Category Neutrality: A Type-Logical Investigation (Outstanding Dissertations in Linguistics)

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Category Neutrality : A Type-logical Investigation Outstanding Dissertations in Linguistics Whitman, Neal. Taylor & Francis Routledge 0415970946 9780415970945 9780203495384 English Grammar, Comparative and general--Grammatical categories, Semantics, Grammar, Comparative and general--Syntax, Neutralization (Linguistics) 2005 P240.5.W49 2005eb 415 Grammar, Comparative and general--Grammatical categories, Semantics, Grammar, Comparative and general--Syntax, Neutralization (Linguistics)

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Page i OUTSTANDING DISSERTATIONS IN LINGUISTICS Edited by Laurence Horn Yale University A ROUTLEDGE SERIES

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Page ii OUTSTANDING DISSERTATIONS IN LINGUISTICS LAURENCE HORN, General Editor PRONOUNS AND WORD ORDER IN OLD ENGLISH With Particular Reference to the Indefinite Pronoun Man Linda van Bergen ELLIPSIS AND WA-MARKING IN JAPANESE CONVERSATION John Fry WORKING MEMORY IN SENTENCE COMPREHENSION Processing Hindi Center Embeddings Shravan Vasishth INPUT-BASED PHONOLOGICAL ACQUISITION Tania S.Zamuner VIETNAMESE TONE A New Analysis Andrea Hoa Pham ORIGINS OF PREDICATES Evidence from Plains Cree Tomio Hirose CAUSES AND CONSEQUENCES OF WORD STRUCTURE Jennifer Hay THE PHONETICS AND PHONOLOGY OF GUTTURALS A Case Study from Ju’hoansi Amanda Miller-Ockhuizen TRUE TO FORM Rising and Falling Declaratives as Questions in English Christine Gunlogson PHONOLOGICAL AUGMENTATION IN PROMINENT POSITIONS Jennifer L.Smith CATEGORY NEUTRALITY A Type-Logical Investigation Neal Whitman THE UPS AND DOWNS OF CHILD LANGUAGE Experimental Studies on Children’s Knowledge of Entailment Relationships and Polarity Phenomena Andrea Gualmini MARKEDNESS AND FAITHFULNESS IN VOWEL SYSTEMS Viola Miglio THE SYNTAX-INFORMATION STRUCTURE INTERFACE Evidence from Spanish and English Eugenia Casielles-Suarez LENITION AND CONTRAST The Functional Consequences of Certain Phonetically Conditioned Sound Changes Naomi Gurevich SYNTACTIC FORM AND DISCOURSE FUNCTION IN NATURAL LANGUAGE GENERATION Cassandre Creswell THE INFLECTED INFINITIVE IN ROMANCE LANGUAGES Emily Scida LEXICAL, PRAGMATIC, AND POSITIONAL EFFECTS ON PROSODY IN TWO DIALECTS OF CROATIAN AND SERBIAN An Acoustic Study Rajka Smiljanic

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Page iii CATEGORY NEUTRALITY A Type-Logical Investigation Neal Whitman ROUTLEDGE New York & London

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Page iv Published in 2005 by Routledge Taylor & Francis Group 270 Madison Avenue New York, NY 10016 www.routledge-ny.com Copyright © 2005 by Taylor & Francis Group, a Division of T&F Informa. Routledge is an imprint of the Taylor & Francis Group. This edition published in the Taylor & Francis e-Library, 2005. To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk. All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Catalog record is available from the Library of Congress ISBN 0-203-49538-1 Master e-book ISBN ISBN 0-203-60665-5 (OEB Format) ISBN 0-415-97094-6 (Print Edition)

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Page v Contents List of Illustrations List of Tables Acknowledgments

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Introduction 1. Empirical Background 1.1 Ambiguity, Vagueness, and Polysemy 1.2 Category Neutrality 2. Theoretical Background 2.1 Different Kinds of Categorial Grammars 2.2 Syntax: The Associative Lambek Calculus 2.3 Semantics 2.4 Conjunction and Disjunction Constructors 2.5 Lexical Issues 2.6 Other Background 2.7 Conclusions 3. Category Neutrality and Mixed- Wh Interrogatives 3.1 Introduction 3.2 Optional NP-Gap Mixed- Wh Interrogatives 3.3 Plural-Noun Mixed- Wh Interrogatives 3.4 Mixed- Wh Interrogatives Without Lexical Neutrality 3.5 Conclusions

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Page vi 4. Category Neutrality and Verbal Argument Alternations 4.1 Introduction 4.2 Previous Analyses of Verbal Dependent Coordinations 4.3 Coordination of Verbal Adjuncts 4.4 Coordination of Verbal Complements 4.5 Coordination of Adjuncts with Complements 4.6 Excursus: Two Sample Derivations 4.7 Miscellaneous Alternations 4.8 Conclusions 5. Category Neutrality and Predicative Phrases 5.1 Introduction 5.2 Categories for the Copula, APs, PPs, and NPs 5.3 Category Neutrality, APs, and PPs 5.4 Category Neutrality and Noun Phrases 5.5 Proposed Reasons for Noun Phrases of Category Pr 5.6 Conclusions 6. Category Neutrality and Adverbial Nouns 6.1 Introduction 6.2 Previous Analyses 6.3 Property 1: Projection of Adverbial NPs 6.4 Property 2: Heading Non- Wh Adverbial Relative Clauses 6.5 Interaction of Property 1 and Property 2 6.6 Category Neutrality 6.7 Conclusions 7. Conclusion 7.1 Summary 7.2 Directions for Further Research 7.3 Implications Appendix A: Attestations of Mixed- Wh Interrogatives Appendix B: Questionnaire Items Bibliography Index

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Page vii List of Illustrations Figure Figure Figure Figure Figure Figure Figure Figure

1: Crossed-understandings test 2: Zeugma test 3: Two possible situations in which w has category 4: Possible groupings of different kinds of mixed- wh interrogatives 5: Different acceptability of optional NP-gap and obligatory NP-gap mixed- wh interrogatives 6: Different acceptability of plural-noun and obligatory NP-gap mixed- wh interrogatives 7: Coordination or nesting of adverb phrases 8: Categories for copula, depending on categories for APs, PPs, and noun phrases

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Page ix List of Tables Table Ordering of wh words in three kinds of mixed- wh interrogatives 1: Table Comparison of mean scores foroptional NP-gap mixed- wh interrogatives and grammatical filler 2: sentences Table Comparison of mean scores for obligatory NP-gap mixed- wh interrogatives (with nominal wh 3: word adjacent to body of interrogative) and grammatical filler sentences Table Comparison of mean scores for plural-noun mixed- wh interrogatives with wh adverbial first 4: and grammatical filler sentences Table Comparison of mean scores for obligatory NP-gap mixed- wh interrogatives (with nominal wh 5: phrase adjacent to body of interrogative) and grammatical filler sentences

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Page xi Acknowledgments This dissertation would not have been possible without the help of many people. I would first of all like to thank my advisor, David R.Dowty, for his intellectual support and guidance. This dissertation became much more coherent under his guidance than it would have been otherwise. His uncompromising nonsense filter caused me to reexamine (and sometimes reject) a number of ideas I had taken for granted; at other times, his persistent encouragement caused me to reexamine (and sometimes salvage) other ideas that I had given up on. In addition, his command of the relevant literature brought to my attention many sources that I would not have thought to look for on my own. Shortcomings or errors that remain are my responsibility alone. Thanks go to Carl Pollard for comments and discussion, especially regarding coordination and foundational issues in type-logical grammar. He also provided a healthy dose of skepticism that led me to some of the conclusions in Chapter 2. Thanks also to Detmar Meurers for comments and critique, in particular in discussing the organization of the lexicon in Head-driven Phrase Structure Grammar and in type-logical grammar. In addition, both his and David Dowty’s stylistic critiques of various chapters have (I hope) made this dissertation more reader friendly for readers who may not be familiar with the formalism used herein. In addition to my dissertation committee members above, other professors and fellow graduate students in the Ohio State University Linguistics Department have helped me during the course of my research. I wish to thank my three previous advisors: Brian Joseph, for his confidence in me from the beginning of my graduate studies; Bob Kasper, for his guidance after I shifted focus from historical to computational linguistics, and for suggestions on earlier versions of what is now Chapter 6; and Chris Brew, for his help in turning an initial computational exploration of lexical rules and underspecification into a

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Page xii more focused topic—which turned out to be more in the realm of theoretical syntax and semantics than computational linguistics. Thanks go to Keith Johnson and Allison Blodgett for their help in setting up the experiment that forms the core of Chapter 3; and to Keith, Chris Brew, and Pauline Welby for their subsequent help in interpreting the results statistically. For useful comments and assistance during various stages of the research presented here, I thank Bob Levine, Martin Jansche, Nathan Vaillette, Anton Rytting, and Mike Daniels. I am also indebted to all the people in the Linguistics Department that I asked for grammaticality judgments at various points. Outside the Linguistics Department, other people who made this dissertation possible include Diane Belcher, former director of the English as a Second Language Composition Program, where I taught for seven years while working toward my degree. Not only did the financial support allow me to continue as a student in linguistics, but the professional support and friendship of many of the faculty in ESL Composition have been a pleasant and memorable experience. Finally, I must thank my family members for their emotional support through the whole process, in particular to my wife Amanda and sons Douglas and Adam, and also to other members, who were uniformly encouraging. I also thank my parents Philip and Elaine Whitman, my brother Glen and my sister Ellen, not only for their emotional support, but also for all the energizing dinner-table discussions of English grammar (yes, English grammar) that we had years ago, whose effect has yet to wear off.

