where distinct pairs of teams x and y are in the competing relation. This version of the semantic operator RECP3 can still capture all of the simpler (core, non-extended; within-group only; across-group only) examples, since P(Z) can be the partition of the whole and P(Z0) can be the partition into singletons.

I now have a semantic operator that captures four different versions of strong reciprocity depending on how the domain of reciprocity and the elements within that domain are partitioned. In the next section, I show how RECP3 can be very slightly modified to capture reflexives.

4.3C APTURING REFLEXIVES

Although similar in their syntactic distribution, reflexives and reciprocals differ in the relations they portray and the readings they yield. Reflexives involve a relation between the antecedent and itself, while reciprocals require the relation to hold among disjoint elements of the antecedent. Reflexives with plural antecedents can have three main readings—distributive, intermediate (subplurality), and cumulative. In what follows, I discuss in more detail the three readings of reflexives and show how the reciprocal operator RECP3 can be trivially modified into REFL3 to capture these three reflexive readings.

98 Chapter 4. The Leaves: Refining the Model

4.3.1R EFLEXIVE READINGS

The DISTRIBUTIVE reading of a reflexive with a plural antecedent occurs when the relation expressed by the verb holds of each element in the plural antecedent and itself; the action is distributed among the parts of the antecedent. For instance, in (96), the distributive reading yields that Noah saw himself (and not Emma) and Emma saw herself (and not Noah), as, perhaps, in a mirror.

(96) Noah and Emma saw themselves.

As with reciprocals, reflexives with a plural antecedent can have a SUBPLURALITY reading, in which a relation holds of contextually salient subpluralities within the whole antecedent. In the sentence in (97), which is simply the reflexive version of (80), imagine once again that there are several subpluralities of boys, each of which is standing on its own platform. In contrast to the reciprocal case, though, now each platform is attached to its own pulley system and each subplurality of boys must (collectively) pull a rope to lift its own platform and thereby the group. The subplurality reading then indicates that the lifting relation holds of each subplurality of boys because each group raises its own platform to lift themselves. (A distributive reading would also be possible in the scenario in which each boy is on his own platform and individually lifts himself.)

(97) The boys lifted themselves.

There is, finally, a CUMULATIVE reading for reflexives that occurs when the relation expressed by the verb holds of the entire plurality and itself—the action is true of the cumulative group. Using the same example, the cumulative reading holds when there is only one group of boys who cumulatively work together to lift their platform and thereby themselves as a whole.

4.3.2R EFLEXIVES AS OPERATORS

In Section 4.2.1, I proposed modeling reflexive meanings by simply replacing the distinctness constraint

(y 6= x) in RECP with an identity constraint (y = x). By making this change to the more expressive operator definition RECP3, I obtain a reflexive operator definition REFL3 defined as follows:

0 0 0 (98) REFL3 ≡ λR . λZ . ∀Z ∈ P(Z) . ∀x : x ∈ P(Z ) . ∀y : y ∈ P(Z ) ∧ y = x . Ryx.

Surprisingly, this definition captures all three readings of reflexives—distributive, subplurality, and cumulative—in a natural manner. For the distributive case, I take the partition P(Z) to be the partition of the

99 4.4. Capturing weakened readings whole (so Z0 is itself Z), and the partition P(Z0) to be the singleton partition. In regards to the previous example, in (97), every boy within the whole group of boys Z lifts his own platform and thereby himself.

For the subplurality reading, I again take the partition P(Z) to be the partition of the whole, but the partition P(Z0) is a partition into the subpluralities that are reflexively participating in the relation. In the example, the group of boys Z0 is partitioned into multiple subpluralities x of boys, each of which stands on its own platform. Each subplurality of boys works together to lift its own platform and thereby themselves.

For the cumulative reading, the domain Z0 can be partitioned itself into a partition of the whole. Thus there is only one set x that contains all individuals in Z. That is, all boys form one group that cumulatively lifts the whole group.

Note that in all these cases, the partition P(Z) is always a partition of the whole; this partition plays no role in the various reflexive readings. This is not surprising, given that there is no use of REFL3 that cannot be generated using P(Z) as the partition of the whole since the second layer of partitioning provides the appropriate subgroupings. Indeed, the definition is equivalent to a simpler variant in which the extra layer of partitioning is eliminated.

(99) REFL1 ≡ λR . λZ . ∀x : x ∈ P(Z) . ∀y : y ∈ P(Z) ∧ y = x . Ryx

REFL1 can be simplified further by removing the second superfluous entity y so the relation holds between x and x:

(100) REFL0b ≡ λR . λZ . ∀x : x ∈ P(Z) . Rxx.

I have shown how the reciprocal operator RECP (and all of its variations) have a parallel reflexive version

REFL (and corresponding variations thereof) that account for the possible reflexive readings. I now return to discussing reciprocals for the remainder of the chapter.

Before turning to the apparent exceptions to strong reciprocity, the weaker readings of reciprocals, I reduce the RECP3 operator definition into a simpler form for ease of discussion. I revert to the base RECP case by removing the partitionings added to capture subplurality readings:

(101) RECP ≡ λR . λZ . ∀x : x ∈ Z . ∀y : y ∈ Z ∧ y 6= x . Ryx

The partitions can easily be added back in to the operator definition at any point, and in fact, I do so in Section 4.4.1.

100 Chapter 4. The Leaves: Refining the Model

2 1 3

Figure 4.4: Schematic depiction of The medalists stood alongside each other.

4.4C APTURINGWEAKENEDREADINGS

As it stands, the RECP relation captures the strong reciprocity reading, as exemplified for instance by sentences like

(102) The medalists congratulated each other.

However, as first noted by Langendoen (1978), there are felicitous reciprocal sentences where strong reciprocity does not hold. As an example, consider the following sentence, similar to (84):

(103) The medalists stood alongside each other.

Under the natural (Olympic medal ceremony) scenario, depicted in Figure 4.4, the gold medalist might be standing alongside the silver medalist and vice versa, as well as standing alongside the bronze medalist and vice versa, but the bronze and silver medalists would not be standing alongside each other. Nonetheless, sentence (103) is true in this scenario, even though strong reciprocity does not hold—the graph of the relation is not a clique.

Dalrymple et al. (1998) attribute this weaker reciprocity reading, which they call INTERMEDIATE

RECIPROCITY, based on a selection among a set of six readings reproduced in Table 4.1. First, the relation of “standing alongside” is symmetric, so the three alternative readings become equivalent to their non-alternative counterparts (SR ≡ SAR; IR ≡ IAR; OWR ≡ IAO). There are now three possible readings to choose from: strong reciprocity (≡ SAR), intermediate reciprocity (≡ IAR), and one-way weak reciprocity (≡ IAO). Starting from the strongest possible meaning, the relation cannot exhibit strong reciprocity based on the non-linguistic fact that people only have two sides, so in groups of three (or more), (at least) two people will not be in the “standing alongside” relation with each other. The next strongest meaning candidate, intermediate reciprocity, can account for the truth conditions of the sentence, though, because every medalist is standing alongside every other medalist either directly or indirectly. The weaker one-way weak reciprocity, and its equivalent intermediate alternative ordering, are also consistent with the sentence’s truth conditions because every medalist is standing alongside some other

101 4.4. Capturing weakened readings medalist. However, the SMH says to choose the strongest truth condition, in this case intermediate reciprocity, which is in fact the meaning of the reciprocal in (103).

According to this method, the process of finding the correct reciprocal meaning thus involves narrowing down six predetermined possible reciprocal meanings according to the symmetry or transitivity of the reciprocal relation and picking the strongest possible one available. Although this process results in the correct meaning, why there are six reciprocal meanings and why the strongest possible meaning is the correct one is unclear.

Instead, I propose a kind of Gricean explanation for the observed reading for (103). Note that the antecedent relation corresponding to “stand alongside” (in the sense used in the example)—call it Rsa—is an inherently nontransitive relation. That is, if Rsa ab and Rsa bc, then it cannot hold that Rsa ac. It follows that

RECP Rsa z must be false for any set of entities z of cardinality greater than two (as in the example). Sentences incorporating “stood alongside each other” must necessarily be false under strong reciprocity.

The infelicity of such sentences leads naturally to a Gricean accommodation for them, and since it is the inherent nontransitivity of the relation Rsa that is at issue, the natural accommodation is to replace Rsa with one generated from it but allowing for transitivity, in particular, the transitive closure of Rsa, which I will T 5 notate Rsa. Doing so indeed generates the appropriate truth conditions for sentences incorporating “stood alongside each other”, namely, they now hold for linear chains of alongside-standing, as in Figure 4.4.

In summary, the analysis proposed here is that all reciprocal expressions are interpreted in terms of strong reciprocity of some relation, but that sometimes that relation is not the overtly expressed one but a relation accommodated from it, for instance, by closing the relation in one or another way in response to properties of the original relation that make it intrinsically incapable of otherwise supporting strong reciprocity.

It is important to note that the trigger for such accommodation is not that the particular relation happens to be nontransitive (say) in a contingent sense, that is, the relation doesn’t happen to hold transitively. For instance, consider a case in which the gold medalist congratulated both the bronze and silver medalist and vice versa, though the bronze medalist did not congratulate the silver medalist and vice versa. By my analysis, the scenario would not be describable by the sentence (102), even though the graph of the relation is identical to that in which sentence (103) was taken to hold. That is because no accommodation would

5The transitive closure of a relation R is the smallest transitive relation that contains R. Similarly, the symmetric closure is the smallest symmetric relation that contains R. Formally,

RT xy ≡ Rxy ∪ ∃z . Rxz ∩ RT zy (4.1) RS xy ≡ Rxy ∪ Ryx . (4.2)

102 Chapter 4. The Leaves: Refining the Model occur, since the relation “congratulate” is not inherently nontransitive, it just happens to be in the scenario depicted. Given the success of this approach in weakening readings for nontransitive relations, I might look for other types of relations that lead to inherent falsity as antecedent relations of reciprocals. I turn to two such examples: inherently nonsymmetric and inherently functional relations. I first consider relations such as “give measles to”, which is (by principles of epidemiology) not only inherently nontransitive but also inherently nonsymmetric. Again, since such a relation R is both nonsymmetric and nontransitive, the proposition RECP Rz cannot ever be true, regardless of z. Here, the transitive closure RT of any such R is insufficient to generate a relation that can be a clique, because the transitive closure of a nonsymmetric relation need not be symmetric, and cannot be for ordered relations such as expressed by “give measles to”. Instead, the relation can be accommodated by taking the symmetric transitive closure RST . Doing so leads us to the accommodated proposition RECP RST z, which again holds just in the desired cases, and exactly captures Dalrymple et al. (1998)’s INTERMEDIATE ALTERNATIVE

RECIPROCITY. What about the case of a relation that is inherently nonsymmetric but not inherently nontransitive? The present approach would predict that reciprocals of such a relation would be accommodated by taking the symmetric (but not transitive) closure of the relation and verifying the reciprocal operator over it. This corresponds to a reading that Dalrymple et al. (1998) refer to as STRONG ALTERNATIVE RECIPROCITY. They report no attested cases of such readings, however. Given my approach, there is now a recipe for finding such cases, viz., to find a relation that is inherently nonsymmetric yet can be transitive and use it as the reciprocal relation. For instance, the “ancestor” relation has the requisite properties. The relation not only can be transitive, it inherently is, yet it is also inherently nonsymmetric; one can’t be the ancestor of one of your ancestors (barring time travel). I would predict, then, that the sentence

(104) a. The people buried in this cemetery were ancestors of each other.

b.

c. would hold just in case the symmetric closure of the ancestor relation of the people in question formed a clique, that is, if the people form a single line of ancestry. This would hold, for instance, of a person buried with a mother and maternal great-grandmother (104b), but not of a person buried with both a grandmother and a grandfather (104c). This matches my intuitions; in the latter case, the grandmother and grandfather are not ancestors of each other, vitiating the relation even as accommodated.

103 4.4. Capturing weakened readings

Finally, consider relations that are inherently (partial) functional, in the sense that for all elements x there exists at most one y such that Ryx. Functions over at least three elements are inherently nontransitive (if Rab and Rbc then Rac and R is not functional on a), but functionality is an even stronger restriction. And as with inherently nontransitive and nonsymmetric relations, the graphs of functional relations can never be cliques. I predict, then, that when used in a reciprocal context, a functional relation will be accommodated to generate a relation that at least potentially satisfies the strong reciprocity relation. Again, this can be done by addressing the particular issue that leads to the inherent falsity of strong reciprocity: In a function, at most one element can be in the range of each input, whereas a clique requires that all elements are in the range of each input. I thus define a transformation that modifies the relation so that if the range of the relation exists, it covers all elements. Define the UNIVERSALIZATION of R relative to the domain Z, R∀Z, as follows:

R∀Z yx ≡ ∃y0 : y0 ∈ Z . Ry0 x

R can be accommodated by transforming it into R∀Z.

By way of example, I examine the relation “stared at”, which has a natural interpretation in context under which it is functional: each person can stare at at most one other person at a time.

(105) The pirates stared at each other.

In this case, it is impossible for a set of more than two pirates to stare at each other in the strong reciprocity sense. But taking instead the universalization of the “staring at” relation over the domain of pirates yields that sentence (105) would hold just in case each pirate stares at at least one (and therefore exactly one) other pirate. This is exactly the ONE-WAY WEAK RECIPROCITY reading that Dalrymple et al. (1998) attribute to the sentence.

For some functional relations, even this accommodation is insufficient to allow for generating a clique. Functional relations are inherently nontransitive, but may or may not be inherently nonsymmetric. The “stared at” relation happens to be potentially symmetric, but the “stacked on top of” relation is a functional relation that is inherently nonsymmetric. For such relations, accommodation by universalization of the symmetric closure is predicted. Thus, the sentence (79) would be deemed to hold just in case there is a single stack of plates, with each plate (except the bottom one) stacked on top of each other. Again, this matches exactly the case of Dalrymple et al. (1998)’s INCLUSIVE ALTERNATIVE ORDERING.

In summary, I have noted three properties of relations—inherent nonsymmetry, nontransitivity, and functionality—that predict that their use as reciprocal relations are unsatisfiable. In Table 4.2 I show the

104 Chapter 4. The Leaves: Refining the Model

Nonsymmetric Nontransitive Functional Reading – – – Strong reciprocity (SR) + – – † Strong alternative reciprocity (SAR) – + – Intermediate reciprocity (IR) + + – Intermediate alternative reciprocity (IAR) – + + One-way weak reciprocity (OWR) + + + Inclusive alternative ordering (IAO) – – + (not instantiable) + – + (not instantiable)

Table 4.2: The eight possible combinations of three relation properties, along with their corresponding read- ings (taken from Dalrymple et al. (1998)). + indicates the relation inherently has the property, − that it does not. † indicates that Dalrymple et al. (1998) claim the reading to be unattested.

eight combinations of the properties. Of these, two are not instantiable (since functional relations are always nontransitive), leaving six cases, each of which corresponds exactly to the six options in the Dalrymple et al. (1998) taxonomy. For each, the natural accommodation of the relation—by symmetric closure, transitive closure, universalization, or combinations thereof—yields exactly the readings noted in the earlier work. This perspective contrasts that of Dalrymple et al. (1998) by claiming that there is just one notion of reciprocity captured under variations of one relation, rather than six separate reciprocal relations. Indeed, the reciprocal notion can be formalized by modifying the RECP relation introduced earlier.

(S)(T)(∀Z) (106) RECP4 ≡ λR . λZ . ∀x : x ∈ Z . ∀y : y ∈ Z ∧ y 6= x . R yx

The parentheses around each parameter indicate that the parameter is optional, depending on the requirements to accommodate the relation. For instance, if a relation is not inherently nonsymmetric, then there is no need to symmetrically close the relation because the base relation already includes the possibility of symmetry needed for generating a clique. However, if a relation is inherently nonsymmetric, the reciprocal relation could not possibly be true; in order for a clique to be possible, the relation therefore must be accommodated through a transformed relation that could be symmetric. Adding the symmetric closure of the relation is this accommodation. Similarly for transitive closure and functional universalization. Returning to the different combinations of these three properties displayed in Table 4.2, I can now provide the appropriate version of the operator RECP4 for each reading. If a property is positive for a certain reading, the relation requires a closure of that property. Table 4.3 portrays the form RECP4 takes for each reading according to its properties along with an example (some adapted from Dalrymple et al. (1998)). All six viable interpretations of reciprocity are thus captured by the semantic operator RECP4, through the use of

105 4.4. Capturing weakened readings

Strong reciprocity λR . λZ . ∀x : x ∈ Z . ∀y : y ∈ Z ∧ y 6= x . Ryx “The teammates refer to each other using nicknames.” Strong alternative reciprocity λR . λZ . ∀x : x ∈ Z . ∀y : y ∈ Z ∧ y 6= x . RS yx “The people buried in the cemetery are ancestors of each other.” Intermediate reciprocity λR . λZ . ∀x : x ∈ Z . ∀y : y ∈ Z ∧ y 6= x . RT yx “The pitchers sat alongside each other.” Intermediate alternative reciprocity λR . λZ . ∀x : x ∈ Z . ∀y : y ∈ Z ∧ y 6= x . RST yx “The students gave each other measles.” One-way weak reciprocity λR . λZ . ∀x : x ∈ Z . ∀y : y ∈ Z ∧ y 6= x . RT ∀Z yx “The pirates stared at each other.” Inclusive alternative ordering λR . λZ . ∀x : x ∈ Z . ∀y : y ∈ Z ∧ y 6= x . RST ∀Z yx “The planks are stacked on top of each other.”

Table 4.3: The various forms of recp4 with example sentences various instantiations of parameters indicating symmetric closure, transitive closure, and functionality.

RECP4 thus demonstrates that all reciprocity is in fact strong reciprocity, which can be accommodated into various weaker forms.

4.4.1U NIFYING THE ANALYSIS

The reader can check that the partitions needed to account for the extended readings can easily be added to

RECP4 to create one all-encompassing semantic operator, RECP5:

0 0 0 (S)(T)(∀Z) (107) RECP5 ≡ λR . λZ . ∀Z ∈ P(Z) . ∀x : x ∈ P(Z ) . ∀y : y ∈ P(Z ) ∧ y 6= x . R yx.

This version of the operator can capture sentences with combined extended and weakened readings, as in the previous example, repeated in (108a), in which there are multiple stacks of plates, as shown in (108b).

(108) a. The plates are stacked on top of each other.

b.

Since each plate is only stacked on top of the one below it within its pile, and there is no “stacked on top of” relation across piles, the plates can be partitioned into separate subpluralities, in which weakened reciprocity (IAO) appropriately holds within each pile of plates. Other combinations of extended and weakened reciprocal scenarios follow similarly.

106 Chapter 4. The Leaves: Refining the Model

The present analysis goes further in predicting that other accommodation types might exist for relations that are unsatisfiable in reciprocal form beyond the three parameters already considered. For instance, Fiengo and Lasnik (1973) pointed out that some sentences exhibit “vagueness” in reciprocity, such as how (109) can refer to a bar room brawl, in which some men do not hit some other men.

(109) The men were fighting each other.

This meaning does not fall under Dalrymple et al. (1998)’s reciprocal meaning taxonomy and the authors do not explicitly explain this reciprocal case other than to refer to it as strong reciprocity used “in a loose way”. My approach as it stands, however, has the potential to account for this case. The “fighting” relation is inherently nontransitive and functional so can be closed under transitivity and universalization. To account for the vagueness, or the men who are not fighting other men, the relation can be accommodated further by adding the few extra edges needed to make a clique possible. Accommodating vagueness can involve adding a pragmatically appropriate small proportion of links to the graph, but determining the constraints for limiting the number of links is left for future work. Accounting for vagueness is thus a natural extension of the analysis that does not require extra tools.

4.4.2C OMPARISON WITH PREVIOUS ANALYSES

The analysis I presented here was devised independently of Winter’s (2001) approach, but seems to yield the same predictions for the six reciprocal interpretations posited by Dalrymple et al. (1998). Instead of adding edges to form a clique, Winter’s (2001) appropriate graph is the maximum subset of the clique to which no other edges can be added. One way to distinguish our two approaches would be to find a scenario in which the graph is maximal, but taking the appropriate closures does not result in a clique. Future work can attempt to tease apart the two approaches for any differing predictions. Nonetheless, my analysis does improve upon both that of Dalrymple et al. (1998) and that of Winter (2001) in a few ways. First, I provide an explanation for why there are only six readings of reciprocals and where to find examples for each. For instance, Dalrymple et al. (1998) posit that there may be a strong alternative reciprocity reading, but do not provide an example of it. Through the possible combinations of parameters, my approach posits up front that such a meaning exists, exemplified in (104a). Second, my analysis not only captures reciprocal interpretations of (distributive) predicates that range over singular individuals, but also of predicates in which reciprocity holds over groups of individuals (across-group readings) and of predicates in which reciprocity holds separately over individuals within various groups, or partitions (within-group readings). The version of the SMH as proposed by either Winter (2001) or

107 4.5. Summary and future work

Dalrymple et al. (1998) applies to distributive predicates ranging over singular individuals, but the authors do not attempt to explain collective predicates or partitioned predicates. (Some version of the SMH may work, but testing is needed to work out the details). Both Winter (2001) and Dalrymple et al. (1998) also restrict their scope to cases involving small groups and ignore larger groups of individuals for which vagueness may affect the interpretation. Handling vagueness follows directly from my analysis, however, with no additional machinery. Finally, my approach naturally extends to additionally capture all of the readings of reflexives, unifying both anaphors under one analysis.

4.5S UMMARY AND FUTURE WORK

In this chapter, I presented a unified analysis of reciprocals, through the use of a semantic operator RECP5, that is founded on the core notion of reciprocity, so-called strong reciprocity, but can be accommodated through choosing different parameters on the relation to account for various weaker reciprocal interpretations. This reciprocal operator can also be extended to reflexives to capture the three main reflexive readings—distributive, intermediate (subplurality), and cumulative—since these anaphors only differ slightly in their semantics. Reciprocals are a multifacted phenomenon and thus a variety of examples remain to be tested that are beyond the scope of this dissertation, such as those in (110). Additionally, determining if the analyses of Dalrymple et al. (1998) or Winter (2001), or a compositional analysis such as that by Heim et al. (1991) or Beck (2001), yield any different predictions from my analysis could help guide further explorations into reciprocal interpretation. In the next chapter, I dig deeper into the roots of the model, breaking down the lexical trees into their morphological components.

(110) a. Quantified antecedents: Many vertebrae are fused to each other.

b. Asymmetric predicates:6

• Comparatives: # The boys are taller than each other.

• Small numbers: ? The three people inherited the house from each other.

• Spatial/temporal relations: # The cities are north of each other.

c. Cultural/natural influences: The plates are stacked underneath each other.7

6Mari (2013) presents a temporal-modal analysis of asymmetric predicates involving the permanency and decidedness of relations. Future work can examine how to account for asymmetric predicates, a challenge for many theories, and how a temporal-modal component, such as that in Mari’s (2013) theory, might fit into the approach presented here. 7Thank you to an anonymous SALT 27 reviewer for pointing out this example.

108 5 The Roots: Digging Deeper into the Model

As seen previously, STAG has the power and flexibility to capture a range of phenomena, such as reflexives and reciprocals. STAG currently only supports these phenomena on the phrase level and defines its elementary units as containing one (or sometimes more than one) lexical element. However, much information is contained in the morphological composition of these lexical elements, especially in languages other than English that heavily rely on morphemes to provide informational content.

One current theory of morphology is the framework of Distributed Morphology (Halle and Marantz, 1993), which holds that words are inherently comprised of hierarchical structure. In other words, morphology is simply more syntax so there is no divide between the construction of words and the construction of sentences. Under this view, which is often originally attributed to Boas (1917), it seems reasonable and possible to extend the lexicalized syntactic elementary trees of TAG down to smaller basic units—morphological elementary trees. These finer-grained trees would then serve as the basic units that would compose together to form the words and then sentences that comprise full TAG derivations. Since morphemes carry semantic information as well, the elementary trees could in fact contain both an elementary morpho-syntactic tree and a corresponding elementary morpho-semantic tree, making morphology possible in STAG as well.

This dissection of lexical items into morphemes has particular significance for reflexives, both in English and in other languages. In English, a reflexive is superficially comprised of two morphemes—a pronoun and -self /-selves—but in other languages, reflexivization can be represented solely by morphemes that generally attach to the verb. Reciprocals in English do not have the same kind of morphological composition as reflexives, but other languages can also express reciprocity with morphemes. No one, to my knowledge, has modeled morphology using STAG. In this chapter, I present an initial attempt at extending STAG down to a

109 word level (for English only1) and conclude with a preliminary approach to modeling the morphology of reflexives in particular.

5.0.1P REVIOUS RELATED WORK

According to the rules of Lexicalized TAG (LTAG) (Abeillé et al., 1999), the elementary unit of LTAG is an elementary tree anchored by (at least) one lexical element, which corresponds to only one semantic unit. In other words, elementary trees consist of one or more words, and are not broken down into morphemes. As a result, any morphological information must be either assumed and ignored or conveyed through another means, such as by using features (Vijay-Shanker and Joshi, 1988) or frame semantics (Kallmeyer and Osswald, 2012, among others).

Several people have worked on morphology using metagrammars, such as eXtensible MetaGrammar (XMG) (Crabbé, 2005), an object-oriented metagrammar framework that facilitates grammar generation especially for lexicalized tree . For instance, Duchier et al. (2012) used XMG to describe the verbal morphology of Ikota, a Bantu language spoken in Gabon. Subsequent applications include Petitjean et al. (2015), who model the derivational morphology of Arabic in XMG, and Andreou and Petitjean (2017), who use a combination of XMG and frame semantics to describe derivational polysemy of the suffix -al on verbs of change of .

In the framework of TAG, Schang (2018) applies TAG implemented in XMG-2, a modular metagrammar compiler developed by Petitjean (2014), to model tense, mood, and aspect markers (TMAs) in Guadeloupean Creole (or Gwadloupéyen). He argues that the TMAs are co-anchors in a complex verbal elementary tree, which was assembled in the morphology. He represents the TMAs in the metagrammar as tree fragments that combine to form elementary trees, but does not provide any more details and describes them not as autonomous morphological units, but rather as extended projections of the verb elementary tree.

Storoshenko (2010) models reflexives in STAG in four languages (English, Korean, Shona, and Plains Cree) and calls for the need to explore on a deeper level of representation how the elementary trees themselves are constructed. This is particularly motivated by Shona, a Bantu language with rich verbal morphology, since some morphemes carry non-trivial semantic content and thus could be represented as separate elementary trees. However, to my knowledge, neither Storoshenko nor others have followed up on

1Due to its impoverished overt morphology, English is certainly not an ideal language to use as a starting point for a morphological investigation. However, since this chapter primarily serves as proof of concept that morphological components can be represented in STAG and since the rest of the dissertation focuses on English, I stick to English examples throughout, in the hopes that future work can expand morphological STAG to more complex phenomena and to other languages.

110 Chapter 5. The Roots: Digging Deeper into the Model this idea of exploring the composition of lexical elementary trees in STAG. This chapter seeks to initiate that exploration.

5.1B UILDINGUPTHEFRAMEWORK

In this section, I show how the lexicalized phrase level elementary trees of STAG can be further decomposed into morpheme word level elementary trees. As in previous chapters, the notational convention is to use category labels on syntactic trees and type labels on semantic trees as abbreviations for full feature structures, except when feature structures are needed to demonstrate the derivation (as described in

Chapter 3.1.1.2). I use the term MORPHO-SYNTAX to refer to syntactic trees on the word level, in contrast to syntactic trees on the phrase STAG level, and MORPHO-SEMANTICS to refer to semantic trees on the word level. Morphology involves the structural build up of a word by starting with the stem (here, the smallest free morpheme) of the word and sequentially adding affixes. In most languages, inflectional morphology is always peripheral to derivational morphology. First, derivational affixes (both prefixes and suffixes) attach to the stem according to the rules of the category with which each affix combines and converts the stem into. Examples of derivational prefixes include re-, un-, and mis- and derivational suffixes include -able,-ness, and -ity, among many others. Then, inflectional affixes (only manifested as suffixes in English) attach after all derivational affixes have attached. In contrast to derivational affixes that potentially change the category of the word, inflectional affixes keep the category the same but add a grammatical property, such as tense (-ed for past), number (-s on nouns), and comparatives/superlatives (-er/-est). To help build the foundation for a morphological account of STAG, I start by examining where to draw the line between word level elementary trees and phrase level elementary trees. After, I look at derivational affixes, showing how they compose with a free morpheme, and then how feature-based STAG can straightforwardly account for interactions across multiple derivational morphemes. Then, I turn to inflectional morphology, followed by the interplay between derivational and inflectional affixes.