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Page 1 CATEGORY NEUTRALITY OUTSTANDING DISSERTATIONS IN LINGUISTICS

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Page 3 Introduction In formal grammars, there has come to be more and more emphasis on the lexicon as the location of grammatical information, and consequently, more emphasis on how to structure the lexicon. For a given language, it would be desirable to have a lexicon that does not consist of simply a list of every form of every word in the grammar. Rather, the lexicon should be organized so that natural word classes can be defined, and generalizations about different kinds of words can be made. In doing this, a fundamental question that must be answered is when two or more senses of a word correspond to multiple lexical entries, and when they correspond to a single one. In other words, when do we have a pair of homonyms, and when do we have a single word that can have different shades of meaning? A conventional assumption is that if a word’s different meanings are associated with different syntactic categories, then multiple lexical entries must exist for them, a situation usually referred to as AMBIGUITY. On the other hand, it is usually assumed that if a word can be used with more than one sense at once, then a single lexical entry must cover those senses of the word, a situation known as VAGUENESS or GENERALITY. However, there are a number of cases in English where a word with different meanings and different syntactic categories can be used with more than one meaning simultaneously, and would thus be ambiguous by the first assumption, and vague by the second assumption. These cases defy conventional wisdom about the lexicon, and in this dissertation the term category neutrality is introduced to refer to them. Though the concept of neutrality has received much attention in recent literature on the coordination of unlikes, discussion has focused almost exclusively on neutrality at the morphosyntactic level, not at the level of syntactic category. Where category neutrality is discussed, it is usually only to claim that it does not exist—a claim that we will see is no longer tenable. In this dissertation, category neutrality will be defined in the framework of type-logical grammar, and investigated in a number of English linguistic phenomena. Chapters 1 and 2 provide the necessary background for an

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Page 4 investigation of category neutrality. Chapter 1 provides the empirical background, situating the concept of category neutrality among the related concepts of ambiguity, vagueness, and polysemy. The second part of this chapter reviews the literature on neutrality (and the closely related topic of the coordination of unlikes), and assesses the reasons linguists have given for denying the existence of category neutrality. Chapter 2 provides the theoretical background. The rigorous framework of type-logical grammar (TLG) will be used in developing the analyses in the later chapters, and in Chapter 2, the basic ontology and rules of TLG will be presented. Special attention will be paid to two kinds of theoretical devices that have been used to encode category neutrality in TLG, and a theorem will be proven showing that no loss in linguistic coverage results if one uses only one of these devices. Also in Chapter 2 is a section devoted to establishing assumptions about the lexicon in a TLG. In this section, the theoretical difficulty (perhaps impossibility) of distinguishing ambiguity from neutrality in a TLG will be discussed. In addition, a discussion of lexical rules is presented, filling what has been a gap in recent type-logical literature. In Chapters 3 through 6, empirically informed analyses are developed for various English linguistic phenomena that manifest category neutrality. These chapters have used naturally occurring data where possible, including corpus data, and where data and theory do not provide a means of choosing between different analyses, psycholinguistic experimentation has been employed. Specifically: Chapter 3 investigates MIXED- WH INTERROGATIVES, illustrated in sentences such as What and when can I eat?, in which a verb or other word must be parsed as having more than one category. For example, in the sample sentence, eat must be both transitive and intransitive in order to be construed with both the what and the when. Other mixed- wh interrogatives require that a word be parsed as both a common noun and a noun phrase, as happens with work in We’ll decide when and whose work is displayed . Although there have been analyses of coordinated-wh interrogatives in the literature, none to my knowledge addresses in detail the mixed- wh variety to be analyzed here. This chapter will make use of corpus data and psycholinguistic experimentation, in addition to presenting a type-logical analysis of mixed- wh interrogatives. Chapter 4 surveys a number of verbal argument alternations, testing them for category neutrality by constructing coordinations whose conjuncts require the verb to be parsed with more than one subcategorization. For example, in *John ate quickly and a sandwich, the adverb quickly requires that ate be intransitive, while the NP a sandwich requires that it be transitive. Though this sentence and others like it have been recognized for years as ungrammatical, they have been discussed only sporadically and piecemeal. Proposed

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Page 5 explanations for their ungrammaticality have often posited ambiguity for the verb, or declared that the coordinated conjuncts are just too different semantically (in a vaguely defined way) to be coordinated. Here, though, more than a dozen alternations are considered with respect to coordination possibilities, each in more detail than has to my knowledge been done previously. Furthermore, coordinations involving these alternations will be considered as part of a larger picture of all coordinations involving verbal complements and adjuncts. It will be argued that it is semantics and pragmatics that are the primary determiners of such a coordination’s acceptability, whether or not the verb is used with more than one meaning at a time. Chapter 5 turns to phrases that can be used predicatively. A common claim is that all predicative phrases, APs, PPs, and NPs alike, have the same semantic type or category. In this way, one avoids having to admit category neutrality for the copula be when faced with coordinations such as Pat is a Republican and proud of it . However, it will be shown that if one avoids category neutrality for be, one is forced to admit it for APs, PPs, and NPs. Chapter 6 concerns a particular set of English nouns that have the ability to form adverb phrases without needing a preposition (the adverbial nouns). A type-logical analysis of these words is developed, and it will be seen that these words can sometimes exhibit category neutrality, being used as both ordinary and adverbial nouns at the same time. In Chapter 7, the results of the preceding chapters will be assessed, and conclusions drawn. In particular, the question of whether there is a true distinction between ambiguity and category neutrality is discussed, and suggestions for further research are given.

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Page 7 CHAPTER 1 Empirical Background What is category neutrality? In this chapter, category neutrality will be distinguished from ambiguity, vagueness, and polysemy, three other concepts that involve the existence of multiple meanings for a single phonological form. Section 1.1 introduces and discusses ambiguity, vagueness, and polysemy. Section 1.2 surveys the literature on neutrality, then defines category neutrality and distinguishes it from the other three concepts. 1.1 Ambiguity, Vagueness, and Polysemy There are many terms for describing situations in which a single phonological form of a word has more than one sense, but three general situations can be distinguished. In one situation, usually referred to as AMBIGUITY, a word’s different senses are so different that it is hard to imagine their existing in a single lexical entry. Indeed, at the word level, ambiguity is often defined as the existence of separate lexical entries for some word. At the other extreme is VAGUENESS, the situation in which a word’s different senses are so close to one another that it is hard to imagine their existing in separate lexical entries. These two situations, discussed in section 1.1.1, would seem to exclude any third situation: Either there is more than one lexical entry, or there is just one. However, when one lays aside the issue of how many lexical entries a word occupies, it is sometimes useful to have a term for a middle ground between ambiguity and vagueness, in which there are two (or more) distinct senses of a word, too distinct to be called vagueness, but too similar to be easily labeled as ambiguity. This is the realm of POLYSEMY, discussed in section 1.1.2.

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Page 8 1.1.1 Ambiguity vs. Vagueness: The Poles Consider first the case in which two senses of a word are apparently completely unrelated to each other. One of the most widely cited examples is bank, with its “financial institution” and “edge of a body of water” senses. Though it happens for this example that both uses of bank can be traced to a single source word, the relationship is synchronically opaque; most current English speakers are unaware of any relationship. Such a situation is referred to as AMBIGUITY, more specifically as LEXICAL AMBIGUITY, and also as HOMONYMY or HOMOPHONY. The latter two names are relational terms—that is, homonymy or homophony can exist only when there are two or more entities to be related as homonyms/homophones. Thus, these terms emphasize the usual assumption (for example, in Kempson 1977:81ff) that unrelated meanings correspond to separate lexical entries. In contrast to ambiguity, there is what Zwicky and Sadock (1975:2) describe as “a single representation corresponding to different states of affairs.” They give a list of names for this situation, including VAGUENESS, INDETERMINACY, and their own suggestion, NEUTRALITY. A commonly used lexical example of vagueness is the word teacher, which can refer to either a male or a female teacher. Presumably, this word occupies a single lexical entry, and its semantics simply does not make reference to gender. Examples such as bank and teacher above are widely used in discussions of ambiguity and vagueness because they are very clear-cut. However, distinguishing ambiguity from vagueness is not at all easy in many cases. A number of diagnostics have been used to help make the distinction, many of them summarized in Zwicky and Sadock (1975). Some of these diagnostics for ambiguity are applicable only at the phrasal level, and cannot be applied to individual words. Those that can be applied at the lexical level will be discussed in sections 1.1.1.1 and 1.1.1.2. 1.1.1.1 Coordination Tests The first kind of diagnostic for ambiguity is what I will call a COORDINATION TEST. To define this term, some terms are needed for the anatomy of a coordinate structure. Given a coordinate structure C, the CONJUNCTS are the coordinated elements in it, and the FACTOR, a term introduced by Pullum and Zwicky (1986:754) is the “material bearing syntactic and semantic relations to C, and thus to all the conjuncts in C,” analogous to the factor x in mathematical expressions such as x(y+z). Some examples are given below, with the conjuncts in square brackets and the factors underlined.

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Page 9 (1) a. Kim likes [toast] and [jam]. b. Kim [likes toast] but [hates jam]. c. [Kim likes toast] and [Robin likes jam]. d. I don’t know whether Kim [likes] or [dislikes] toast. A coordination test, then, is a phrase in which a putatively ambiguous word w, with senses σ1 and σ2, is in the factor of a coordination, whose conjuncts are chosen so as to see whether this single token of w can be interpreted with both senses. If w is ambiguous, the reasoning goes, then it occupies two lexical entries, only one of which is the appropriate choice in the coordination at hand. Therefore, if w is ambiguous, it will not be able to have both senses in the coordination. On the other hand, if w CAN have both senses in the coordination, then it must be vague with respect to σ1 and σ2. There are two kinds of coordination tests: the CROSSED-UNDERSTANDINGS TEST, and the ZEUGMA TEST, discussed below. As described in Zwicky and Sadock (1975:17–20), in a crossed-understandings test, it is possible for each conjunct to be construed individually with the ambiguous word w in the factor, with sense σ1 or σ2. Schematically, a crossed-understandings test can be represented as in Figure 1:

Figure 1 Crossed-understandings test As shown in the figure, w can be used with either sense with either conjunct. Therefore, four readings are logically possible: two in which w is used with only one sense (either σ1 or σ2), and two in which sense σ1 is appropriate for one conjunct, and sense σ2 for the other. The latter two readings are the crossed-understandings readings. If all four readings exist in reality, then it can be concluded that w is vague with respect to senses σ1 and σ2. But if w is ambiguous, then only one sense will be usable at a time, ruling out the crossed understandings. For example, a crossed-understandings testing for teacher to see if it is ambiguous between the “male teacher” and “female teacher” senses is given in

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Page 10 (2). Here, the conjuncts are Kim and Robin, and the rest of the sentence is the factor: (2) Kim and Robin each spoke to a teacher. This sentence could be truthfully said if Kim spoke to a male teacher, and Robin to a female teacher. Thus, the evidence indicates that teacher is vague with respect to these two readings; in other words, that there is a single lexical entry for teacher, which fails to specify gender. On the other hand, bank fails the crossed-senses test in (3): (3) Kim and Robin each went to a bank. The reading in which Kim went to a financial institution and Robin went to the edge of a river is possible only in a joking context. One possible conclusion is that bank is ambiguous between these two senses. As described in Lascarides et al. (1999:3), a zeugma test is a coordination test in which one conjunct is much more plausible with sense σ1, and the other much more plausible with sense σ2. Schematically, a zeugma test has the structure of Figure 2:

Figure 2 Zeugma test Consequently, instead of the four possible readings in a crossed-understandings test, in a zeugma test there is effectively only one: a crossed-understandings reading. If this reading is grammatical, then w must be vague with respect to senses σ1 and σ2. The example of a zeugma test for teacher given in Lascarides et al. is shown in (4): (4) Teachers may take maternity or paternity leave. (Lascarides et al. 1999, (11a))

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Page 11 Here again, one can conclude that teacher is vague with respect to gender, since the sentence is grammatical even though the conjunct maternity strongly favors the sense of “female teacher,” and paternity strongly favors the sense of “male teacher.” On the other hand, (5) is acceptable only in a humorous context; that is, it is an instance of zeugma. (5) ?Bank robbers and dam busters blow up banks. (Lascarides et al. 1999, (12)) Real-world knowledge induces the “financial institution” sense of bank with respect to the conjunct bank robbers, and the “edge of a body of water” sense with respect to the conjunct dam busters, but this reading is nonetheless zeugmatic. A possible conclusion is that bank is ambiguous. Lascarides et al. limit their zeugma tests to those in which it is pragmatics that decrees which sense of the word in the factor goes with which conjunct. However, if the different senses correspond to different syntactic categories, then syntax can make the determination. For example, break can be used as an intransitive verb meaning “to undergo a change of state, from existence in one piece to existence in more than one piece,” or as a transitive verb meaning “to cause to undergo” the said change of state. Therefore, in (6) below, it is the syntax that determines that the adverbial conjunct into three pieces is to be used with break in its intransitive sense, and that the NP conjunct the scissors is to be used with break in its transitive sense. The coordination results in zeugma of the highest order. (6) *The rock broke the scissors and into three pieces. (i.e., rock broke scissors, and rock itself broke into three pieces) The problem with both kinds of coordination tests is that the absence of crossed understandings alone does not justify the conclusion that a word is ambiguous. That is, although ambiguity implies the absence of crossed understandings, the converse is not true. There could be other reasons for the impossibility of a crossed-understandings reading, in particular, pragmatics, as argued by Lascarides et al. (1999). They point out that sometimes a sentence still sounds strange even when the putatively ambiguous word appears twice, a fact that the existence of separate lexical entries cannot explain. For example, even in (7), the reading involving the two senses for bank is still dispreferred. (7) Kim went to a bank and Robin went to a bank.

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Page 12 For these cases, they formalize a means of pragmatic reasoning that predicts the infelicity of the crossed understandings. 1.1.1.2 “Appeals to Semantic Differentiae” Another test for ambiguity discussed in Zwicky and Sadock (1975) is a very intuitive one: Is the difference between the senses of some word small enough that it could plausibly be a case of lack of specification? If not, then the word is more likely ambiguous. Using this reasoning, most people would probably agree that bank is ambiguous, while teacher is vague. Break, however, is still a problem. On the one hand, the intransitive and transitive meanings are clearly related semantically, but are very different in terms of what role their subjects play. Zwicky and Sadock discuss another line of reasoning for cases like these: Is the difference one that is formally marked in any language? If so, then the word may be part of a systematic ambiguity, since there are other languages in which it occupies separate, phonologically distinct, lexical entries. This is the case for break, since causative verbs are often morphologically marked in various languages. However, whether this means that break is ambiguous in English is open to debate. Zwicky and Sadock maintain that the only safe conclusion is that ambiguity is plausible, but not a certainty: …from the facts that a particular semantic differentia is simple and that it is formally marked in some language we can conclude nothing about the status of this distinction for any particular example in any language; both lack of specification and systematic ambiguity are consistent with these facts (5). On the other hand, depending on one’s view of linguistic universals, the existence of distinct lexical entries for a meaning difference in one language might be given much more weight than Zwicky and Sadock give in determining whether a word is vague or ambiguous in another language. Even with these caveats, though, the problem with appeals to semantic differentiae is that it is a subjective judgment whether some semantic difference is simple. It can probably be safely used for very obvious cases such as teacher or bank, but where such a test is really needed (i.e., in the difficult and less clear-cut cases), its usefulness is limited.

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Page 13 1.1.2 Polysemy: The Middle Ground These difficult and less clear-cut cases are often referred to as POLYSEMY. A precise definition of polysemy does not seem to exist yet, judging from a survey of the topic by Ravin and Leacock (2000b), but it generally involves different senses of a word that are too close to be called ambiguity, but too different to be called vagueness. Whether a polysemous word occupies multiple lexical entries or a single one is also not agreed upon. One factor that some take into consideration is whether the different senses are predictably related or not. For example, consider again the verb break, which can be transitive (I broke the glass, in its causative sense) or intransitive (The glass broke, in its inchoative sense). This alternation is very productive in English, so some would argue that causative-inchoative verbs should be represented in single lexical entries. Fellbaum (2000:55) encapsulates this idea in a principle: “Verbs linked by semantic relations that yield predictable readings do not require distinct lexicalizations.” Even with this principle, though, there is room for disagreement over whether a polysemous word such as break occupies one or two lexical entries. There could be a single, underspecified representation, with some rule indicating the different ways in which a token could instantiate it; or there could be two lexical entries, with one derived from the other by a lexical rule. Furthermore, if there is a transparent enough semantic relationship between the two senses of a word, a case could be made for a single lexical entry even if the relationship is not predictable or regular. For example, consider the alternation seen in behave: It usually takes a manner-adverbial complement (behave poorly), but when such a complement is omitted, the understood sense is “behave well” (McConnell-Ginet 1982). This semantic relationship is unique, but the meanings seem so similar that one might hesitate to put them into separate lexical entries; this is the position taken for this and other verbs by Fellbaum (2000). The above examples involved a difference in semantic category, but perhaps the best known examples of polysemy involve different senses for nouns, with no change in category. For example, there is the “physical object” vs. “information” sense of book, even though book has the same category (N) regardless of sense. These cases have received much attention in the Generative Lexicon work of Pustejovsky and others (for example, Pustejovsky 1995). If there were a clear, accepted definition for polysemy, it might be a good term to use to refer to the kinds of cases to be considered in this dissertation. However, given the competing conceptions of polysemy, a new term needs to be defined in order to clearly establish the boundaries of the cases to be considered in this dissertation. This term is CATEGORY NEUTRALITY, the focus of the rest of this chapter.

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Page 14 1.2 Category Neutrality CATEGORY NEUTRALITY is an extension of the concept of neutrality that has evolved in the literature on coordination of unlikes—more specifically, coordination of constituents that are unlike with respect to values for morphosyntactic features such as case, number, or gender. Thus, a discussion of category neutrality needs to begin with a discussion of neutrality at the level of morphosyntactic features. This aspect is covered in section 1.2.1. Section 1.2.2 shows how the concept of neutrality has changed in recent years. Sections 1.2.3 and 1.2.4 discuss category neutrality specifically. 1.2.1 Precursor: Feature Neutrality The use of the term NEUTRALITY (or NEUTRALIZATION) in discussing phonologically identical forms with more than one value for certain morphosyntactic features (or sets of features) seems to have begun with Zaenen and Karttunen (1984), and been reinforced Pullum and Zwicky (1986), who contrasted it with AMBIGUITY. This is a potential source of confusion, since a decade earlier, Zwicky and Sadock (1975) used the same terms to discuss not morphosyntactic features, but semantics, as recounted above. For clarity, I will maintain the term AMBIGUITY to refer to a single phonological form occupying separate lexical entries, each with different semantics; I will use the term VAGUENESS to refer to a single phonological form occupying a single lexical entry that is unspecifled for some semantic difference. At the level of morphosyntactic features, I will use the term FEATURE AMBIGUITY to refer a single phonological form with different values for some feature (or bundle of features) occupying separate lexical entries, and FEATURE NEUTRALITY to refer to a single phonological form occupying a single lexical entry that is underspecified with respect to some feature or bundle of features. Three varieties of feature neutrality can be distinguished. One kind is ARGUMENT NEUTRALITY. This kind of neutrality is seen when two verbs that take different kinds of arguments (for example, an accusative vs. a dative object) are coordinated, and an argument is provided that manages to fulfill the requirements of both verbs at once. VERB NEUTRALITY, by contrast, is seen when a single verb that can take more than one kind of argument (for example, either an NP or a that -clause) is given an argument consisting of a coordination of both. Lastly, there is NEUTRALITY WITHOUT COORDINATION, which is seen any time some constituent is able to meet conflicting requirements imposed on it from different parts of a larger phrase. Pullum and Zwicky (1986) examined only the first two kinds; Ingria (1990) was the first to cover instances of all three .