5.1.1M ORPHOLOGY AS SYNTAX

Before figuring out how to represent affixes, it is necessary to look at free morphemes to see where the line should be drawn between their phrase level syntactic representation and their word level morpho-syntactic representation. Both levels have a corresponding synchronous semantics side to them, so I focus on the syntax side distinction for demonstration. On the phrase level, STAG elementary trees contain all

111 5.1. Building up the framework

(a) V eet (b) N et (c) A het,eti (d) Adv het,eti

do do dog dog proud proud quickly quickly

Figure 5.1: Base morphological forms for (a) verbs, (b) nouns, (c) , and (d) and structural information for each lexical item. The clearest example is a verb. An intransitive verb contains not only the verbal head for the , but also a substitution slot for the subject and a sentence level root for the whole sentence. Transitive verbs contain the same with the addition of a substitution slot for an object as well. Ditransitives follow similarly with two objects. Elementary verb trees thus serve as the backbone of the entire sentence’s syntactic (and semantic) structure. On the word level, though, the morphology of a verb in English cannot include the verb and its arguments because derivational affixes must be permitted to adjoin, potentially changing the word’s category, and therefore the word’s syntactic context. For instance, the derivational suffix -ing converts verbs into nouns

([V view ] + -ing → [N viewing ]). The approach I propose is that, on the word level, each stem comprises the stem as a terminal node and its head category as its root. For example, a verb is represented by a V head and a terminal node containing the verb. Its synchronous morpho-semantic tree would be the equivalent except headed by type rather than category. By representing verbs on the word level with only their head V category, the suffix -ing can compose with the verb to create a noun without conflicting with the rest of the syntactic elementary tree. The root N category then correctly blocks composition with the syntactic phrase level elementary verb tree. I explain this in more detail in the subsequent sections. Figure 5.1 contains these base morphological forms for the categories of verb, noun, adjective, and . Now the question becomes how to integrate these base morphological trees into their ultimate syntactic phrase level STAG representation. Using verbs once again as an example, the goal is to take a verb resulting from any affixation and add in its argument structure. The strategy adopted here is to posit that there is an interface unlexicalized tree between the word level and phrase level, which accepts the word level head tree via substitution to form the lexicalized phrase level elementary tree. Under this view, each free morpheme first undergoes all needed morphological operations, constrained by features, and then substitutes into the interface unlexicalized elementary STAG tree it selects for based on its subcategorization.2 Each interface tree carries a feature expressing the kind of word it can accept and the root of each morphological tree

2One drawback to this approach is the loss of the capability of preserving arguments. For instance, in verbal nominal- ization, a derivational affix converts a verb into a noun, as in (111). (111) Noah destroyed the city. Noah’s destruction of the city

112 Chapter 5. The Roots: Digging Deeper into the Model

(a) S 1 2 t 1 2 (b) transV (c) S 1 2 t 1 2

3 DP↓ 1 VP et e↓ 1 do DP↓ 1 VP et e↓ 1

V↓ 3 DP↓ 2 eet↓ 3 e↓ 2 V DP↓ 2 eet e↓ 2

do do Figure 5.2: (a) Unlexicalized interface transitive verb tree set that accepts the morphological verb form via substitution, as shown by the derivation tree in (b), to form the lexicalized phrase level elementary tree set of STAG in (c)

carries a feature indicating its type. These features must unify in order for the word level tree to substitute into the interface tree, thus forming the lexicalized phrase level tree.

Free morphemes are grouped into sets that subcategorize for particular elementary STAG trees. By way of example, for a transitive verb, such as do, the unlexicalized syntactic interface tree (and its semantic counterpart) would be as in Figure 5.2(a). As shown by the derivation tree in (b), the morphological verb (as in Figure 5.1(a)) is a transitive verb so simply substitutes into these interface transitive verb trees to yield the familiar phrase level STAG tree set in (c). (From now on, I will italicize unlexicalized interface trees in derivation trees to differentiate them from word level and lexicalized phrase level trees.) This same strategy applies across all categories, with each free morpheme item headed only by its category and not by a phrase level projection. An example unlexicalized interface form for a noun, adjective, and adverb are in Figure 5.3.

This approach is similar to that of XTAG (The XTAG Research Group, 2001), in which each lexical word

(called an ANCHOR) selects for a family of trees based on its lexical properties. For instance, the anchor like (verb) subcategorizes for a subject and object to appear in its tree. All verbs that have this same subcategorization are grouped into a class that selects for the transitive verb tree. The transitive verb tree is further grouped into a tree family, which contains all other trees related to it via syntactic transformations, such as passivization and imperatives. Therefore, an entire class of anchors selects for a tree family as long as each tree in the tree family is valid for each word in that class. Applied to the present strategy, morphological trees form a class, such as the transitive verb class, which is assumed to subcategorize via features for certain syntactic trees, such as the transitive verb tree (family).

Under the approach I propose, the arguments of the verb are strictly on the phrase level so do not factor in on the word level and thus are not incorporated into the word or phrase level representations of the noun; however, under certain readings, verbal generally inherit their argument structure from the verb (Wood, 2018). Future work should consider alternative approaches to building word level elementary trees into their phrase level STAG forms in order to preserve, or introduce, argument structure appropriately.

113 5.1. Building up the framework

(a) NP et↓ 1 (b) NP et (c) VP et

N↓ 1 AP NP∗ het,eti↓ 1 et∗ AdvP VP∗ het,eti↓ 1 et∗

A↓ 1 Adv↓ 1 Figure 5.3: An example unlexicalized interface tree set for (a) a noun, (b) an adjective, and (c) an adverb.

5.1.2D ERIVATIONAL MORPHOLOGY

To build up the morphological STAG framework, I start with a simple derivational example, redo. Redo is composed of two morphemes: the derivational prefix re-, which attaches to verbs to form a new verb, and the free morpheme do, a verb. There are three possible approaches to representing the interaction between a free morpheme and an affix that combines with it. One approach is to represent affixes as initial trees that substitute into empty slots in the free morpheme elementary tree. In fact, this is the approach Abeillé (1992) uses to represent clitics in French. However, representing all affixes as initial trees leads to unwieldy free morpheme elementary trees that require a plethora of empty substitution sites for each possible morpheme combination and some kind of extra constraint to restrict morpheme order. For instance, do would need a single potential substitution slot for one prefix, such as re-(redo) or un-(undo), as well as potential slots for one or more suffixes, such as -able (doable), or both -able and -ity (doability). This example is fairly manageable, but for more versatile words that can combine with a variety of affixes, such as establish (disestablish, disestablishment, disestablishmentarian, antidisestablishmentarian), having all the possible substitution sites quickly becomes unwieldy, and even impossible if the affixation process is unboundedly generative. Representing affixes as auxiliary trees, rather than initial trees, avoids this problem. Free morpheme elementary trees keep a simple one level structure, into which affixes can adjoin, thus significantly simplifying the approach in terms of consistency between current STAG and its morphological extension. This is the approach I adopt. The third alternative, though, may also be feasible, in which an affix accepts a stem via substitution, rather than adjoining into the stem. Determining if one of these two approaches is superior over the other is left for future work. Returning to the example of redo, Figure 5.4 shows the elementary tree sets for each morpheme (a and b), the derivation tree (c), and the derived trees (d). In (a), on the morpho-syntax side, re- appropriately has both the foot and root node as the category V. On the morpho-semantics side, since re- combines with transitive verbs (rethink, restate), the foot and root nodes have type he,eti. As discussed previously, for free morpheme elementary trees, such as for the verb do, instead of the full phrase level elementary trees containing the

114 Chapter 5. The Roots: Digging Deeper into the Model

(a) V eet (b) V 1 eet 1 (c) do (d) V eet

1 do do re V re eet re V∗ re eet∗ re do do Figure 5.4: Elementary tree sets for (a) the prefix re and (b) the free morpheme do; the derivation tree is in (c) and the derived trees are in (d).

+V −V +N adjective noun −N verb preposition

Table 5.1: Classification of syntactic categories based on binary verbal and nominal features

verb’s subcategorization, on a word level, do is only headed by V. This allows affixes to adjoin to the V head that may change its category, such as to a noun (doer) or adjective (doable), without conflicting with the rest of the tree. The derivation proceeds according to the derivation tree in (c) to produce the derived trees in (d).

5.1.2.1D ERIVATIONAL AFFIXES THAT CHANGE CATEGORY

As seen in the previous example, the prefix re- can only combine with verbs, and simply converts verbs into new verbs. However, some derivational affixes completely change the syntactic category of the word with which they combine. For instance, the suffix -able can convert either a verb into an adjective or a noun into an adjective. The auxiliary tree for the V→A-able is shown in Figure 5.5(a). Feature structures are used here as the node labels in lieu of the abbreviated category/type labels for demonstration. The syntactic features are based on Chomsky’s (1970) classification of verbal and nominal properties, as shown in Table 5.1. Adjectives have both verbal and nominal properties, while prepositions have neither verbal nor nominal properties. Verbs have verbal but not nominal properties and nouns have nominal but not verbal properties. Using this four-way classification, four syntactic categories can be expressed using only two features that are either present (+) or absent (−). The syntactic feature structure for a verb (+V, −N), for instance, would thus be as in Figure 5.5(b).

Returning to the example, this version of -able converts verbs into adjectives so the foot node is verbal,

115 5.1. Building up the framework

h i h i h i h i (a) " # (b) " # 1 (c) do V + h i V + h i 1 het,eti he,eti 1 N + ¨H N − able ¨H ¨¨ HH ¨¨ HH able h i do " # he,eti do V + able N − h i h i * * h i h i ∪ h i h i ∪ " # V + h i (d) " # (e) het,eti V + h i N + het,eti ¨H N + ¨H ¨¨ HH PP ¨¨ HH PP  PP h i  PP " # able he,eti able h i V + " # he,eti able V + able N − N − h i h i do ∪ he,eti " # do h i V + ∪ N − do

do Figure 5.5: Elementary tree sets for (a) the suffix -able and (b) the free morpheme do now with features; (c) contains the derivation tree, (d) the composed trees pre-unification, and (e) the final derived trees post- unification for doable.

+V and −N, but its root node is adjectival, +V and +N.3 (In contrast, re- only converts verbs into other verbs so has +V and −N at both its root and foot node.) On the morpho-semantics side, type labels can also be represented as feature structures, where the feature is the type. For -able, the foot node has the type of a transitive verb (he,eti), while the root node has the type of an adjective (het,eti). Figure 5.5(a) contains the elementary tree set for the suffix -able. The morpho-syntactic and morpho-semantic root features appear in the root’s bottom feature structure, representing how the tree is seen from below. The features on the foot node, in contrast, appear in the foot’s top feature structure,

3The definition of TAG states that the root and foot nodes of a TAG auxiliary tree must have the same label, but as noted by Rambow and Vijay-Shanker (1998), this label matching requirement is in fact not essential. The crucial part of the definition is that the auxiliary tree has a foot node, but the label itself does not a priori matter. Moreover, since I use feature-structure-based STAG, which is equivalent to TAG in generative capacity since feature structures are bounded (Vijay-Shanker and Joshi, 1988), syntactic categories and semantic types are realized as feature values rather than as strict node labels.

116 Chapter 5. The Roots: Digging Deeper into the Model representing how the tree underneath will be seen from above. On the morpho-semantics side, to maintain consistency with semantic phrase level STAG trees, both prefixes and suffixes appear to the left of the head since affixes serve as functions, taking the free morpheme as an argument.

Figure 5.5(b) contains the same elementary tree set for do as in Figure 5.4(b) except with feature structures instead of the abbreviated categories/types. Since do is a verb (as seen from below), the bottom feature structure of its head V node contains the features +V and −N. The top feature structure is empty to allow for the possible adjunction of an affix that changes its category. The derivation tree is in (c) and the pre-unification composed trees are in (d). Following Vijay-Shanker and Joshi (1988), since -able adjoins into do, the top root feature structure of -able must unify with the top feature structure of do, while the bottom foot feature structure of -able unifies with the bottom feature structure of do. The post-unification derived trees are in (e).

5.1.2.2A MBIGUOUS DERIVATIONAL AFFIXES

As with -able, another morphological phenomenon to account for is affixes that can combine with multiple categories. For example, the prefix un- both converts verbs to other verbs (undo) and converts adjectives to other adjectives (unhappy). For these cases, the feature values can be underspecified, as shown in Figure 5.6(a). On the morpho-syntax side, the root and foot nodes have the feature +V, which excludes nouns and prepositions, and a variable (α) for N, indicating that the N value can be either plus (adjective) or minus (verb). When un- adjoins into a verb or adjective, the features unify, with α adopting the appropriate N feature value. Since the root and foot nodes both have the same variable for N, the value stays consistent from the morpheme into which it adjoined. On the morpho-semantics side, the root and foot nodes have the semantic type feature hσ,eti, in which σ can stand for either e (for transitive verbs of type he,eti) or et (for adjectives of type het,eti). As on the morpho-syntax side, when un- adjoins into a verb or adjective, the features unify and σ adopts the appropriate type.