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Page 15 kinds under one analysis; and it was Bayer (1996) who crystallized Ingria’s insight into the three-way classification given above (and also coined the phrase NEUTRALIZATION UNDER PHONOLOGICAL IDENTITY to refer to feature neutrality in general). 1.2.1.1 Argument Neutrality An example of argument neutrality is shown in the often-cited German example in (8) from Pullum and Zwicky (1986). Here, findet ‘finds’ governs the accusative case, while hilft ‘helps’ governs the dative. In (8a, b), the argument is either accusative or dative, but not both, and these sentences are ungrammatical. However, it just so happens that Frauen ‘women’ is identical for both these cases in the plural, and so (8c) is grammatical. Frauen, then, is said to be neutral1 between accusative and dative (and nominative and genitive for that matter). (8) (Pullum and Zwicky 1986, (37), (40)) a. *Sie findet und hilft Männer. She finds and helps men.ACC b. *Sie findet und hilft Männern. She finds and helps men.DAT c. Er findet und hilft Frauen. He finds and helps women.ACC/DAT Other examples involving German, English, and Xhosa can be found in Pullum and Zwicky (1986); they and Ingria (1990) also bring up French examples from Kayne (1975). Bayer (1996) cites Dyla (1984) and Franks (1993) for Polish and Russian examples. Some Icelandic and Finnish examples can be found in Zaenen and Karttunen (1984). One Finnish example, shown in (9), is particularly interesting in that more than one morphosyntactic feature is involved in the neutrality. Here, the object of the verb lukivat ‘read’ alternates in 1. Pullum and Zwicky actually draw a distinction between two kinds of examples. They reserve the term NEUTRAL for cases in which the phonologically identical form is part of a regular pattern in the language; for example, most verbs in German are identical in their first and third person present plural forms (as seen in the next example), so the relevant form of the verb could be said to be neutral between first and third person. For cases like Frauen, in which the identical form is accidental, they speak of PHONOLOGICAL RESOLUTION OF AMBIGUITY. Others who have written on this topic tend to ignore this distinction, considering all the cases of nonambiguity to be instances of neutrality, which is the stance that will be taken here.

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Page 16 case, and must be genitive in order to be grammatical with the subject he ‘they’, and nominative for the subject me ‘we’. Furthermore, the adjective uusiman ‘newest’ is singular, while the adjective parhaat ‘best’ is plural. To satisfy all these requirements, the N factor will have to be both a genitive singular form, to go with he and uusiman, and a nominative plural form, to go with me and parhaat. As it happens, kirjansa ‘book(s)’ is both. (9) He lukivat hänen uusiman ja me hänen parhaat They read his newest and we his best Kirjansa. book.GEN-SG/NOM-PL ‘They read his newest book and we read his best books.’ (Zaenen and Karttunen 1984, (18)) Cases like (8) and (9), in which a single form can have more than one value (or set of values) for a feature (or cluster of features), are referred to as SYNCRETISM by Levy and Pollard (2002), and Levine et al. (2001). They are also referred to as FEATURE INDETERMINACY by Levy and Pollard, and Daniels (2002), though Daniels makes an additional distinction, reserving this term for cases involving one feature, and using INDETERMINACY ACROSS FEATURES for cases involving more than one feature. 1.2.1.2 Verb Neutrality An example of Russian verb neutrality from Levy and Pollard (2002) is shown in (10). Here, ožidal ‘expected’ is neutral between governing an accusative object and a genitive object, so that the coordination of the accusative and genitive NPs is allowed. (10)Včera vec’den’ on ožidal svoju podrugu yesterday all day he expected self’s. ACC g’friend.ACC Irinu i zvonka ot svoego brata Grigorija. Irina ACC and call.GEN from self’s brother Gregory. ‘Yesterday he waited all day for his girlfriend Irina and for a call from his brother Gregory.’ (Levy and Pollard 2002, (3b))

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Page 17 Pullum and Zwicky (1986:757) also present a case of verb neutrality from German, taken from Eisenberg (1973). Verb neutrality is also referred to as FUNCTOR NEUTRALIZATION by Levy and Pollard (2002). This term nicely contrasts with the term “argument neutrality,” since a functor is something that takes an argument. This term is also more general than “verb neutrality,” since it does not assume that verbs will be the only kind of neutral functors. Levy and Pollard also refer to verb neutrality as NEUTRALIZABLE POLYVALENCY. Yet another term, used by Daniels (2002), Levy and Pollard, and probably others as well is COORDINATION OF UNLIKES. (More misleading still is Levy and Pollard’s occasional shortening of this term to just COORDINATION.) Although the use of the term “coordination of unlikes” to refer to verb neutrality is not incorrect, it can be misleading, since these authors use it exclusively to refer to verb neutrality, even though argument neutrality also involves coordination of unlikes (specifically, unlike verbs). The misleading usage of the term may be a holdover from Sag et al. (1985), to my knowledge the earliest widely read discussion of coordination of unlike categories, which dealt only with verb neutrality. A more accurate usage of this term would be to specify whether one means a coordination of unlike arguments (in other words, verb neutrality) or unlike verbs (in other words, argument neutrality). Bayer (1996) uses the term “coordination of unlikes” to refer to both verb and argument neutrality, but acknowledges its common restriction to the former kind. 1.2.1.3 Neutrality Without Coordination Bayer (1996) coins the term NEUTRALITY WITHOUT COORDINATION to refer to two examples discussed in Ingria (1990). Ingria’s first example involves German free relative clauses, based on data from Groos and van Riemsdijk (1981). There is a requirement in German that the free relative pronoun agree in case both with the gap in the clause that it introduces, and with the position in the matrix sentence that the free relative clause fills. This issue is familiar to any English speaker who has ever wondered whether they should say, “I’m going to kill WHOEVER did this!” or “I’m going to kill WHOMEVER did this!” After all, one reasons, as the object of kill, the pronoun should be whomever, but as the subject of did this, it should be whoever . The prescriptive rule for Standard English has the lower clause taking priority, so that the choice should be whoever, but there are plenty of people who give priority to the matrix sentence, and choose whomever. In German, the pronoun has to agree in both places, and a sentence like the above must simply be avoided. Therefore, the German examples in (11a, b) are ungrammatical, since nehme ‘take’ takes an accusative

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Page 18 object, vertraust ‘trust’ takes a dative, and the pronouns wen and wem ‘who’ cannot be both at once. In (11c), however, where gegessen ‘eat’ takes an accusative and war ‘be’ takes a nominative, the coordination works because the pronoun was ‘what’ is neutral between accusative and nominative case. (11) (Ingria 1990, (5b), (7)) a. *Ich nehme, wen du vertraust. I take who.ACC you trust ‘I take who(ever) you trust.’ b. *Ich nehme, wem du vertraust. I take who.DAT you trust ‘I take who(ever) you trust’ c. Ich habe gegessen was noch übrig war. I have eaten what.ACC/NOM still left was. ‘I ate what was left.’ Ingria’s second example comes from Hungarian, as first described in Szamosi (1976). Both it and the German example might less formally (but more intuitively) be called UPSTAIRS-DOWNSTAIRS NEUTRALITY, since (picturing trees in the phrase-structural tradition) the neutral form has requirements imposed on it from something that dominates it, and from something that it dominates. However, the upstairs-downstairs analogy is not appropriate for all cases of neutrality without coordination. Parasitic gaps can give rise to neutrality without coordination, too. Bayer (1996:589) credits J.Bayer (1988) with such cases in German. Levine et al. (2001) give an example in English, shown in (12). (12) Robin is someone who even good friends of___believe___should be closely watched. (Levine et al. 2001, (46)) Here, the gap after friends of must be accusative, while the gap before should be closely watched must be nominative. The pronoun who, neutral between accusative and nominative case (in most dialects) is able to fill both gaps simultaneously. In this case, both requirements on the neutral form are imposed from downstairs, by (different parts of) a constituent that the neutral form dominates. 1.2.2 The Evolving Definition of Neutrality As of Pullum and Zwicky (1986), neutrality was a transparent concept: A neutral word is unspecified with respect to some feature value (or values), and

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Page 19 therefore can be used even when conflicting requirements are placed on it. However, when Johnson and Bayer (1995) and Bayer (1996) proposed a particular analysis of feature neutrality, the term lost some of its transparency. In their analysis, instead of being specified as having NEITHER of two (or more) possible values for some feature, a neutral word is specified as having BOTH, a situation sometimes referred to as OVERSPECIFICATION. A different analysis of feature neutrality that does not involve overspecification is proposed in Heylen (1997, 1999); nevertheless, the term “neutrality” is associated often enough with the Bayer/Johnson style analysis that it seems to be firmly in place, regardless of whether the analysis proposed is intuitively “neutral” or not. 1.2.3 From Feature Neutrality to Category Neutrality In light of the existing literature on feature neutrality, CATEGORY NEUTRALITY is a natural extension: It is simply any case in which some phonological form has more than one syntactic category. It is distinct from lexical ambiguity, in that a neutral word occupies a single lexical entry, instead of multiple lexical entries. 1.2.3.1 Category Neutrality vs. Vagueness It is less clear that category neutrality is distinct from vagueness. Certainly, it is distinct from most conceptions of vagueness, since the latter term seems to be used only in cases where the word in question has only one syntactic category for the senses under discussion. For instance, teacher has category N for both its “male” and “female” senses. In response to this observation, one suggestion might be just to revise the definition of vagueness so that it can cover category differences. However, since almost all of the discussion in this dissertation will be dealing exclusively with cases involving different categories, it will be convenient to have a separate term that does not have the common understanding of like categories that the concept of vagueness has. Second, there is an intuitive difference between the range of different meanings available in a case of vagueness and a case of category neutrality. For example, while teacher is vague with respect to gender, it is also vague with respect to many other things: age, subject area, teaching style, etc. By contrast, if a categorial difference is involved, the vagueness (if one were to call it that) will range only over some fairly small number of categories. For example, consider the transitive and intransitive readings for eat. The only categories involved are