Another example of an ambiguous suffix is -ing, which converts a verb into either an adjective or a noun. Its elementary tree set is shown in Figure 5.6(b). On the morpho-syntax side, the foot node has features for a verb (+V, −N), while the root node has +N but a variable for V, so is underspecified for verbal properties, meaning it yields adjectives and nouns. On the morpho-semantics side, since -ing can combine with intransitive, transitive, and ditransitive verbs, the semantic type in the foot feature structure is disjunctive with the alternative options of he,ti (intransitives), he,eti (transitives), or he,he,etii (distransitives). The semantic type in the root feature structure is also disjunctive, with the alternative options of het,eti

117 5.1. Building up the framework

h i h i h i h i (a) " # (b) " # V + h i V α h i hσ,eti et,et|et N α ¨H N + !a ¨H ¨¨ HH ¨H !! aa ¨¨ HH ¨¨ HH un h i ing h i " # hσ,eti " # et|eet|eeet un V + V + ing N α h i N − h i h i * h i * * * Figure 5.6: Elementary tree set for (a) the prefix un- and (b) the suffix -ing showing underspecified feature values to represent the affix’s ability to combine with and yield multiple categories/types

h i h i h i h i (a) " # 1 (b) " # V + h i 1 V − h i het,eti et N + N + ¨H ¨H ¨¨ HH ¨¨ HH happy ness h i happy " # het,eti V + ness N + h i h i * * Figure 5.7: Elementary tree sets for (a) the free morpheme happy and (b) the suffix -ness

(adjectives) or et (nouns).

5.1.2.3I NTERACTIONS BETWEEN DERIVATIONAL AFFIXES

To see how multiple derivational affixes interact with each other, I will look at the example unhappiness.4 Unhappiness is composed of three morphemes: the prefix un-, which in this case converts adjectives into adjectives, the free morpheme happy, an adjective, and the suffix -ness, which converts adjectives into nouns. The elementary tree sets for the latter morphemes are in Figure 5.7(a) and (b). Since both bound morphemes adjoin into the root node of happy, there are two possible derivations. Following the extended definition of derivation described by Schabes and Shieber (1994), one possible derivation is for un- to adjoin at the root of happy, as shown in Figure 5.8(a), and then -ness to adjoin at the root of unhappy, as in (b). Unification succeeds and the derived trees are shown in (c). The derivation tree

4Orthographic differences resulting from morphological composition are not relevant here.

118 Chapter 5. The Roots: Digging Deeper into the Model for this ordering of morphemes, in which un- adjoins (shown as the left branch) followed by the adjunction of -ness (shown as the right branch), is in (d). The other possible derivation is for -ness to adjoin at the root of happy, as shown in Figure 5.9(a), and then un- to adjoin at the root of happiness, as shown in (b). However, as seen previously, un- can only combine with adjectives (σ adopts the type et to form het,eti) and verbs (σ adopts the type e to form he,eti), not nouns like happiness (type et), so this derivation should not be possible. In fact, the features do not unify, shown in red in (b), so the derivation crashes. On the morpho-syntax side, the value for V is positive in the top feature structure but negative in the bottom feature structure; on the morpho-semantics side, σ must have a null value to unify, but can only take the values et or e). The derivation tree, which this time shows -ness as the left branch and un- as the right branch, is in (c). With this foundation of handling derivational affixes, I now turn to inflectional affixes.

5.1.3I NFLECTIONAL MORPHOLOGY

In English (and across most languages), inflectional suffixes attach to the stem after all derivational affixes have attached and contribute grammatical, rather than lexical, features to the stem. As a result, inflectional suffixes do not change the category or type of the stem. For the STAG trees, this means that the primary contribution is in the morpho-syntax in the form of inflectional suffixes contributing a tense, number, or case feature, while in the morpho-semantics, the type node labels remain the same since the denotational semantics contributes the added meaning. I assume that irregular inflectional morphology, such as (child/children, foot/feet) and ablaut (sing, sang, sung), is the result of a separate process so I do not include it in the discussion. Since English is an analytic language (relying more on word order and helper words, such as particles, prepositions, and modifiers, than on inflectional morphemes to convey the role of words in a sentence), future work would greatly benefit from examining agglutinative languages, which contain distinct morphological components. However, for the present purposes, I will focus on two main inflectional morphemes in English: number (nouns) and tense (verbs).

5.1.3.1N UMBER INFLECTIONAL (NOUNS)

For nouns in English, number is contributed overtly by allomorphs of the morpheme /s/plur, namely [-s], [-z], or [-Iz]. These carry the feature +plural (+plur for short) and combine with a noun. In this preliminary investigation into STAG morphology, I assume that all nouns are singular by default so carry the feature

119 5.1. Building up the framework

h i h i ∪ h i h i ∪ (a) un + happy " # V + h i hσ,eti N α !a !a !!! aaa !!! aaa h i " # un h ,eti un V + σ N α h i h i ∪ het,eti " # h i V + ∪ N + happy

happy h i h i ∪ h i h i ∪ (b) unhappy + ness " # V − h i et N + PP PP  PP  PP ness h i " # het,eti V + ness N + h i h i het,eti ∪ " # ¨H V + h i ¨¨ HH ∪ N + un h i ¨H het,eti ¨¨ HH " # un V + happy N +

happy " # V − h i (c) Derived trees et (d) Derivation tree happy 1 1 N + ¨H PP ¨¨ HH  PP un ness h i " # ness het,eti V + ness ¨H N + ¨¨ HH ¨H h i ¨¨ HH un het,eti un " # V + N + happy

happy Figure 5.8: (a) contains the first derivation step of un + happy, (b) contains the second derivation step of unhappy + ness, (c) contains the successful derived trees, and (d) the derivation tree for this ordering of com- position. 120 Chapter 5. The Roots: Digging Deeper into the Model

h i h i ∪ h i h i ∪ (a) happy + ness " # V − h i et N + !a !a !! aa !! aa ness h i " # ness het,eti V + N + h i h i ∪ h i h i ∪ happy happy

h i h i ∪ h i h i ∪ (b) un + happiness " # V + h i hσ,eti N α ¨H PP ¨¨ HH  PP h i " # un h ,eti un V+ σ N α h i h i ∪ et " # ¨H h i V − ¨¨ HH ∪ N + ness h i ¨H het,eti ¨¨ HH " # V + ness happy N +

happy

(c) Derivation tree happy 1 1

ness un Figure 5.9: (a) contains the first derivation step of happy + ness, (b) contains the second derivation step of un + happiness when the derivation crashes due to a feature clash (shown in red), and (c) contains the deriva- tion tree for this ordering of composition.

121 5.1. Building up the framework

−plur. The elementary tree set for the plural suffix is in Figure 5.10(a). On the morpho-syntax side, the foot node is singular from above so has a −plur feature; the root node contains the +plur feature so the noun is plural. The general /s/plur morpheme is used in the tree rather than a particular allomorph because the focus here is again on the morphological tree structure rather than on morphological orthography. On the morpho-semantics side, the plural morpheme can be represented as an auxiliary tree containing a plural operator, PLUR, which is a function from a predicate that holds of an individual noun to a predicate that holds of sets of nouns. Detailing the semantic denotation of the operator PLUR is beyond the scope of this dissertation, but refer to Bennett (1974), Scha (1981), and Link (1983), among many others, for various accounts of plurality.

The morphological tree set for the dog is in (b). Similar to derivational affixes, inflectional affixes adjoin at the head of the free morpheme. The composition of the plural suffix with the stem morpheme proceeds as in (c). The composed derived trees pre-unification are in (d) and the post-unification fully derived trees are in (e).

5.1.3.2T ENSE INFLECTIONAL SUFFIXES (VERBS)

In English, tense has two separate components: an inflectional suffix that attaches to the end of the verb and an , which can be either phonologically null, such as for present or past tense, or an overt auxiliary verb, such as the future will or the have/had. I propose the strategy of building up each of these components separately in the morphology before composing them into the unlexicalized interface verb tree set.5 In order to make the derivation as clear as possible, I first show the high-level unlexicalized interface verb tree set and where each component composes. Then I describe the derivation of building up each component from the word level to the phrase level to produce the fully derived sentential tense tree set. I start with past tense as an in-depth example, and then demonstrate the derivation more succinctly using future tense. I leave figuring out how to account for multiple tenses, as in the future perfect will have eaten, for future work.

Figure 5.11 portrays the high-level unlexicalized interface elementary tree set for an intransitive verb, now including two links, 2 and 3 , for the two separate tense components. On the syntax side, the 2 link appears on the V, indicating where the morphologically fully composed lexical verb + inflectional tense item substitutes. On the semantics side, the corresponding morpho-semantic component containing the lexical

5Representing these two tense components as one multicomponent tree set requires delayed tree-locality, so I instead represent each component as a separate tree set for a simpler and more straightforward derivation. This approach may be better suited for tense in other languages, but future work will determine whether this is indeed the case.

122 Chapter 5. The Roots: Digging Deeper into the Model

h i h i h i h i     1 (a) V– (b) V– h i h i 1     N +  et N +  et NUM +plur ¨¨HH NUM –plur P ¨ H  PP h i dog  P PLUR et   dog V– /s/plur h i   N +  NUM –plur * h i h i h i * ∪ h i h i ∪   (c) dog (d) V– h i 1   N +  et /s/ !a plur NUM +plur !! aa XX  XXX h i PLUR et   V– /s/plur h i h i   ∪ et N +  NUM –plur dog   V– h i   ∪ N +  NUM –plur

dog

  V– h i (e)   N +  et ¨H NUM +plur ¨¨ HH PP  PP h i PLUR et   V– /s/   plur N +  dog NUM –plur

dog Figure 5.10: Elementary tree set for (a) the plural suffix and (b) a noun with both category and number fea- tures; (c) contains the derivation tree, (d) the derived trees pre-unification, and (e) the final derived trees post- unification for the plural noun dogs.

123 5.1. Building up the framework

S hi,ti 3

DP↓ 1 VP 3 he,hi,tii↓ 2 e↓ 1

V 2 Figure 5.11: High-level unlexicalized interface elementary tree set for an intransitive verb with links for both tense components

verb also substitutes at link 2 . In order to account for the semantics of tense, all semantic types can be augmented with the index i, which stands for world-time pairs (hw,ti). In fact, I assume that i is always present in the semantic types, but only show it when relevant to the discussion.

The 3 link, for the second tense component, appears on the VP in the syntax and on the root in the semantics. On the syntax side, as in Chapter 3, I treat the auxiliary tense verb tree as any other verb or modal tree, namely a recursive auxiliary (in the STAG adjunction sense) tree with root and foot VP nodes that

6 adjoins into the verb tree at 3 as allowed by its features. On the semantics side, the auxiliary tense component contains a tense operator, similar to the plural operator for number seen previously, that adjoins at the root of the intransitive verb tree at link 3 in order to (appropriately) have scope over the entire sentence.

Now I will drill down to the low-level morphological components of tense and show how they build up to forms that substitute into this unlexicalized interface intransitive verb tree set. To demonstrate by way of example, Figure 5.12 shows the relevant tree sets for the first part of the derivation of the past tense for the verb walk: the left side of the figure has the word level tree set derivation for the first component (walked) and the right side has the word level and unlexicalized interface tree set derivation for the second component (the null auxiliary). (Figure 5.13 shows the second part of the derivation that produces the fully composed sentential past tense on the phrase level).

Starting on the left, I represent the first component morphologically by an inflectional suffix (/@d/past ) in the morpho-syntax and a degenerate placeholder tree in the morpho-semantics, as shown in (a). The morpho-syntactic tree contains the inflectional past tense suffix (/@d/past ) to represent the possible allomorphs of past tense—[-@d]/[-d]/[-t]. The V foot and root nodes carry an additional feature, Vform, that indicates the verbal form of the tree from above and below. Since the morphological suffix takes in a stem, the Vform feature value is +bse (base) in its foot node; since it converts the stem into an inflected form, the

6Once again, the approach shown here uses an S sentential root and recursive VP trees for auxiliaries and verbs, rather than a tense projection (TP), but both strategies are feasible, as demonstrated in Chapter 3.1.1.1.

124 Chapter 5. The Roots: Digging Deeper into the Model

(a) Past tense suffix word level tree set (d) Past tense auxiliary word level tree set h i h i eit|eeit|eeeit   V hit,iti V + h i N–    * Vform +fin /0past PAST PP  PP   V + /@d/past   N–  Vform +bse h i * (b) Intransitive verb word level tree set (e) Past tense interface auxiliary tree set h i h i h i 1 h i   1 V + " # h i VP h i N–  he,iti hi,ti   Vform +fin !a Vform +bse P !! aa  PPP walk h i " # hit,iti↓ 1 hi,ti walk V↓ 1 VP Vform +fin h i h i * * (c) Composed verb + past tense suffix (f) Composed past tense auxiliary tree set h i   h i V + h i N–  he,iti " #   VP h i Vform +fin hi,ti Vform +fin PP !a  P walk P !! aa  P  PPP   h i V + " # hi,ti /@d/past VP N–  hit,iti   Vform +fin h i Vform +bse V h i PAST * /0past walk * Figure 5.12: Left: (a) the past tense suffix (/@d/past ) and (b) the intransitive verb walk word level tree sets, and (c) the composed walked tree set; Right: (d) the word level and (e) the unlexicalized interface tree sets of the past tense auxiliary, and (f) the composed (phrase level) past tense auxiliary tree set

125 5.1. Building up the framework

(a) Unlexicalized interface intransitive verb tree set (b) Derivation tree for past tense

S hi,ti 3 intransV PP  PP 2 3

DP↓ 1 " # he,hi,tii↓ 2 e↓ 1 VP walk past tense aux Vform +fin 3 1 1 " # VP /@d/past /0past

Vform x

  V +   N– Vform x ↓ 2 (c) Fully derived phrase level past tense tree set S hi,ti XX  XXX " # PAST hi,ti DP↓ 1 VP Vform +fin ``` he,hi,tii e↓ 1 ``` " # V VP walk Vform +fin /0past   V +   N–  Vform +fin PP  PP   V + /@d/   past N–  Vform +bse

walk Figure 5.13: (a) Low-level unlexicalized interface intransitive verb tree set and (b) the derivation tree and (c) the derived trees for the past tense of an intransitive verb (walked)

root node has the value + fin (finite).7 The morpho-semantic tree is simply a placeholder tree because I represent the past tense meaning in the second component, the auxiliary verb tree set, shown on the right side of the figure. Since the past tense can compose with any kind of verb, the semantic type is once again

7These Vform values are based on those proposed by Gazdar et al. (1982).

126 Chapter 5. The Roots: Digging Deeper into the Model disjunctive, as in Section 5.1.2.2, with three alternative options depending on the of the verb, but this time augmented with the index i—he,iti (intransitives), he,he,itii (transitives), or he,he,he,itiii (distransitives).