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Page 20 VP/NP and VP,2 but within the entry for each category, there is the same kind of vagueness seen in teacher: For example, intransitive eat is vague as to whether the understood meal is breakfast, lunch, dinner, or perhaps just a snack. 1.2.3.2 Category Neutrality vs. Polysemy As mentioned earlier, the pre-existing term that comes closest to category neutrality is POLYSEMY. For both polysemy and category neutrality, the different meanings of the given word will clearly be related in some way, as with eat or break . Furthermore, the cases that will be investigated in this dissertation involve (at least somewhat) regular and predictable relations between the meanings, a commonly accepted property of polysemy, as discussed above. However, CATEGORY NEUTRALITY will be maintained as a distinct term for several reasons. First of all, the term suggests a natural class: instances in which a single phonological form has two or more possibly distinct syntactic categories. Though some cases of polysemy fit this description, not all do, and the most commonly discussed cases definitely do not. Second, polysemy is usually understood to refer to RELATED meanings for a word, but I wish to leave open the possibility of unrelated meanings. Third, the different senses for a word exhibiting category neutrality may crosscut the different senses that come to mind when polysemy is invoked. A good example is adjectives. It will be argued in Chapter 5 that adjectives may be neutral with respect to their predicative and attributive categories (i.e., This book is good vs. a good book). In contrast, linguists concerned with polysemy would focus on the difference between This book is good or a good book on the one hand, and This lawyer is good or a good lawyer on the other. Fourth, polysemy is an exclusively lexical phenomenon, whereas category neutrality can arise in the syntax. Though most of this dissertation will be examining lexical category neutrality, there will be a few cases in which a phrase can have more than one category simultaneously, even though no word within it does. Finally, the term CATEGORY NEUTRALITY clearly links this concept with previously existing literature on neutrality at the feature level. 2. The notation VP/NP for transitive verbs, and VP for intransitives, anticipates the formal presentation of categories to be given in Chapter 2.

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Page 21 1.2.4 Category Neutrality in the Literature Examples of category neutrality are rare in the literature. As far as I know, only two kinds of examples have been discussed, both instances of verb neutrality, and both introduced by Sag et al. (1985). The first case involves coordinated NP and AP complements to a copula, as in (13), where the neutral verb is underlined: (13) Pat is a Republican and proud of it. (Sag et al. 1985, (2b)) Pullum and Zwicky (1986) mention this example early in their paper, but never return to it once they move on to feature neutrality. The other cases brought up in Sag et al. have coordinated NP and that clause arguments to verbs like remember or frighten: (14) (from Sag et al. (1985), (123)) a. Pat remembered the appointment and that it was important to be on time. b.That Himmler appointed Heydrich and the implications thereof frightened many observers. In searching the literature for category neutrality, what one finds instead of further examples is a refusal to believe that category neutrality can exist when the categories come with different semantics. (Notable exceptions are Morrill 1994 and Hendriks 1995, who analyze the examples from Sag et al. by way of category neutrality.) However, this opinion is never sufficiently justified. Consider the argument presented in Heylen (1996:76), which takes the word square as an example, and rejects allowing its noun and adjective senses to be included in a single lexical entry, because doing so “fails to express that there are actually two expressions square which happen to be homophonous.” Heylen (1996) does not attempt to justify this assertion about the homophony of square, but Heylen (1999:194) elaborates: “… there are no occurrences of square which are both adjective and noun at the same time.” In other words, square cannot have a crossed-understandings reading in a coordination test. But as noted in section 1.1.1.1, such evidence does not prove ambiguity, since other influences could be responsible for the test results. More generally, absence of evidence for some proposition p is not a sound basis for concluding ¬p . Moreover, making judgments of ambiguity and neutrality based solely on coordination test data says nothing informative about ambiguity or neutrality; it just turns these terms into diacritics indicating whether a word can have crossed understandings in a coordination test.

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Page 22 Bayer (1996:606–7) makes essentially the same argument as Heylen, except that he uses a much more obviously ambiguous word: can, with its meanings as a modal auxiliary and as a transitive verb. If category neutrality is allowed in the type-logical framework, then it will be possible to use can both ways at once, as in the following from Pullum and Zwicky (1986): (15) *I can tuna for a living and get a new job tomorrow if I want. (Pullum and Zwicky 1986, (42c)) Bayer equates his position with that of Zaenen and Karttunen (1984:316), who propose an ANTI-PUN ORDINANCE (APO) to the effect that “A phrase cannot be used in two different senses at the same time.” In fact, Bayer seems to misunderstand Zaenen and Karttunen. Their APO does not forbid a lexical entry to specify more than one sense; it just forbids them to be used simultaneously. As Zaenen and Karttunen say in introducing the APO (p. 316, emphasis mine), “It seems to us that the unacceptability of [relevant examples] is essentially SEMANTIC, not SYNTACTIC.” This is a stance that seems quite reasonable, and which will be explored further later in this dissertation, especially in Chapter 4. Nevertheless, Bayer does highlight a troubling point about formalizing category neutrality in a typelogical grammar: It does not matter whether there exists a reasonable set of guidelines for determining whether a word is ambiguous or neutral. Even if it can be determined with 100% accuracy whether any given word is ambiguous or neutral, the two are formally indistinguishable in a type-logical grammar under current definitions. This point will be expanded in Chapter 2, section 2.5.1. In addition to the above theoretical problems, taking Heylen’s and Bayer’s stance presents an empirical problem: How are the data from Sag et al. to be analyzed if category neutrality is not allowed? For cases like (13) Pat is a Republican and proud of it, the usual way out has been to say that both adjectives and NPs can be predicative, which is what the copula selects for. This approach predates type-logical analyses of these sentences: In their Generalized Phrase Structure Grammar account, Sag et al. (1985) do this by proposing the feature PRED for adjective and NP feature structures, a solution that is still in place in Head-driven Phrase Structure Grammar (Pollard and Sag 1994). Partee (1987) reinforces this idea, proposing that there are (possibly universal) typeshifting rules for NPs that allow them to be used quantificationally, referentially and (the relevant case here) predicatively. More recent type-logical accounts (Bayer 1996, Carpenter 1997) take a similar approach. Thus, sentences like (13) are explained away as not cases of verb neutrality at all, but ordinary instances of coordination of like categories.

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Page 23 Sentences such as (14a), He remembered the appointment and that it was important to be on time, are more difficult to account for. The analysis presented by Sag et al. allows complementized sentences to have category NP. However, as Bayer (1996:608–10) shows, this analysis seriously overgenerates. Bayer’s proposal hints at a solution similar to the one he proposes for predicative NPs, but making use of event-based semantics in order to avoid having category neutrality. Nevertheless, the rejection of category neutrality is tenable only as long as other cases of apparent category neutrality, not so easily explained away, do not arise. Such cases do arise in English, and are the focus of this dissertation.

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Page 25 CHAPTER 2 Theoretical Background This chapter presents the theoretical background for type-logical grammars (also known as Lambek categorial grammars), with special focus on the logic of the conjunctive and disjunctive category constructors, and on the organization of the lexicon. Section 2.1 distinguishes type-logical grammars from categorial grammars in general. Section 2.2 defines the logic of categories for the Associative Lambek Calculus, which will form the basis for the type-logical grammar to be used in this dissertation. Section 2.3 specifies the relation between categories, types, and terms, and shows how to augment the rules in section 2.2 with semantic information, so that semantic and syntactic derivations can proceed in parallel. The information in these three sections can be found in many introductions to type-logical grammar; the presentation here borrows heavily from chapters 2, 5, and 6 of Carpenter (1997), as well as from Moortgat (1997). Readers familiar with type-logical grammar may wish to skip to section 2.4. Section 2.4 introduces the conjunctive and disjunctive category constructors and which allow a single token of an expression to have more than one category. Section 2.5 discusses issues involving the interaction of conjunctive types with the lexicon. Section 2.6 covers some additional necessities: the semantics for the coordinating conjunction and, since it and other conjunctions will be used in so many examples of neutrality later on; and the scoping constructor which will be used in Chapters 5 and 6. 2.1 Different Kinds of Categorial Grammars Before going further, the term TYPE-LOGICAL GRAMMAR (TLG) needs to be defined, which has been used thus far instead of the perhaps more familiar CATEGORIAL GRAMMAR (CG). In fact, those who use the term TLG use it to refer

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Page 26 to a subset of CGs, so a definition of CG will be given first. CG refers to grammars in which (i) syntax is encoded in the lexicon by means of the syntactic categories assigned to individual lexical entries; and (ii) syntactic and semantic derivation proceed in parallel, because of a systematic linkage between syntactic categories and semantic types. There is a theoretically infinite number of categories in any CG, generated by taking the transitive closure of a small set of basic categories (often S, NP, and N) over a small set of category constructors (usually/and\). For example, since S and NP are categories, so are S/NP, NP\S, and (NP\S)/NP. A set of general rules governs the behavior of the category constructors. The most familiar of these rules (sometimes referred to as rules of FUNCTIONAL APPLICATION, or FA) state how a constructor can be eliminated: (16) Functional Application (FA) Rule (16a) states that if an expression of category B occurs immediately to the right of an expression of category A/B, then the concatenation of the two expressions will have category A. Rule (16b) states that if an expression of category B occurs immediately to the left of an expression of category B\A, then the concatenation of the two expressions will have category A. For example, if the NP Kim occurs immediately to the left of the NP\S sings, then the concatenation Kim sings will have category S. Over the years, two main varieties of CG have developed. One is sometimes referred to as the DEDUCTIVE (or LAMBEK-STYLE) approach, and is typified by the work of linguists such as Michael Moortgat, Richard Oehrle, and Glyn Morrill. As used by categorial grammarians, the term TLG refers to this kind of categorial grammar. In this approach, the rules are defined as a logical system. Specifically, FA is taken as an analog of Modus Ponens in first-order logic. The Modus Ponens schema states that if you know that p →q is true, and also that p is true, then you can conclude that q is true. In the FA rules, the A/B or B\A on the top line corresponds to p →q; the B on the top line corresponds to p; and the A on the bottom line corresponding to q . From there, analogs of Conditional Proof are added. In a firstorder logic Conditional Proof, one hypothesizes a p, uses it to prove q, and then withdraws the hypothesized p in order to prove p →q . Similarly, in a type-logical framework, if one hypothesizes a B, and uses it to derive an A, and subsequently withdraws the hypothesized B, then one has derived an A/B (or a B\A). In other words, there are now two pairs of rules specifying the behavior of / and \: a pair of Modus Ponens analogs showing how any category A/B or B\A can be used, and a pair of Conditional Proof analogs