This word level suffix tree set adjoins into the word level verb tree set (walk), shown in (b), at link 1 . The morpho-syntactic verb tree has the Vform feature value of +bse since it is the stem of the word; this +bse value unifies with the +bse value of the foot of the past tense suffix morpho-syntactic tree from (a) upon adjunction. The morpho-semantic verb tree contains the appropriate semantic type he,iti for an intransitive verb. When the past tense suffix morpho-semantic tree adjoins, its top feature structure chooses the value he,iti based on the intransitive verb walk tree and the features unify. This composition produces the fully composed word level past tense verb + suffix form (walked) shown in (c). This composed tree set will then compose into the unlexicalized interface intransitive verb tree set, but I will show this in the next figure.

Turning to the right side of the figure, I represent the second component, the auxiliary tense verb, morphologically by a phonologically null placeholder tree (/0past ) in the morpho-syntax (since the past tense does not use an auxiliary verb in English) and a tense operator (PAST) in the morpho-semantics, as shown in

(d). The PAST tense operator stands for a more complex denotational semantics, such as that in (112), although the denotation could be adjusted if needed. In this denotation, the PAST operator takes the entire verbal proposition as an argument and states that there is a time t0 that exists before the current time t, in which the proposition holds of that world and time.

(112) PAST ≡ λ p . λw . λt . ∃t0 : t0 < t ∧ p(w)(t0)

This word level auxiliary verb tree set is morphologically fully composed so now substitutes into the past tense auxiliary verb unlexicalized interface tree set, shown in (e). The syntax auxiliary verb interface tree has VP root and foot nodes and accepts the morphological auxiliary verb via substitution at link 1 . Both root and foot VP nodes have the Vform feature value + fin because the past tense auxiliary takes a finite morphologically composed verb from below and preserves this value in its root node so the top features unify and the sentence as a whole is finite. Different tenses will have different Vform features (±inf (infinite), ±psp (past ), ±cop (copula), ±pass (passive)) depending on the requirements of the auxiliary verb. The semantic interface auxiliary verb tree, however, remains consistent across tenses because the meaning of the tense resides in the tense operator on the word level. The semantic interface auxiliary verb tree takes in a verbal proposition (hi,ti) and, via the tense operator it accepts via substitution at link 1 , produces a proposition of the same type that incorporates the world and time at which the proposition holds. This tree will ultimately adjoin at the root of the phrase level verb tree to allow tense to have scope over the

127 5.1. Building up the framework entire sentence. The result of the composition of the word level and interface auxiliary verb tree sets, which produces the phrase level auxiliary verb tree, is in (f).

The tree sets from (c) and (f) now compose into the unlexicalized interface intransitive verb tree set, shown at a high-level in Figure 5.11 and at a low-level with features in Figure 5.13(a), at links 2 and 3 respectively. On the syntax side, both the V node and the bottom feature structure of the VP node have a variable x for their Vform value, indicating that the Vform value of the V that substitutes in is carried up to the bottom feature structure of the VP, where it must unify with the VP’s top feature structure. For the past tense in Figure 5.12(c), the root node has the value + fin so the variable x adopts + fin as its value when the verb walked substitutes at link 2 . The morpho-semantic walk tree synchronously substitutes at the 2 link in the semantic interface intransitive verb tree. The phrase level auxiliary tree set in Figure 5.12(f) composes into the intransitive verb tree set at the 3 links: at the VP node in the syntax, in which the features all unify, and at the root hi,ti in the semantics, so the past tense operator takes scope over the sentence. The derivation tree for the entire tense composition is in Figure 5.13(b) and the fully derived trees are in (c).8

Other tenses follow a similar strategy. Figure 5.14 shows the equivalent for the future tense. On the left, (a) contains the future tense (null) suffix word level tree set since verbs do not inflect for future tense in English. As a result, here both root and foot Vform features have the value +bse since the future suffix does not change the verb stem, unlike the past tense. The result of the composition of this suffix tree set with the morphological verb walk (same as in Figure 5.12(b)) is in (b). On the right, (c) contains the future tense auxiliary word level tree set, this time with the lexical item will in V, rather than a null placeholder as in the past tense. The morpho-semantic tree has the tense operator FUT, which can take a similar denotational semantics as the PAST operator as in (113a), or an additional denotation that incorporates a modal reading, as in (113b). The latter accounts for cases such as (113c) in which the house does not yet exist but will exist in the future: if there is a possible future w0 for world w that is the of world w, then there is a time t0 that occurs after t in which the proposition holds of w0 and t0.

(113) a. FUT ≡ λ p . λw . λt . ∃t0 : t < t0 ∧ p(w)(t0)

0 0 0 0 0 0 b. FUTmodal ≡ λ p . λw . λt . λw . Con(w,w ) → ∃t : t < t ∧ p(w )(t )

c. Noah will build a house.

The phrase level result of the composition of the word level and the unlexicalized interface future tense

8For illustration, the feature structures on all nodes have been unified. However, further operations, such as adjoining more auxiliaries or modals, could be performed at the nodes along the spine so feature unification is not necessary at this step. Testing the various interactions among auxiliaries and modals is left for future work.

128 Chapter 5. The Roots: Digging Deeper into the Model

(a) Future tense (null) suffix word level tree set (c) Future tense auxiliary word level tree set h i h i eit|eeit|eeeit   V hit,iti V + h i N–    * Vform +bse will FUT PP  PP   V + /0 f ut   N–  Vform +bse h i * (b) Composed verb + future tense (null) suffix (d) Composed future tense auxiliary tree set h i   h i V + h i N–  he,iti " #   VP h i Vform +bse hi,ti Vform +fin PP !a  PP walk !a !! aa !!! aaa   h i V + /0 f ut " # hi,ti VP N–  hit,iti   Vform +bse h i Vform +bse V h i FUT * will walk *

Figure 5.14: Left: (a) future tense null suffix and (b) composed walk f ut tree set; Right: (c) word level future tense auxiliary and (d) composed (phrase level) future tense auxiliary tree set

auxiliary tree sets is in (d). Since the auxiliary will takes in a stem and produces a finite form, its foot node feature structure has the value +bse and its root node has the value + fin.

As with the past tense, these two composed tree sets now compose into the unlexicalized interface

intransitive verb tree set from Figure 5.13(a) at links 2 and 3 , respectively, to form the derived trees shown in Figure 5.15(a). Note that the adjunction of the future tense auxiliary tree set is forced due to a feature clash at the VP node in the intransitive verb tree: the VP’s top feature structure has the value + fin but the bottom feature structure has the value +bse. The future tense auxiliary tree, however, has the value + fin at its root and the value +bse at its foot so upon adjunction, the features unify appropriately.

129 5.1. Building up the framework

(a) Fully derived phrase level future tense tree set (b) Derivation tree for future tense S hi,ti intransV XX  XXX 2 3 " # VP FUT hi,ti DP↓ 1 walk fut tense aux Vform +fin X 1  XX he,hi,tii e↓ 1 1  XXX " # /0 f ut will V VP walk Vform +bse will   V +   N–  Vform +bse PP  PP   /0 f ut V +   N–  Vform +bse

walk Figure 5.15: (a) Derived trees and (b) derivation tree for the future tense of an intransitive verb (will walk)

5.1.4I NTERPLAY BETWEEN DERIVATIONAL AND INFLECTIONAL MORPHOLOGY

So far, nothing in the model forces derivational affixes to appear closest to the stem and inflectional affixes to appear outside of all derivational affixes. To ensure this order, an inflectional feature can be used. Each inflectional suffix can carry an INFL feature in its root and foot nodes: the INFL feature is negative in its foot node but positive in its root node, indicating that the suffix takes something that is not inflected and turns it into something that is inflected. This feature also provides a protection against multiple inflectional suffixes adjoining: if a second inflectional auxiliary tree tried to adjoin into a verb + inflectional suffix tree, the incoming negative value in the foot INFL feature would fail to unify with the positive value in the root INFL feature of the verb + inflection tree and the derivation would crash.9

Derivational affixes are simply negative for the INFL feature in both their root and foot nodes. Therefore, multiple derivational affixes can adjoin into a word without a feature clash. The stem can, by default, be

9In languages that allow multiple inflectional suffixes, the foot node of the inflectional suffix could be underspecified for the INFL feature, meaning the suffix could adjoin into another inflectional suffix if needed. Again, capturing the interactions of multiple tenses in English is left for future work, so this preliminary approach of using an INFL feature may need to be revised.

130 Chapter 5. The Roots: Digging Deeper into the Model

negative, allowing both derivational and inflectional affixes to adjoin. Figure 5.16(a) shows a derivational suffix tree and (b) shows an inflectional suffix tree (future tense) with the INFL features included. Although more work is needed to further specify tense, especially capturing the interactions among multiple tenses, this section has helped laid the foundation of morphological STAG. The next section examines one of the main issues morphological accounts encounter: bracketing paradoxes.

h i h i h i h i   eit|eeit|eeeit   V + (a) V + (b) h i N–  h i     N + het,eti   ¨H Vform +bse * INFL – ¨¨ HH PP INFL +  PP able h i PP he,eti  PP   V + able   h i V + /0 N– f ut   N–  *   INFL –   Vform +bse h i INFL – * h i * Figure 5.16: The morphological tree set for (a) the derivational suffix -able and (b) the inflectional future tense suffix, now including an inflectional feature

5.2B RACKETING PARADOXES

A well-known challenge for various morphological accounts is bracketing paradoxes. A BRACKETING

PARADOX occurs when the morphophonological constituent structure does not match the semantic constituent structure. In other words, the morphophonological structure is not isomorphic to the semantic structure. The term “bracketing paradox” has been given to a variety of phenomena, but I focus on the two canonical kinds. The first is strictly morphological, involving a difference in the scopes of a prefix and a suffix (unhappier, unluckier), and the second involves attribute phrases of the type Adjective + Noun (nuclear physicist, criminal lawyer). I argue that in both cases, there is in fact no bracketing paradox for synchronous analyses, in the sense that the morphophonological structure takes a different form from the semantic structure. Instead, for strictly morphological cases the semantic structure is the only possible one, and for attribute phrase cases the readings are solely contingent upon the semantics of the adjective.

131 5.2. Bracketing paradoxes

5.2.1M ORPHOLOGICALBRACKETINGPARADOXES

Looking at the strictly morphological kind first, the bracketing paradox arises due to ambiguity in whether the prefix or suffix first attaches to the stem. For the example unhappier, the order of affix attachment is not dictated by category restrictions because both the prefix un- and the comparative suffix -er attach to an adjective to return an adjective. The bracketing paradox arises because the compositional meaning of unhappier is [ [ un happy ] er ] (more unhappy), while the phonological structure is [ un [ happy er ] ] (not happier). The phonological structure reportedly takes this form because the comparative -er cannot attach to words of more than two syllables; in those cases, the periphrastic more is preferred instead.

There have been a variety of approaches to explaining this paradox, such as assimilating the semantic bracketing to the morphophonological (Sproat, 1985), positing that the semantic interpretation is derived from the morphophonological (Kiparsky, 1983; Pesetsky, 1985), and claiming that trisyllabic stems that take -er are simply lexically listed (Spencer, 1988). An alternative view, based on experimental evidence by Graziano-King (1999), is that frequency, rather than phonological constraints, determines whether the comparative is formed via suffixation or periphrasis. Experimental results showed that adult native speakers preferred the comparative suffix form over the periphrastic form in 99% of high-frequency monosyllabic adjective examples, but in only 15% of low-frequency monosyllabic adjective examples. A parallel experiment using nonce words resulted in preference for the comparative suffix over the periphrastic in exactly 50% of examples.

Bobaljik (2012) interprets these results to mean that the strategy by which comparatives are formed is acquired by the language learner based on statistical regularities in the input. Under the theory of Distributed Morphology, Bobaljik (2012) proposes that, grammatically, adjectives that form the comparative via suffixation (Merger applies) are marked by a [+M] diacritic, while adjectives that form the comparative via periphrasis (no Merger applies) are marked by a [−M] diacritic. Under this hypothesis, if a diacritic, or some kind of feature in the case of STAG, is inherent to the stem, then there is no bracketing paradox because the restrictions on using -er versus more to form the comparative are no longer determined by affix ordering. Instead, the diacritic or feature dictates comparative formation, leaving the semantic bracketing as the only possible grammatical one.

My morphological STAG account can capture this by including an equivalent feature to the [±M] diacritic of Distributed Morphology. In fact, to prevent overgeneration, on the morpho-syntax side, there are two new features: COMP (comparative) and DEG (degree). COMP can either take the value +periph(rasis), meaning the comparative is formed using the word more, or −periph(rasis), meaning the comparative is formed using

132 Chapter 5. The Roots: Digging Deeper into the Model the comparative morpheme -er. DEG is either positive, indicating that the node carries some kind of comparative or superlative value, or negative, indicating that the node does not have a comparative or superlative value. The necessity of the latter feature in particular will become clear shortly. To be comprehensive, I first show how to account for the difference between adjectives that form the comparative via suffixation and adjectives that form the comparative via periphrasis. Then, based on this approach, I show how the apparent bracketing paradox straightforwardly ceases to exist. All adjectives and comparatives carry both COMP and DEG features. Figure 5.17(a) shows the elementary morpho-syntactic tree with these new features for happy (a suffixation comparative adjective) and apt (a periphrastic comparative adjective). The semantics remains the same as before so is not shown. Adjectives like happy take the comparative -er so have the −periph feature and adjectives like apt take more so have the +periph feature for COMP. Since neither adjective has been modified for degree yet, they both are negative for DEG. The comparative -er elementary trees, as shown in (b), adjoin into an adjective that has a −periph feature to produce a comparative adjective that is now specified as positive for DEG because it has received a comparative modification. In contrast, the word level elementary trees for more, shown in (c), are initial trees that carry a +periph feature (since it is the periphrastic comparative form) and a positive DEG feature (since it is itself a comparative).Even though more is a free morpheme that does not take any affixes so could be automatically represented on the phrase level, to remain consistent with other adjectives, I represent more as a word level adjective that then substitutes into an unlexicalized interface comparative adjective tree, shown in (d). This now lexicalized phrase level tree set as a whole adjoins into a phrase level adjective that is +periph for COMP and negative for DEG. The derivation and derived trees for happier are in Figure 5.18(a) and for more apt are in (b). Looking at these derived trees demonstrates how both COMP and DEG features are needed to prevent overgeneration. For suffixation comparatives like happier, the analysis must prevent the formation of *more happy, *more happier, and *happierer. *More happy is prevented because happy carries a −periph feature, which is carried through to the phrase level, so that when the comparative adjective tree containing more tries to adjoin at the root of the happy phrase level tree, the −periph of happy clashes with the +periph of more. *More happier is doubly prevented: first, in the same way as *more happy, and second, due to a clash in DEG feature between the root of -er and the foot of more. Lastly, *happierer is prevented because the negative DEG feature at the foot of the second -er clashes with the positive DEG feature at the root of the first -er that adjoined. For periphrastic comparatives like more apt, the analysis needs to prevent the formation of *apter, *more

133 5.2. Bracketing paradoxes

h i h i h i

1 h i     (a) V +  V + (b) V + N +  N +  h i N +            het,eti COMP –periph COMP +periph COMP –periph ¨H   ¨¨ HH DEG – DEG – DEG + PP er h i  PP het,eti apt happy V +  h i er N +    * COMP –periph h i   DEG – h i h i V +  (c) * N + h i     hhet,eti,het,etii COMP +periph DEG + more

more h i h i   (d) AP   h i COMP +periph het,eti DEG + XXX (((hhh  XXX ((( hhh ( h h i   h i het,eti AP hhet,eti,het,etii     CompAP COMP +periph ↓ h i COMP +periph DEG –   * DEG + h i * V +  N +      COMP +periph DEG + ↓ 1 Figure 5.17: The word level tree sets with COMP and DEG features for (a) the adjectives happy and apt, (b) the comparative suffix -er, (c) the periphrastic comparative more, and (d) the unlexicalized interface trees for a comparative adjective

134 Chapter 5. The Roots: Digging Deeper into the Model apter, and *more more apt.10 *Apter is prevented by a feature clash between the +periph COMP feature on apt and the −periph COMP feature on the adjoining -er. *More apter is already prevented by the feature clash for *apter because all word level operations apply before phrase level ones: first, the morphological operation to form *apter applies, which creates a feature clash that prevents the derivation from proceeding to the phrase level where more would try to adjoin. Finally, *more more apt is blocked due to the foot node of the phrase level comparative adjective tree, which contains a negative DEG feature. After the grammatical formation of more apt, the root of the derived tree has a positive DEG feature. When the second comparative adjective tree containing more tries to adjoin at the root of more apt, the degree features clash and the derivation fails. Now that I have motivated the COMP and DEG features and obtained the correct comparative adjective forms, I can return to the bracketing paradox example of unhappier. Since the prefix un-, shown in Figure 5.19(a), attaches to adjectives to form new adjectives, it also has both COMP and DEG features. For COMP, it has a variable in both its root and foot, indicating that it preserves whichever feature value is carried by the adjective into which it adjoins. Since prefixes do not inherently have a degree in English, the DEG feature is negative on both the foot and root. This negative degree feature setting ensures that the prefix adjoins before the comparative suffix: if un- adjoined after -er, the negative DEG feature on the foot node of un- would clash with the positive DEG feature on the root node of -er. As a result, only the semantic bracketing is allowed, and there is no problematic bracketing paradox. The derived trees for unhappier are in (b).

5.2.2A TTRIBUTEPHRASEBRACKETINGPARADOXES

Another commonly claimed bracketing paradox involves attribute phrases of the form Adjective + Noun, such as nuclear physicist. The morphological bracketing of such cases is [ nuclear [ physics ist ] ], which corresponds to the meaning “a physicist who exhibits nuclear properties” (or something similar), while the semantic bracketing of the salient reading is [ [ nuclear physics ] ist ], a doer of nuclear physics. Unlike unhappier in the previous example, which only yields one reading, here, technically both readings are possible and, given the appropriate context, both could be entirely reasonable, especially in other examples such as criminal lawyer—a lawyer who has done something criminal or a doer of criminal law, respectively. In fact, Beard (1991) claims that attribute phrases can yield as many as four readings, with each possible structure yielding at least one meaning. As a result, a structural reanalysis solution is not possible because

10This restriction assumes that the use of two periphrastic comparatives is only grammatical via a prosodic mechanism separate from the morphology.

135 5.2. Bracketing paradoxes

V +  N +  h i (a)   het,eti happy COMP –periph   ¨H 1 ¨¨ HH DEG + er PP h i  PP er het,eti V +  er happy N +      COMP –periph DEG –

happy

  AP h i (b)   COMP +periph het,eti XX DEG +  XXX ``` ```` h i h i hhet,eti,het,etii het,eti     CompAP AP     COMP +periph COMP +periph more apt DEG + DEG –

    CompA A AP     1 COMP +periph COMP +periph DEG + DEG – CompAP apt

1 more apt more

Figure 5.18: The derived and derivation trees for (a) happier and (b) more apt

136 Chapter 5. The Roots: Digging Deeper into the Model

h i

h i   (a) V + (b) happy N α h i 1 1     hσ,eti COMP x ¨H   ¨ H un er DEG – ¨ H P h i  PPP un hσ,eti un V +  h i N α   *   COMP x  DEG – h i *

V +  N +  h i (c)     het,eti COMP –periph ¨H   ¨ H DEG + ¨ H X  XX er h i  XXX het,eti ¨H V +  er ¨¨ HH N α  un h i   het,eti   COMP –periph DEG – happy PP  PP   un V + N +      COMP –periph DEG –

happy

Figure 5.19: (a) The word level tree set for the prefix un- now with COMP and DEG features and (b) the derivation tree and (c) the derived trees for unhappier

137 5.2. Bracketing paradoxes restructuring the bracketing would not predict the full range of possible readings. Others have proposed alternative solutions as well, including subjoining semantic features of the attribute phrase constituents rather than their morphological components (Beard, 1991), or attributing the paradox to the , such as via proportional analogy (Williams, 1981; Spencer, 1988). However, these accounts either do not capture the full range of examples or do not account for the underlying issue.

At its core, the problem seems to be a semantic one. The stance adopted here is that these attribute DPs are actually not bracketing paradoxes at all but are solely contingent upon the semantics of the adjective. For cases like nuclear physicist, the adjective nuclear can be either subsective or intersective. SUBSECTIVE

ADJECTIVES return a subset of the denotations of the noun, while INTERSECTIVEADJECTIVES indicate an independent property of the noun (as in red balloon—the fact that the balloon is red is independent of the fact that the entity is a balloon) (Partee, 1995). Under the salient reading of nuclear physicist, the adjective nuclear is subsective (and not intersective), which results in the reading that there is a subset of physicists and that subset contains the physicists who study nuclear physics. Under the reading that the doer of physics is nuclear (or exhibits nuclear properties), nuclear is intersective, thus identifying all things nuclear, and here specifically identifies physicists who are nuclear.

Another sign that semantics is most likely at the core of the problem comes from parallel examples such as nuclear chemist. In contrast to the other examples seen so far, chemist cannot be decomposed into a morpheme indicating a scientific field plus -ist since the scientific field is chemistry. Nonetheless, this attribute phrase exhibits the same issue of either meaning “a doer of nuclear chemistry” or “a doer of chemistry who is nuclear”. Thus, the meaning of the expression derives from the adjectival semantics, rather than the morphology.

Implementing such an approach in the STAG analysis proceeds as follows. Using the example of nuclear physicist, the morpheme -ist combines with physics on the word level to create a noun. On the phrase level, the adjective nuclear composes into the noun physicist. Whether the adjective is subsective or intersective is simply determined by its denotational semantics. The next section returns to testing the capabilities of STAG to handle morphology by delving into the more complicated issue of modeling the morphology of English anaphors.

138 Chapter 5. The Roots: Digging Deeper into the Model

5.3C APTURINGANAPHORS

On the surface, English reflexives are morphologically complex pronouns, while English reciprocals are fixed syntactic forms (one lexical unit) that do not inflect morphologically.11 As a result, reciprocals are uninteresting morphologically so this section focuses on reflexives instead, yet future morphological STAG work should examine reciprocity crosslinguistically. English reflexives are superficially comprised of two morphemes: a pronoun and -self /-selves. In first and second person, the pronoun superficially resembles a possessive pronoun (my, your, our), and in third person the pronoun takes the form of a personal pronoun (him, them). There are a few possible interpretations of these two morphemes, and in fact, the status of each remains an open question. However, before turning to their current status, it is important to understand their past.

5.3.1B RIEF HISTORY OF THE ENGLISH REFLEXIVE FORM

A variety of attempts have been made to describe the origin and evolution of the morphological makeup of English reflexives. As summarized by Sinar (2006), the standard view of the development of the modern reflexive proceeds as follows. In Old English (OE), personal pronouns were used to indicate the reflexive, for lack of an alternative dedicated reflexive form. At the end of OE and the beginning of (MidE), a new morphologically complex reflexive pronoun appeared, comprised of a (dative) pronoun and the intensifier self (c.1250). These two reflexive forms co-occurred until the beginning of Early (EModE), when the morphologically complex reflexive form replaced the pronoun reflexive form (c.1500). Accounts differ with respect to why the morphologically complex form appeared, which kind of pronoun comprises it, what the role of self is, and why the complex form later replaced the pronoun, as well as what the distribution of the two forms was when they co-occurred. For the present purposes of creating a morphological STAG account of modern English reflexives, only the nature and makeup of the pronoun + self are relevant. Looking first at the pronoun, there are two different accounts—one phonological and one syntactic—of the difference between the first and second person reflexives, which appear to use possessive pronouns, and the third person reflexives, which seem to use (accusative) personal pronouns. The phonological account holds that the first and second person forms are due to vowel reduction in unstressed syllables. Keenan (2002), following the Oxford English and other etymological sources, claims that the pronoun in first and second person singular was originally dative but underwent phonological reduction (mi self < me

11Once again, for the present purposes, I only consider the fixed reciprocal forms of each other and one another.

139 5.3. Capturing anaphors self ), a process that corresponds to the change from OE long close e to MidE short i (Lass, 1992). Since first and second persons are the only dative pronouns consisting of a single light syllable (the others being closed—him, us, hem—or disyllabic or diphthongal—hire, eow), they are most likely to be the first to phonologically reduce. The reduced forms were then identified as resembling , and the pattern extended to the first and second plural forms in the mid-1300s via Pattern Generalization, when “a pattern that applies to a restricted class of cases extends to new cases” (Keenan, 2002). Therefore, under this view, the pronoun component of the complex reflexive originated as uniformly dative across all persons and number and thus should be treated as a personal pronoun rather than a possessive, the latter of which seems to appear in first and second person due to coincidental similarity in appearance.

The syntactic account, on the other hand, claims that a possessive pronoun and a nominal self fused to form the reflexive (Penning, 1875; van Gelderen, 2000). Keenan (2002) opposes this syntactic account based on evidence that in the 1200s, when the complex reflexive form arose, possessives did not exist in first and second person plural or in third person singular or plural. First and second person plural possessive forms are not attested until the mid-1300s and meanwhile, the dative forms were in use. Additionally, although some texts contain mi self, most possessive forms were min(e) or þin(e), which never occurred with self. Based on this evidence, it seems unlikely that first and second person reflexives were formed using a possessive pronoun.

For the morpheme self /selves, there is general consensus that self derived from the once independent OE intensifier self. According to Keenan (2002) and van Gelderen (2000), among others, morphologically, this self inflected for case, number, and gender. Syntactically, it was an independent word that carried stress and modified NPs, immediately following them and agreeing in case, number, and gender. Semantically, it supplied a contrast between the referent of the NP with which it agreed and a set of alternatives. In its evolution from OE to ModE, though, self lost its intensifier meaning, stopped occurring as an independent word, and was reanalyzed as a morpheme signalling coreference (Sinar, 2006).

5.3.2C URRENT STATUS OF THE ENGLISH REFLEXIVE FORM

Fast-forwarding to the current status of English reflexives, once again there is no general consensus and multiple opinions exist on their morphological compositionality. (The following is by no means an exhaustive account.) As just discussed, some (König and Siemund, 2000b; Keenan, 1996; Farr, 1905) argue that modern English reflexives compositionally derive from the fusion of two independent elements: a dative pronoun and the original OE intensifier, self. With slight variations depending on the account, the reflexive

140 Chapter 5. The Roots: Digging Deeper into the Model form is considered to be only weakly grammaticalized, thus having retained most, if not all, of its morphological and semantic parts. Even though the contrast meaning of self was lost, it adopted a role in local binding so still provides an individual contribution.

Others (Rooryck and Wyngaerd, 2011; Sinar, 2006) contend that modern English reflexives have been grammaticalized and thus are not compositional, but instead are a single morphological unit, as the other English pronouns. Under this view, modern reflexives are not decomposable into a pronoun and an intensifier. Evidence for this view primarily comes from the decreased transparency in the modern reflexive’s compositionality, potentially due to both the loss of case endings in the transition from MidE to ModE, and the inconsistency in the pronominal form (possessive versus personal) used with -self .

Another view is that reflexives are syntactically complex, but semantically simple. For example, Ahn (2015) maintains that syntactically, reflexives are ultimately compositional because the pronoun and self can be separated by modifiers, such as the expletive in She said her damn/goddamn self that she’d come. Semantically, though, the reflexive is interpreted as a simple pronoun (an idea dating back to Lees and Klima (1963)) and involves only an index and an assignment function that determines the reference of that index, making pronouns and reflexives semantically equivalent except for the value of the index. Safir (1996) takes an opposing view, however, claiming that the morphological components of anaphors do contain meaningful semantic content that in fact plays a key role in determining anaphoric distribution and interpretation.

In sum, many aspects of the morphological makeup of English reflexives remain unresolved. This inconclusiveness makes providing a robust theoretical account of English reflexive morphology challenging, but also opens the door for insights into their behavior. In the next section, I present one possible approach to representing English reflexives morphologically in STAG.