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Page 27 showing how any category A/B or B\A can be proven. Therefore, these rules are sometimes known respectively as RULES OF USE and RULES OF PROOF. The deductive approach is characterized by having both a rule of use and a rule of proof for each category constructor (/, \, and any others in the inventory), and no other rules specifying the behavior of these constructors. The RULE-BASED approach is the other main variety of categorial grammar, often known as COMBINATORY CATEGORIAL GRAMMAR (CCG), and typified by the work of Mark Steedman and others. In this approach, instead of trying to develop the rules as a logical system, one adds rules based on empirical linguistic need. For example, CCGs usually contain a rule of TYPE RAISING (TR), also known as LIFTING, which is useful in coordinating proper names with quantificational noun phrases, as well as in analyzing non-constituent coordination. Another typical rule seen in CCGs is FUNCTION COMPOSITION (FC), often used in analyzing extraction phenomena. These rules are shown in (17a) and (17b). (17) CCG rules of Type Raising (TR) and Functional Composition (FC) a. Type Raising b. Function Composition

Although TR and FC as written here are stated very generally, with A, B, and C standing for any category, rules in a CCG can also be restricted to apply only to certain categories, which is another fundamental difference between CCGs and TLGs. Each approach has its advantages and drawbacks. The type-logical approach of keeping to a minimum of very general rules (in this case, rules of use and rules of proof) is in line with various attempts by syntacticians to avoid the stipulativeness of a grammar that has a multitude of language-specific rules to cover every syntactic construction in a language. Examples of the strategy of having a small number of maximally general rules include the metarules of GPSG, and the limited set of phrase schemata of HPSG. Furthermore, proponents of TLG point out that many of the rules stipulated for CCGs (including TR and FC) can be derived as theorems in a TLG (see for example Moortgat 1988). On the other hand, proponents of CCG (see for example Steedman 1994, 1999) observe that simple Lambek CGs both overgenerate and undergenerate. For example, *Who walks and he talks? (attributed to Lambek 1961 in Steedman 1994) is generated in the Associative Lambek Calculus (defined in section 2.2), while discontinuous dependencies (for example, between the verb

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Page 28 and particle in fix it up ) are not. Moreover, without the option of adding rules as needed, or restricting rules to apply only to certain categories, the type-logical grammarian must resort to other means of covering linguistic phenomena, such as multimodal systems.3 Therefore, they argue, CCGs are less stipulative than TLGs, since the “small number of operations” (Steedman 1994:471) postulated for CCGs is based on linguistic need. Nevertheless, the type-logical approach wiil be used in this dissertation, since it is in this framework that the categories that will be used to describe semantic and category neutrality have been defined and explored. 2.2 Syntax: The Associative Lambek Calculus This section defines and presents rules of inference for syntactic categories in a TLG, specifically in the ASSOCIATIVE LAMBEK CALCULUS. It should be noted that CATEGORY and TYPE are sometimes used as synonyms; here, however, the term “category” will be used to discuss syntax, and “type” to discuss semantics. Thus, labels such as NP and S are categories in this terminology, while Ind, Bool, and Ind→Bool are examples of types (specifically, individuals, Boolean values, and sets of individuals). 2.2.1 Categories The syntactic categories are members of a set which will be notated (following Carpenter 1997) as Cat. BasCat is the subset of Cat consisting of the basic, or atomic categories. BasCat is usually taken to be {S, N, NP}, i.e., sentences, common nouns, and noun phrases, although other basic categories will be introduced later in this dissertation. Complex categories arise when two or more categories are combined by a category constructor; for now, the set of category constructors will be taken to consist of /, \, and •. The set Cat is the transitive closure of BasCat under all category constructors, and can thus be recursively defined as in (18): (18) a. b. If then Categories constructed with / or \ are known as FUNCTOR CATEGORIES, with the category below the slash as the ARGUMENT, and the category above the slash 3. For a definition and discussion of multimodal TLGs, see Moortgat (1997).

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Page 29 as the RESULT. For example, NP/N (the category for a determiner) is a functor taking an N argument, and resulting in an NP. The forward slash / indicates that the N is to be found to the immediate right of the NP/N. Similarly, the backslash in NP\S indicates that this expression looks for an NP argument to the immediate left in order to form an S.4 An example of an NP\S could be sings, which can combine with the NP Kim to its left to form the S Kim sings. (In other words, NP\S is the category for an English VP, and in fact, VP will often be used as an abbreviation for NP\S throughout this dissertation.) Categories constructed with • are known as PRODUCT CATEGORIES. An expression of category A•B is a phrase consisting of an expression of category A and an expression of category B immediately to the right of the A. For example, in addition to the category S, Kim sings also has the category NP•VP. Indeed, any expression—not just Kim sings—belongs to more than one category in a TLG. To see that this is so, one need look no further than the theorem TR: an expression of category A will also have category B/(A\B), C/((B/(A\B))\C), etc. Though it may seem counterintuitive for expressions to have more than one category, it is crucial that they do, a point which will be explained in section 2.2.2. 2.2.2 Interpretation of Categories The preceding discussion of functor and product categories gave an intuitive idea of how categories are intended to work in a TLG. The key to making this system work is a category interpretation function ν (sometimes called the VALUATION FUNCTION), which assigns an INTERPRETATION to each syntactic category, consisting of all the expressions in the language that have that category. Note that this kind of interpretation is not the same as semantic interpretation of an expression: The category interpretation function ν maps categories to sets of linguistic expressions, while semantic interpretation maps linguistic expressions to semantical objects (individuals, sets of individuals, etc.). For instance, the category interpretation of NP is ν(NP), which might be {Kim, the sandwich, one of my friends,…}; on the other hand, the semantic interpretation of Kim is the individual denoted by this expression, represented on paper as kim′. In general terms, for any category A in language L, ν(A) is 4. In the notation to be used here, functor categories will always have the argument category below the / or \; thus, B is the argument category in A/B and B\A. Some linguists, however, prefer to have arguments always appear to the right of the / or \, and the result category on the left. In that system, B is still the argument category in A/B, but in B\A, A is the argument category.

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Page 30 simply the set of expressions in L that are assigned category A. If A is a complex category (that is, if A is a category constructed with one of the constructors), its interpretation is as specified in (19), the FRAME SEMANTICS: (19) Interpretation of complex categories (frame semantics) a. b. c. In this definition, R is a ternary relation over strings. Most commonly R is the append or concatenation relation, so that Rxyz means that x is the concatenation of y and z.5 Thus, (19a) states that the expressions in ν(A/B) are those expressions y which, when concatenated with any expression z in ν(B) on the right, result in an expression x in ν(A). Similarly, (19b) states that the expressions in ν(B\A) are those expressions z which, when concatenated with any expression y in ν(B) on the left, result in an expression x in ν(A). (19c) states that the expressions in ν(A•B) are those expressions x which are the concatenation of an expression y in ν(A) and an expression z in ν(B). To see how these definitions work, suppose that one wants to prove that (i.e. has category S), given that and that By clause (19b), since (i) and (ii) R(Kim sings)(Kim)(sings), and (iii) it can be concluded that (iv) Now suppose that we want to say that any concatenation of an NP and an NP\S results in an S. Suppose that we have an arbitrary string x that is the concatenation of an NP and an NP\S—in other words, that there exist a y and a z such that Rxyz, and and Then by clause (19c) it can be concluded that Furthermore, clause (19b) again guarantees that We have now proven that in the general case, or that S is DERIVABLE from NP•(NP\S)). More generally still, for any categories A and B, B is said to be derivable from A iff For derivability even to be defined, then, it is imperative that expressions can be members of more than one category, just as x was a member of both NP•(NP\S) and S in the example here. 5. The reason that this is stated in terms of the variable R is that it is sometimes desirable to assemble expressions in other modes than concatenation (for example, by a wrapping operation for discontinuous constituents). Abstracting away from the particular way in which the expressions are linearly ordered allows for a more compact definition of complex categories.

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Page 31 However, the subset notation is usually not used in grammatical reasoning. Instead of writing type-logical grammarians will write to be read “B is derivable from A.” For to be an accurate replacement for the relation needs to be defined so that it is sound and complete with respect to the frame semantics. For to be sound, it needs to be true that if then For to be complete, it needs to be true that if then As it happens, the following three axioms guarantee soundness and completeness; for proof, see Moortgat (1997:102). (20) Axioms guaranteeing soundness and completeness of with respect to frame semantics a. REFLEXIVITY: b. TRANSITIVITY: if and then c. RESIDUATION: iff iff Even without going into the proof, one can get a sense of how these axioms re-create the properties of the frame semantics. The first two axioms are familiar just from the properties of the subset relation. Regarding REFLEXIVITY, since the subset relation is reflexive, Therefore, has to satisfy the condition that As for TRANSITIVITY, since the subset relation is transitive, if and then Therefore, has to satisfy the condition that if and then The third axiom, RESIDUATION, covers the clauses in the frame semantics definition in (19). Informally, it requires that if an expression of category C can be derived from the concatenation of two expressions of categories A and B (that is, if then either expression can be categorized as a functor category, with the category of the other expression as its argument, and C as its result. Thus, A can be categorized as C/B, and B can be categorized as A\C. To give an arithmetic analogy, the multiplication (*) and division (/) operators are residuated: b =c/a iff a*b=c iff a=c/b. Though these axioms ensure soundness and completeness of with respect to the frame semantics, the problem with this approach is that proof searches cannot be performed systematically. The root of the problem is the Transitivity axiom: It is in general undecidable whether as there are infinitely many B’s that must be checked in order to cover all possible proofs involving Transitivity. For instance, suppose one attempts to prove that by proving that for some category B1, and To prove that one could show that for some category B2, and Such recursion could go on indefinitely. However, there is another means of presenting the logic of proven to be equivalent to the axiomatic presentation, which nevertheless guarantees that any

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Page 32 proof search will terminate. This is the GENTZEN SEQUENT presentation, which will be defined in section 2.2.3. 2.2.3 Gentzen Sequent Presentation The Gentzen sequent rules defining the Associative Lambek Calculus are a presentation that is equivalent to the axiomatic presentation of the previous section, but which guarantees that any proof search will terminate. This section is divided into three parts: 2.2.3.1, which discusses the rule of Associativity, and how it is often left implicit in the rules of inference; 2.2.3.2, which presents the actual rules; and 2.2.3.3, which shows how the Gentzen sequent rules can guarantee the termination of any proof search. 2.2.3.1 Implicit Associativity Before introducing the Gentzen rules, a discussion of Associativity is necessary, in order to make sense of the notation. The Associative Lambek Calculus is so named because of the associativity of the product constructor•Consider the category A•B•C. Technically, this category should be written as either A•(B•C) or (A•B)•C, following the rules for category constructors in (18). However, in the Associative Lambek Calculus, a rule of Associativity6 states that and the bracketing is often omitted. More commonly, • is simply replaced by a comma, so that instead of thinking of an expression with the complex category A•B•C, one can think of a SEQUENCE of expressions, with categories A, B, and C. In terms of sequences, the axiom of Residuation would look as follows: (21) Axiom of Residuation, in terms of category sequences iff iff 6. This rule of Associativity involving the product constructor should not be confused with the following theorem: This theorem is called Associativity in Moortgat (1988:11), but in fact can only be proven by making use of what is referred to as Associativity here: This fact is noted by Moortgat (1997:111), who clarifies the nomenclature by renaming the theorem Restructuring.

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Page 33 2.2.3.2 Gentzen sequent calculus for the Associative Lambek Calculus With the idea of sequences introduced, the Gentzen sequent presentation of the Associative Lambek Calculus can proceed. The rules are shown in (22); following them is an explanation of the general anatomy of a Gentzen sequent rule, and then a discussion of the individual rules. (22) Gentzen sequent calculus for the Associative Lambek Calculus

In a Gentzen sequent rule, the material above the line comprises the PREMISE(S), and the material below the line, the CONCLUSION It can be seen in (22) that each rule requires at least one premise, except for the Axiom, which states that the conclusion can be proven from no premises at all (the equivalent of Reflexivity in the axiomatic presentation). Each premise or conclusion is known as a SEQUENT. The material to the left of the in a sequent is known as the ANTECEDENT, and consists of a sequence of categories. Capital Greek letters are used as variables over sequences, so that well-formed sequences include not only “A, B,” but also Γ, or Δ, or combinations such as “Γ1, A/B, Δ, Γ2,” seen in the /L rule. The material to the right of the is known as the CONSEQUENT (or SUCCEDENT). Unlike the antecedent, which must be a sequence of categories, the consequent is a single category. As mentioned above, the equivalent of Reflexivity is the Axiom rule. The equivalent of Transitivity is the Cut rule, which states that if a C is derivable from the sequence “Γ1, A, Γ2,” and the A in turn is derivable from some sequence Δ, then one can conclude that a C is derivable from the sequence “Γ1, Δ, Γ2.” The remaining rules form the equivalent of Residuation. They are

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Page 34 divided into L(EFT) RULES (/L, \L), which specify the behavior of a constructor on the left-hand side of a conclusion, and R(IGHT) RULES (/R, \R), which specify the behavior of a constructor on the right-hand side of a conclusion. These are, respectively, the rules of use and rules of proof for / and \, mentioned in section 2.1. The L rules state that from the premises and Γ1, A, one can conclude that Γ1, A/B, Δ, or that Γ1, A, B\A, The R rules state that from the premise Γ, (or B, one can conclude that (or To see how these rules enforce Residuation, and to illustrate how a Gentzen sequent derivation proceeds, it will be proven in (23) that given that A, and vice versa. A Gentzen sequent proof consists of a tree, whose root is the conclusion sequent, and each of whose subtrees instantiates one of the rules of inference, and each of whose leaves is an instance of an axiom. In the first proof in (23), the desired conclusion is that the root of the proof tree. The \R rule says that this conclusion can be made if it is true that A, which is given (i.e., treated as an axiom). (The step labeled Given is not a true step in a Gentzen proof; rather, it abbreviates whatever steps would actually appear in a proof with real categories instead of A, B, and C.) In the second proof, the desired conclusion is that A, the root of the proof tree. The Cut rule says that if and A, then this conclusion can be drawn. It is given (i.e., an axiom for purposes here) that so this leaf of the proof tree is licit, and the only task remaining is to prove that A, The \L rule states that this can be proven if it is true that and As these are both instances of the Axiom, the proof is complete. Similar proofs can be done to show that given that A, and vice versa. (23) Proof of axiom of Residuation

To illustrate how the rules work, the rules of Type Raising (TR) and Function Composition (FC) from section 2.1 are derived as theorems in (24). For linguistic examples, derivations of Kim sings as an S, and Kim likes as an S/NP are shown in (25) and (26).

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Page 35 (24) Gentzen sequent derivation of TR and FC

(25)

Gentzen sequent derivation of Kim sings as S

(26)

Gentzen sequent derivation of Kim likes as S/NP

As a final note, there are also L and R rules for the product constructor •, which allow conversion between notation with this constructor and the comma notation. These rules can be useful when a derivation requires a functor to take all its arguments at once, instead of one at a time (that is, when the functor needs

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Page 36 to be “uncurried”); such a usage will be seen in Chapter 3. The rules are shown in (27), and a proof of the Curry and Uncurry theorems in (28). (27) Gentzen sequent rules for • (28)

Proof of Curry and Uncurry theorems a. Curry

b.

UnCurry

Now that the Gentzen sequent rules have been presented, it can be shown how they allow for termination of any proof search.

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Page 37 2.2.3.3 Cut Elimination and Decidability In section 2.2.2, it was seen that the axiom of Transitivity was responsible for the potential undecidability of possible theorems. However, the Gentzen sequent rules for the Associative Lambek Calculus still contain the Cut rule, equivalent to Transitivity. The reason that any proof search performed using these rules can still be guaranteed to terminate is that the Cut rule can be eliminated with no loss in proving power. In other words, any proof involving Cut can be converted into a proof without Cut. This claim was proven by Gentzen (1934), and extended to the Associative Lambek Calculus by Lambek (1958). For an explanation of the algorithm for converting a proof to a Cut-free proof, see Moortgat (1997:108–110). With Cut removed from the inventory of rules, it is possible to see how the Gentzen sequent calculus allows decidability: In each L or R rule (reading from bottom to top—in other words, starting from the sequent to be proven), a constructor is eliminated, so that each branch of the tree will ultimately end in a premise containing no constructors at all. To such a premise, either the Axiom rule can be applied (in which case that branch of the proof is complete), or it cannot (in which case that branch of the proof fails). Furthermore, in each rule, no categories appear in the premises that do not appear in the conclusion, a fact known as the SUBFORMULA PROPERTY. As a result, the infinite recursion problem discussed at the end of section 2.2.2 can never arise. 2.2.3.4 Summary The Gentzen sequent presentation of the Associative Lambek Calculus provides a decidable means of conducting proof searches which is sound and complete with respect to the frame semantics. However, these rules can be rather cumbersome and awkward to work with. At this point, a more convenient notation will be introduced, namely, natural deduction. 2.2.4 Natural Deduction Rules for the Associative Lambek Calculus Though the Gentzen sequent rules (minus Cut) ensure that proof searches terminate, a (usually) more compact and more readable notation for these rules is the NATURAL DEDUCTION format. The correspondence between natural deduction rules and Gentzen sequent rules is established in Prawitz (1965). The natural deduction presentation of the rules for the Associative Lambek Calculus is given in (29); discussion follows.

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Page 38 (29) Natural deduction rules for the Associative Lambek Calculus

A natural deduction proof is a tree, whose root is the category to be derived, and whose leaves are lexical entries, and each of whose subtrees instantiates one of the natural deduction rules of inference. In natural deduction format, rules of use (or Left rules) are referred to as Elimination (E) rules, since (as seen above), a constructor in one of the branches of the tree is eliminated in the root. Similarly, the rules of proof (or Right rules) are referred to as Introduction (I) rules, since a constructor is introduced in the root of the tree. The • constructor is implicit: Instead of being represented by a comma (as in the Gentzen sequent rules), it is indicated in natural deduction rules by juxtaposition of categories. Also implicit is Associativity. The /E rule in (29) states that from an A/B and a right-adjacent B, an A can be derived. The /I rule states that if an A can be derived when a B is hypothesized (indicated by the square brackets) on the expression’s right periphery, then an A/B is derived when the hypothesis is withdrawn. The \E and \I rules work similarly. The rules for • are omitted, as this is a case where Gentzen sequent style is more perspicuous. (For presentation and discussion of the •E and •I rules, see Carpenter 1997:167.) As was done with the Gentzen sequent presentation, derivations of TR, FC, Kim sings and Kim likes are given in (30)–(32) to illustrate how the natural deduction rules work.