5.3.3M ORPHOLOGYOF ENGLISH REFLEXIVES IN STAG

For the purposes of providing a first attempt at capturing the morphology of reflexives in STAG, I adopt the following hypothesis. The English reflexive is indeed compositional and is composed of two morphemes. The first morpheme is a personal pronoun that plays the role of a bound variable pronoun that agrees with its antecedent in φ features. This word level pronoun differs from other phrase level pronouns in three main ways. First, this pronoun is not possessive because it originated across persons and number as a (dative) personal pronoun, and the appearance of the first and second person pronouns as having a possessive surface form is due to extraneous (phonological) circumstances. Second, the morphological pronoun in a reflexive is not a regular (accusative) personal pronoun: regular personal pronouns must be locally free (as prescribed

141 5.3. Capturing anaphors by theories such as Chomsky’s (1981) Condition B), whereas the pronoun in a reflexive, but more generally the reflexive as a whole, must be (locally) bound (Chomsky’s (1981) Condition A). Finally, as a result of the first and second explanations, this morphological pronoun is also not identical to other phrase level bound variable pronouns. English pronouns function as bound variables when they are possessors, as in (114a), or subjects, as in (114b).12 However, as previously discussed, the morphological pronoun in reflexives is neither possessive nor a subject. As a result, it is not exactly equivalent to these phrase level bound variable pronouns, although it does seem to function as a bound variable on some level, to be discussed shortly.

(114) a. Every girli loves heri father.

b. Every girli believes that shei is intelligent.

The second morpheme is -self /-selves, which originated as an intensifier in OE, but was reanalyzed as coreference and now serves as a two-place identity relation. Maintaining consistency with the morphological framework presented thus far and the STAG reflexive tree set presented in Chapter 3, Figure 5.20 presents the of the reflexive herself. The word level tree set for the -self morpheme component is in (a) and that for the bound pronoun morpheme component her- is in (c). The unlexicalized interface tree set for a reflexive is in (d) and the derivation tree for composing the phrase level reflexive is in (b). In (a), the word level -self tree set has a self noun in the morpho-syntax and the reflexive operator carrying the two-place predicate identity relation in the morpho-semantics.13 Crucially, this self comprises its own lexical entry so is not the same self as other phrase level uses, such as the self or self-aware. This tree set then composes into the unlexicalized interface reflexive tree set shown in (d) at its 3 links: the morpho-syntactic -self substitutes into the N slot and the morpho-semantic REFL substitutes into the appropriate slot in the operator tree. This reflexive tree set also accepts the word level reflexive bound pronoun her- tree set, shown in (c), at the 2 links. Following Storoshenko (2010) and Déchaine and Wiltschko (2002), her- is treated as a determiner in the morpho-syntax, rather than as a full DP, another indication that this pronoun is not identical to a regular phrase level pronoun but constitutes its own lexical entry. Morpho-syntactically, the pronoun’s main role on the word level is to contribute φ features that are linked to its antecedent’s φ

12Storoshenko and Han (2013) provide these examples in their STAG analysis of bound variable pronouns, but they focus specifically on bound variable pronouns separate from the English reflexive. Determining whether their bound variable analysis can be unified in any way with the analysis presented here of the pronoun comprising reflexives is left for future work. 13For now, I have chosen to semantically represent self in this way, although I acknowledge that there are several other theories on the role of self in reflexives and leave further investigation to future work.

142 Chapter 5. The Roots: Digging Deeper into the Model

(a) -self (word level) (b) Derivation tree h i h i " # reflexive V– h i heet,eti 1 3 N + 2 antecedent her self REFL self

(c) her- (word level) " # " # Det DP φ y h i φ y S∗ S∗   t∗ t∗ e Det h i h i eet φ 3sgF *   ¨H a CASE acc ¨¨ HH λa h i et her h i

(d) reflexive (unlexicalized interface) * " # DP

φ x S 1 2 S 2 DP t 1 2 e t 2 e 2 ∗ 2 ∗ P ∗ ↓  PP h i  P τt τ↓ 1 D↓ 2 NP !a b !! aa " # heet,τti↓ 3 h i DP N↓ 3 eet x φ 2 ↓ 1 h i et @@ λb t∗ Figure 5.20: (a) Word level elementary tree set for the reflexive component -self ; (b) is the derivation tree for the composition of her- and -self into the phrase level STAG reflexive tree set; (c) is the word level elementary tree set for the bound pronoun component her- and (d) the unlexicalized interface tree set for a reflexive.

143 5.3. Capturing anaphors

Derived reflexive tree set for herself

S∗ 1 DP S∗ DP t 1 e t∗ e ``` ``` DP 1 D NP et e 1 ↓ P ↓ b a  PPP her N h i h i ∪ eet self heet,eti h i eet REFL !a !! aa λa h i et h i h i ∪ et @@ λb t∗ Figure 5.21: Derived reflexive tree set, herself

features, via the y variable, to ensure agreement. Additionally, her- carries accusative case that will propogate up to the root DP node in the reflexive tree set. Morpho-semantically, the pronoun provides a lambda expression as well as a variable that will be bound by the lambda expression later in the derivation.

Turning to the unlexicalized interface reflexive tree set in (d), on the syntax side, the first two syntax trees accept the antecedent at the 1 links. Notice that the DP has been split into two separate nodes, a strategy also used for picture-DPs and raising verbs in Chapter 3, to enable adjunction of the bound pronoun’s φ features for agreement with the antecedent at the top DP node (link 2 ), as well as substitution of the lexical antecedent itself at the bottom DP node (link 1 ). The second two syntax trees are dedicated to the reflexive. The DP is the same as the previous STAG version, except instead of the shorthand of showing herself as simply a DP, here it has been broken down into its morphological components with the pronoun as the determiner and self as the noun, as is standard in the literature. The determiner her- contributes its accusative case and φ features to the substitution D node, from which the features propogate up to the root DP node (feature structures not shown in the figure) so the DP as a whole carries the appropriate features.

On the semantics side, the first tree accepts the REFL operator via substitution at link 3 , the reflexive bound pronoun via adjunction at the 2 links, and the antecedent at the 1 links. The adjunction of the reflexive bound pronoun into this tree is required by the mismatch in the features: the top feature structure at the relevant node has type eet but the bottom feature structure has type et. The lambda expression in (c)

144 Chapter 5. The Roots: Digging Deeper into the Model must adjoin here in order to ensure feature unification. The bound variable component in (c) substitutes into the entity substitution node, thus completing the elementary reflexive tree set. The derivation steps for forming the phrase level reflexive are shown in the derivation tree in (b). The derivation proceeds as usual with the antecedent tree set composing into the reflexive tree set at the 1 links and then the whole antecedent + reflexive tree set composing into the relevant verb tree set as dictated by the sentence. The phrase level reflexive tree set resulting from the composition of her- and -self into the unlexicalized interface reflexive tree set from (d), familiar (after feature unification) from Chapter 3, is shown in Figure 5.21.

5.4S UMMARY AND FUTURE WORK

This chapter provides a first attempt at extending the STAG framework from a phrase level down to a word level. Based on the idea that morphology is essentially more syntax, I showed how the phrase level trees currently assumed to be the basic elementary units of STAG can in fact be decomposed further into word level elementary trees. The ability to straightforwardly capture patterns of derivational and inflectional morphology using the feature-based multicomponent STAG formalism employed throughout this dissertation holds promise for future applications to other phenomena both in English and crosslinguistically. There are a plethora of directions to pursue to test and expand morphological STAG, so I mention only a few here. Clearly, applying morphological STAG to agglutinative, and then fusional, languages would be an ideal test of its capabilities. This exploration would be particularly interesting for languages that represent reflexives and reciprocals morphologically. Within English, it would be useful to figure out how to capture multiple tenses, how to represent different kinds of nouns (mass, count, kind) and how to account for interactions in agreement (subject-verb, determiner-noun in other languages).14 Finally, further probing into the nature of the morphological bound pronoun of English reflexives and its relation to other English pronouns would be useful in verifying or improving the preliminary approach presented here as well as determining if it can be unified with the bound variable pronoun approach presented by Storoshenko and Han (2013). In the next chapter, I resurface from the roots and take a step back to survey potential further directions for research beyond the trees. I conclude by summarizing the main contributions of this dissertation to the understanding of the syntax, semantics, and morphology of reflexives and reciprocals.

14In this last case, a straightforward solution would be to include an additional agreement feature on the word level trees that must unify with the interface level tree nodes’ features upon composition and then propogate up the tree.

145 6 Beyond Trees: Expanding the Model

6.1F UTUREDIRECTIONS

The previous chapters have presented a foundation for modeling the syntax, semantics, and morphology of both reflexives and reciprocals in a unified way. However, there are a variety of directions in which to extend this work. In addition to the future work mentioned at the end of each chapter, in this chapter, I discuss two preliminary extensions I have begun. The first extends my anaphor analysis crosslinguistically, primarily to ; the second initiates a machine learning approach to understanding the distribution of anaphors. I conclude this chapter with a summary of the primary findings and contributions of the dissertation.

6.1.1P RELIMINARY CROSSLINGUISTIC EXPANSION

As mentioned in Chapter 3, a promising next step in testing my STAG anaphor analysis is applying it to anaphors crosslinguistically. Reflexives and reciprocals are represented crosslinguistically through verbal affixes, verb , clitics, specialized pronouns, or a mix of these (Maslova and Nedjalkov, 2013). I now present a preliminary assessment of how this analysis could potentially capture each of these.

Languages such as Finnish represent reflexivization with a verbal affix that detransitivizes the verb into an intransitive verb, thereby reducing the valency of the verb by deleting the direct or indirect object (Büring, 2005). Büring (2005) explains that in Finnish, the verbal reflexive marker is not a syntactic argument or clitic, providing support for a derivation tree in which the verb accepts just one argument, the subject. In the derivation of my analysis (and Frank’s (2008)), the verb also accepts only one argument, but this single argument contains both the antecedent and the reflexive/reciprocal. Although these two derivations are not exactly the same, the structure is still more similar than non-reflexive derivation trees of transitive verbs that accept two separate arguments. Languages that use verb reduplication would pattern similarly. The details of such derivations are a worthwhile task for future work.

146 Chapter 6. Beyond Trees: Expanding the Model

In Romance languages, reflexives can be represented by clitics or reflexive pronouns, and reciprocals can be represented by clitics, reciprocal pronouns, or a combination of both. In French, reflexives only take the form of a clitic (se 3sg), and reciprocals require the reflexive clitic plus the reciprocal pronoun (l’un l’autre). In Italian, reflexives can be represented either by a clitic (si 3sg) or by a reflexive pronoun (se stesso 3sg). Reciprocals can generally be represented by the reflexive clitic (in which case the sentence is ambiguous with reflexives) or by the clitic plus the reciprocal pronoun (l’un l’altro). The STAG analysis of reflexives and reciprocals from Chapter 3 can capture all of these cases. Once again, the person and number of the pronoun or clitic are captured through feature unification. Before turning to reflexive clitics, though, I will start with a brief overview of clitics in general and how they fit into STAG, and then show how the STAG analysis of reflexive clitics follows directly from this.

6.1.1.1C LITICS

In Romance languages, clitics are pronominal elements that take the place of a nominal element in the verb’s argument structure (Bleam, 2000).1 They differ from their full DP version, though, in where they occur in relation to the verb: the DP form follows the verb, while the clitic precedes the verb, unless the verb is non-finite, in which case the clitic attaches to the end of the verb. Bleam (2000) points out an exception to this, called CLITICCLIMBING, in which the clitic can also occur in a clause higher than the one containing the verb on which it thematically depends. Clitic climbing occurs in almost all Romance languages, except French. These clitic configurations are shown in (115) for a direct object in Italian.

(115) a. Full DP: Noè ed Emma vedono il film. Noah and Emma see the movie.

b. Pre-verb clitic: Noè ed Emma lo vedono. Noah and Emma see it.

c. Non-finite verb clitic: Noè ed Emma vogliono vederlo. Noah and Emma want to see it.

d. Clitic climbing: Noè ed Emma lo vogliono vedere. Noah and Emma want to see it.

Clitics cannot co-occur with the object they replace, but there can be multiple clitics in a sentence as long as each has a different syntactic function (Abeillé, 1992). Clitics differ from NPs because they cannot coordinate with NPs or take NP modifiers and usually have their own category, Clitic (Abeillé, 1992). Several languages that employ clitics have further specifications, but these properties are sufficient for the present purposes.

1Some (e.g. Miller (1992)) argue that clitics are inflectional affixes rather than arguments of the verb, but I follow other work in STAG that treats clitics as arguments.

147 6.1. Future directions

6.1.1.2P REVIOUS STAG ACCOUNTSOFCLITICS

There are three main previous approaches to capturing clitics with STAG. Abeillé (1992) focuses on French and proposes that the elementary tree for a verb contains extra branches with substitution nodes for all possible clitic realizations. Each syntactic clitic node and its corresponding alternative NP object node are linked to one node in the semantics; since only one substitution is allowed into each semantic node, the clitic and object cannot co-occur. The synchrony of the syntax and semantics thus serves as a well-formedness condition in the grammar (Abeillé, 1992).

Another approach, by Bleam (2000), focuses on Spanish and has the clitic originate as an auxiliary tree within the multicomponent elementary tree set of the verb on which it is thematically dependent. Through set-local MCTAG, the clitic and verb can adjoin into the same tree set but do not have to adjoin into the same specific tree. This allows the appropriate flexibility for the different positions in which a clitic can occur in Spanish through clitic climbing.

The last account is by Dras and Bleam (2000) in response to the observation by Shieber (1994) that for translation, clitics potentially pose a problem for STAG since the derivation trees of both languages are not isomorphic. Shieber (1994) observed that some languages seem to allow unbounded material between the clitic and the lexical item with which it is semantically related. This is especially true for languages with clitic climbing since several verbs can intervene between the clitic and the verb on which it thematically depends. This is challenging for STAG because the derivation tree for a clitic (climbing) language will have a different shape than that for a non-clitic language, but STAG requires isomorphic derivation trees. To resolve this discrepancy, Dras and Bleam (2000) propose a metagrammar (originally from Dras (1999)) that serves as an initial step for creating an isomorphism between two languages’ derivation trees and then leads to the object-level derivation trees.

All three STAG accounts of clitics address different issues posed by clitics and all employ different approaches to capture those issues. Here, I am concerned with anaphors, which are restricted to certain locality configurations, so I limit the discussion to clitics found next to the verb on which they thematically depend.2 I will demonstrate on Italian.

Figure 6.1 contains the proposed analysis of clitics for the sentence in (115b). The clitic tree set in (a) parallels that for other DPs, except on the syntax side instead of the placeholder S∗ tree, there is a V-rooted auxiliary tree containing the lexical clitic that adjoins at the V node in the verb tree. Since a clitic cannot

2Clitics that are separated from the verb on which they thematically depend by another verb, as in clitic climbing, generally involve raising or ECM verbs and are left for future work.

148 Chapter 6. Beyond Trees: Expanding the Model co-occur with its DP argument, if the clitic tree is present, the normally overt DP is instead filled by the empty string. This approach is reminiscent of cataphora. The meaning of the sentence does not change based on whether a pronoun or a clitic appears, so the semantic trees stay the same, with an e-rooted lexical tree and a scope t∗ tree.

The syntactic verb tree in (b) has simply added a 20 link to the V node and object DP node where the clitic tree set will adjoin. Following the strategy used for representing both coindexations of distransitives, adding this alternative set of links captures both the clitic (operating at the 20 links) and the non-clitic

(operating at the 2 links) derivations in one verb tree. The derivation tree in (c) shows the use of the 20 link by the clitic lo and matches the derivation tree from Section 3.1.1 for non-reflexive transitive verbs. With the exception of the new clitic tree set, expanding the analysis to clitics does not require or add anything beyond the original STAG framework.

(a) V DP t∗ e

lo lo V∗ ε

(b) S 1 2 t 1 2 20 (c) vedono 1 20

DP 1 VP et e 1 ↓ ↓ noè+emma lo

V 20 DP↓ 2 20 eet e↓ 2 20

vedono vedono Figure 6.1: Elementary trees for (a) a clitic and (b) the verb tree with added 20 links for the clitic; (c) is the derivation tree for Noè ed Emma lo vedono.

6.1.1.3R EFLEXIVE/RECIPROCALCLITICS

The analysis of reflexive clitics follows directly. As mentioned previously, in Italian there are three main ways of representing reflexives and/or reciprocals: a reflexive pronoun (reflexives only), a clitic (ambiguous between reflexives and reciprocals), and a clitic plus reciprocal pronoun (reciprocals only). I show how this clitic approach can account for each of these in turn. The reflexive pronoun is the simplest case because it parallels the English derivations and requires simply replacing the English lexical items with their Italian counterparts: himself/themselves with se stesso/se stessi.3

3Stesso/stessi literally translates to self/selves and se indicates third person, so although in Italian the reflexive is two words, the approach used here is to group them together as one lexical item, just as for each other.

149 6.1. Future directions

The ambiguous reflexive/reciprocal clitic case follows from the non-reflexive clitic analysis and the previously presented reflexive/reciprocal analysis, as illustrated on the left in Figure 6.2 for the Italian sentence in (116).

(116) Noè ed Emma si vedono. Noah and Emma see themselves/each other.

Instead of a separate clitic tree set as for non-reflexive clitics, the reflexive clitic trees are simply part of the reflexive/reciprocal tree set, which is parallel to that for English, as in Figure 6.2(a). On the syntax side, the DP that originally contained the lexical reflexive/reciprocal now contains the empty string, and a V-rooted auxiliary tree containing the lexical reflexive/reciprocal clitic si has replaced the anaphor’s degenerate S∗ trees. In the semantics, the notion of reflexivity comes from the operators, not a lexical item, so there is no e-rooted tree with the clitic. The semantics is thus consistent with that of non-cliticized reflexives and reciprocals (so is not shown), supporting that clitics are fundamentally a syntactic phenomenon. The syntactic derived tree in (b) and the derivation tree in (c) follow directly from the non-reflexive clitic example. In addition to the reflexive clitic that precedes finite verbs, there is also a reflexive clitic that follows (or more accurately, attaches to) non-finite verbs. (This is true for non-reflexive clitics as well.) In this case, the clitic occurs in the same position in the syntactic tree as a lexical reflexive/reciprocal, so one approach is to have the clitic simply replace the lexical anaphor, as in (d). Since the clitic is functioning more as an object than as a cliticized pronoun, si can use the 2 link in the verb tree (rather than the 20 link). The right side of Figure 6.2 shows the relevant trees for the subject control sentence in (117). As seen in Section 3.5.5, anaphors with subject control verbs utilize delayed locality; this derivation proceeds as the one for English shown in Figure 3.21. The syntactic derived tree is in (e) and the derivation tree is in (f).

(117) Noè ed Emma vogliono vedersi. Noah and Emma want to see themselves/each other.

The more complex case of clitic climbing, as in (118), would require delayed locality in addition to a condition that allows the clitic to float to a higher V. The details of such cases are left for future work.

(118) Noè ed Emma si vogliono vedere. Noah and Emma want to see themselves/each other.

The final anaphor case is when the reflexive clitic and the reciprocal pronoun co-occur. In Italian (among other Romance languages), if the reciprocal pronoun appears, the clitic must also obligatorily appear, as shown in (119). To ensure this, I assume that the reflexive clitic is simply part of the lexical entry of the reciprocal pronoun (l’un l’altro) and therefore an overt clitic appears in the tree set.

(119) a. Noè ed Emma si vedono l’un l’altro. Noah and Emma see each other.

150 Chapter 6. Beyond Trees: Expanding the Model

(a) S∗ 1 DP↓ 1 V DP (d) S∗ 1 DP↓ 1 S∗ DP

si V∗ ε si (b) S (e) S

DP VP DP VP

Noè&Emma V DP Noè&Emma V S

si V ε vogliono DP VP

vedono PRO V DP

vedere si (c) vedono (f) vedere

1 20 1

si 2 vogliono 1 1 noè+emma si

1 noè+emma

Figure 6.2: Left: (a) Elementary trees for a reflexive/reciprocal clitic with finite verb; (b) is the derived syntac- tic tree and (c) the derivation tree for Noè ed Emma si vedono. Right: (d) Elementary trees for a reflexive/reciprocal clitic with non-finite verb; (e) is the derived syntactic tree and (f) the derivation tree with delayed locality for Noè ed Emma vogliono vedersi.

S∗ 1 DP↓ 1 V DP

si V∗ l’un l’altro Figure 6.3: Elementary trees for a clitic + reciprocal pronoun construction, as in Noè ed Emma si vedono l’un l’altro.

b. * Noè ed Emma vedono l’un l’altro.

This derivation also follows straightforwardly by changing the DP lexical tree from the empty string to the reciprocal pronoun, as in Figure 6.3. The semantics remains unchanged. The derivation then proceeds as on the left side of Figure 6.2. To be consistent, I could in fact include the clitic trees in the reflexive/reciprocal tree set at all times, and simply fill the clitic node with the empty string if no clitic is present. These extra trees would have no effect on the derived expression, but would still appear as placeholders. The derivation tree for languages using clitics and/or reflexive and reciprocal pronouns (and potentially verbal affixes and verb reduplication as well) thus parallels the one I have proposed for English, providing more support for the hypothesis that reflexives follow a different derivation than transitive verbs. Although

151 6.1. Future directions more work remains on crosslinguistic applications of this analysis, the prospects seem promising.

6.1.2M ACHINELEARNINGAPPROACHES

The corpus examination presented in Chapter 2 revealed that reflexives and reciprocals have a complicated and sometimes unexpected distribution. Developing an annotation scheme based on the literature and corpus findings elucidated some patterns. However, training a model on the data could perhaps reveal other insights into the data not previously considered via a human perspective. Since override reflexives seem to be the most challenging kind of anaphor, my colleagues, Elbert Gong and Simas Sakenis, and I conducted an experiment to test the ability of various models to predict the appearance of a reflexive versus a pronoun in a given sentence. In this section, I briefly describe the data and methods we used and the results we obtained. I conclude that a machine learning approach to distinguishing anaphors from pronouns could provide much needed insights into their distribution that theoretical approaches cannot attain.

6.1.2.1D ATA AND MODELS

Based on the findings from my literature review and corpus investigation, override reflexives seem to be the least understood out of all of the kinds of reflexives and reciprocals, and overrides occur most in first person singular. Therefore, for our first attempt, we focused exclusively on sentences containing myself and sentences containing me. I wrote a Python script to extract 30,000 total sentences containing the word me or myself (15,000 sentences of each) from COCA. We only used sentences containing one me or myself to avoid double counting or sentences containing lists of pronouns/reflexives. The task followed an encoder-decoder framework, in which we replaced all instances of me and myself in the sentences with a token and the model had to determine whether a pronoun or a reflexives should appear in that place. As a baseline, we used a bag-of-words approach in which the vocabulary consisted of the most common words in COCA above a certain threshold frequency. We used NLTK’s word tokenizer to tokenize each sentence and turn it into a vector of the same size as the vocabulary, where each number represents the number of times the corresponding vocabulary word appears in a given sentence. We split the data into 3 parts—a training set (70%), a validation set (10%), and a test set (20%)—and trained a multinomial Naive Bayes classifier from Python’s scikit-learn library using 8-fold cross-validation. We also tested n-grams greater than one, in which the vocabulary consisted of the most common n-grams above an appropriate threshold frequency, using padding symbols at the beginning and end of each sentence, and each sentence was vectorized as before. We trained separate models for n-grams of different sizes and

152 Chapter 6. Beyond Trees: Expanding the Model used a multinomial Naive Bayes classifier with 8-fold cross-validation, as before. Additionally, we tested out model variations, such as restricting the data to only include words in various fixed size windows around the target word as well as discarding the words in the sentence before or after the target word. Finally, since COCA also provides tags for each word in the dataset, we tested all of the above models using part of speech tags instead of words.

After this preliminary testing, we ran more complex models, including a convolutional neural network (CNN) and a long short-term memory (LSTM) network, with various vocabulary sizes and parameter settings, on both word and part of speech datasets. The data was first cleaned, then read into torchtext. The CNN model used was as described in Kim (2014). The LSTM architecture was bidrectional with a word2vec embedding layer and a linear (softmax) layer on final hidden states.

In order to determine an external baseline against which to assess the machine learning models, we ran a human judgment experiment. Using a subset of the COCA data with the target word elided, we asked native English-speaking participants to predict whether a pronoun (me) or a reflexive (myself ) should appear in the elided position.

6.1.2.2R ESULTS

The overall accuracy for humans on the prediction task was 93%. The left-to-right only LSTM came closest to this at 88.8% accuracy (right-to-left only LSTM at 62.8%), while the CNN attained 83.4% accuracy. It is possible that the LSTM could achieve even higher accuracy with additional model adjustments, such as adding more hidden layers or altering the gate. The most accurate n-gram approach, at 88.5% accuracy, was a trigram model over part of speech tags with a window size of seven that only considered words appearing before the target, using a vocabulary threshold size of 10,000. (A window size of five with the same other features obtained the next best accuracy at 87.3%.) Over a vocabulary of words rather than part of speech tags, the best n-grams model, at 87.1% accuracy, was a bigram model with a window size of seven that only considered words appearing before the target. The baseline bag-of-words model using a vocabulary of most frequent words appearing more than 10,000 times obtained 78.3% accuracy, and the same for part of speech tags obtained 78.4% accuracy.

Since myself is often overtly triggered by the appearance of I earlier in the sentence, it is not surprising that using words preceding the target, both for the n-grams models and the LSTM, would be most efficient. Additionally, the frequent appearance of I in the same sentence as myself, but not as regularly in conjunction with me, could also contribute to why the n-gram models performed so well despite being a simplistic

153 6.2. Conclusion bag-of-words approach.

6.1.2.3F UTUREEXTENSIONS

This first attempt looked at reflexives, specifically myself, but future work can look at all different reflexives, as well as extend to reciprocals and look at any differences between reflexives and reciprocals. Variations on the models used in this attempt could also be tested. Another task could be to compare the frequency of reflexives in certain contexts with that of reciprocals in those contexts to better understand how much their distribution overlaps. Lastly, one could run a clustering algorithm on sentences containing reflexives to see if the clusters correspond to the theoretical divisions of reflexives.4

6.2C ONCLUSION

In this dissertation, I have presented an analysis of reflexives and reciprocals in the framework of synchronous tree adjoining grammar that models their syntax, semantics, and morphology. The goal was to unify both anaphors under a single analysis to provide a simpler and more elegant way of representing two phenomena that behave similarly. The analysis is unified in three main ways. First, I model both anaphors in STAG, which pairs syntactic representation with semantic representation and constrains operations on both to occur synchronously. This analysis builds on a previous STAG analysis of only reflexives by Frank (2008) by incorporating reciprocals and applying to a variety of examples. Although the analysis utilizes a novel extension of the STAG framework—the ability for a tree set to operate at multiple links—I show how this augmented STAG is no more powerful than standard STAG. With the extension of delayed tree-locality, the analysis can account for more complex anaphor cases. Second, the semantics of both anaphors is represented using parallel operators that abstract out the notions of reflexivity and reciprocity. These operators can be adjusted in various ways to capture not only the canonical distributive reflexive and strong reciprocity readings, but also readings involving subpluralities, cumulativity, and for reciprocals, variations of weaker reciprocity. These operators function as interchangeable options on a leaf node in the anaphor elementary tree set. The third way the analysis is unified is that it additionally represents the morphology of anaphors through a novel extension of STAG. I decompose the STAG basic unit—lexicalized elementary trees—into morphological elementary trees. I show how these morpheme-anchored trees follow the same rules as

4I would like to thank Yonatan Belinkov for this idea.

154 Chapter 6. Beyond Trees: Expanding the Model lexically-anchored trees in STAG in order to form words and how features constrain the trees in the appropriate ways to only produce grammatical derivations. Using anaphors as a test case, I demonstrate how reflexives can be decomposed into morphological components that then combine to form my exact phrase level anaphor tree set. Other contributions of this dissertation include a clarification of the vast literature on reflexives in particular, a corpus investigation into the distribution of reflexives and any differences across the reflexives, a preliminary extension of the analysis crosslinguistically, and an initial application of machine learning models to anaphor data to predict their distribution. In sum, through corpus, theoretical, and computational means, I have provided a unified analysis of the syntax, semantics, and morphology of both reflexives and reciprocals.

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