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Page 39 (30) Natural deduction derivation of TR and FC

(31)

Natural deduction derivation of Kim sings as S

(32)

Natural deduction derivation of Kim likes as S/NP

In this work, natural deduction will be used for almost all derivations, the exceptions being a few for which Gentzen sequent format is more readerfriendly than natural deduction. 2.3 Semantics In this section, semantic composition in type-logical grammars will be discussed. Whereas in section 2.2 the focus was on categories, in this section it will be on TYPES and TERMS. In section 2.3.1 the set of types will be defined, and their relation to categories specified. In section 2.3.2 the set of terms will be defined, and their relation to types specified. In section 2.3.3, the interrelationship of categories, types, and terms in a TLG will be established, and the rules of inference from section 2.2 will be augmented to show semantic as well as syntactic information.

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Page 40 2.3.1 Types The set of types will be notated as Typ, with BasTyp indicating the subset comprising basic, or atomic, types. BasTyp will include the type Ind for individuals, Prop for propositions,7 and Bool for truth values (1 and 0). Complex types are constructed from simpler types by means of type constructors. For now, the constructor inventory will consist of → and ×. The set Typ is the transitive closure of BasTyp under all type constructors, and can thus be recursively defined as in (33). Lowercase Greek letters are used as variables over types. (33) a. b. If then σ→τ, Types constructed with the → connective are known as FUNCTIONAL TYPES; those constructed with×are known as PRODUCT TYPES. Each syntactic category is mapped to a semantic type by the function Typ, a subset of Cat×Typ. The type for the atomic categories S, N and NP is shown in (34): (34) Category Type S Prop N Ind→Prop NP Ind For complex categories, Typ is defined as follows for /, \, and •: (35) a. Typ(A/B)=Typ(B)→Typ(A) b. Typ(B\A)=Typ(B)→Typ(A) c. Typ(A•B)=Typ(A)×Typ(B) For example, sings has category VP (that is, NP\S), so its type will be Typ(NP\S)=Typ(NP)→Typ(S)=Ind→Prop. Kim sings has category NP•VP, 7. In fact, propositions are not actually basic types; they are functions from possible worlds to truth values. That is, Prop=World→Bool. For example, the denotation of Kim sings is a function that returns 1 for all possible worlds in which Kim sings, and 0 for all possible worlds in which Kim does not sing. However, following Carpenter (1997:419), propositions will be treated as basic types for purposes of this dissertation.

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Page 41 so its type will be Typ(NP•VP)=Typ(NP)×Typ(VP)=Ind×(Ind→Prop).8 Of course, Kim sings also has category S, and therefore type Prop; this fact will be discussed further in section 2.3.2. 2.3.2 Terms The set of terms, formulated in the λ,-calculus, will be notated as Term. The connection between terms and types is that Term is partitioned into subsets Termτ for each τ in Typ, and each of these subsets Termτ contains only terms of type τ. Following is an enumeration of all possible kinds of term for any set Termτ. First of all, Termτ can contain VARIABLES, noted as Varτ, and CONSTANTS, noted as Conτ, as indicated in (36a,b). (36) a. b. Each set Termτ can contain FUNCTIONAL APPLICATIONS, defined in (37) as terms of form α(β), where α has type σ→τ, and β has type σ. In other words, functional type α is applied to argument type β. For example, since and (37) if and If τ is a functional type σ→ρ, then the set Termτ will consist of FUNCTIONAL ABSTRACTIONS, defined in (38) as terms of form λx.α, where x is a variable of type σ, and α is of type ρ. For example, since and we know that (38) if τ=σ→ρ and and If τ is a product type σ×ρ, then the set Termτ will consist of ORDERED PAIRS, defined in (39) as terms of form where a has type a and β has type ρ. Returning to the Kim sings example from 2.3.1, the semantic term for this phrase in its NP•VP categorization is this is a member of TermInd×(Ind→Prop), since and In this example, the semantic term can be regarded as a functor and an argument before 8. I am abusing the terminology here, since types are assigned to categories and terms, and not to linguistic expressions. I do so because it is easier to refer to “an expression of type τ” than to “an expression whose category is of type τ.”

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Page 42 the actual functional application has been carried out. However, there need not be any such dependency between the elements of an ordered-pair semantic term. For example, the phrase see the has category (VP/NP)•(NP/N), and semantics (39) if τ=σ×ρ and and Finally, the projection functions π1 and π2 can extract elements from ordered pair terms, as specified in (40a,b). For example, if α is then π1(α) is kim′, and π2(α) is sing′. These terms can be members of any set Termτ, as appropriate. (40) a. b. Variables will be named according to the conventions in (41). Most of the letters used are in accordance with common practice: x, y, z for variables over individuals; p, q, r for variables over propositions. P, Q and R are used essentially as in formal semantic tradition, except that Prop has replaced Bool. For variables over certain other types, U, V, and W will be used, with subscripts indicating the semantic type or (for better readability) syntactic category. For example, if a variable U is used for something of category it will be subscripted as not U((Ind→Prop)→Prop)×(Ind→prop). In addition, this subscript will be suppressed after the first usage, unless it is needed for clarity. (41) Variable naming conventions Semantic type Variable name(s) Ind x, y, z Prop ψ, p, q, r Ind→Prop P, Q Ind→(Ind→Prop) R (Ind→Prop)→Prop D (for determiner ) Prop→Prop A (for adverb ) Other U, V, W with subscript indicating category at first usage, if necessary With types and terms introduced, the rules of inference can now be enhanced to carry out syntactic and semantic derivation in parallel, the focus of the next section.

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Page 43 2.3.3 Adding Semantics to the Rules of Inference The connection between categories, types and terms is as follows: The semantic term for any expression of category A must have type Typ(A), i.e. be a member of TermTyp(A). For example, the semantic term corresponding to any expression of category S will have to be of type Prop, since Typ(S)=Prop. Likewise, any term corresponding to an expression of category NP\S will have to be of type Ind→Prop, i.e., Typ(NP\S). For individual lexical items, appropriate categories and terms are assigned in the lexicon; for example, the verb sings, with category NP\S, can be assigned the term λx.sing′(x), which will have type Ind→Prop, as required. For phrases, however, it is the rules of inference for the TLG that will ensure that the semantic term for any expression of category A will have type Typ(A). The Associative Lambek Calculus will now be presented in both Gentzen sequent and natural deduction format, with categories decorated with term assignments, following van Benthem (1988). (As in section 2.2, the natural deduction rules of inference for • are omitted.) With these rules, syntactic and semantic derivations can proceed in parallel. The Gentzen sequent rules are presented first, in (42): (42) Gentzen sequent rules for the Associative Lambek Calculus, with semantic terms added

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Page 44 To illustrate how the L and R rules for / and \ work, the theorems of TR and FC, and the strings Kim sings and Kim likes are derived again below, this time with semantic labels included. (43) Gentzen sequent derivation of TR and FC, with semantics included a. TR

b.

FC

(44) Gentzen sequent derivation of Kim sings as S/NP

(45) Gentzen sequent derivation of Kim likes as S/NP

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Page 45 The natural deduction rules for the Associative Lambek Calculus with term decorations are given in (46); derivations of TR, FC, Kim sings, and Kim likes follow. (46) Natural deduction rules for Associative Lambek Calculus, with semantic terms decorations

(47)

Natural deduction derivation of TR and FC, semantics included a. TR

b.

FC

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Page 46 (48) Natural deduction derivation of Kim sings as S, semantics included

(49) Natural deduction derivation of Kim likes as S/NP, with semantics included

This concludes the presentation of the basic workings of a TLG. In the remainder of the chapter, the less commonly used conjunction and disjunction constructors will be defined and discussed; their interaction with the lexicon will be explored; and a few miscellaneous semantic issues will be addressed that will be relevant in later chapters. 2.4 Conjunction and Disjunction Constructors In addition to /, \ and •, a type-logical grammar may contain other constructors. In particular, those of interest here are the conjunction and disjunction constructors, and introduced by Lambek (1958). To add these constructors to the inventory, the recursive definition of Cat will now be extended with the following clause: (50) If then Categories constructed by means of and will be referred to as CONJUNCTIVE and DISJUNCTIVE CATEGORIES, respectively. The idea behind these constructors is that since category interpretations are sets of linguistic expressions, it is possible to have interpretations that correspond to set intersection and union.

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Page 47 2.4.1 Conjunction Constructor: The interpretation of a category is the intersection of the interpretations for A and B, as noted in (51). The type for is given in (52). (51) Interpretation of conjunctive categories (52)

Type for conjunctive categories

Comparing (52) here to (35c) in section 2.3.1, it can be seen that both A•B and have the same type: Typ(A)×Typ(B). Consequently, expressions of category A•B and will each be associated with the same kind of term—an ordered pair of terms—which can be operated on by the same projection functions π1 and π2. What maintains the distinction between these two constructors is the frame semantics. For comparison, while Whereas a member of is a single expression that is a member of both ν(A) and ν(B), a member of ν(A•B) is the concatenation of two expressions, one in ν(A) and one in ν(B). In the Gentzen sequent format, the rules state that if C: γ is derivable from a sequence containing an A: α, or from a sequence contain a B: (β, then C: γ is also derivable from a sequence identical in every way except that instead of an A: α, or a B: β, it contains an The rule states that if both an A:α and a B:β can be derived from the IDENTICAL sequence Γ, then it can be concluded that is derivable from Γ. (53) Sequent-style rules of inference for

In the natural deduction format, the Elimination rules are as in (54).

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Page 48 (54) Natural-deduction style Elimination rules for

These rules state that from an a, either an A: π1(α) or a B: π2(α) can be derived. In other words, if an expression is both an A and a B, then (i) it is certainly an A, and (ii) it is certainly a B. The Introduction rule, however, is awkward in this style, and will not be shown here. (It can be found in Carpenter 1997:191.) When the rule of proof for needs to be used, the Gentzen-style rule will be employed. Concerning linguistic applications of the conjunction constructor, Morrill (1994) suggests it could be used to compactly represent prepositions as projecting either adnominal or adverb phrases. Instead of giving a preposition the two categorizations (N\N)/NP (to show that it takes an NP complement to form a noun modifier) and (VP\VP)/NP (to show that it takes an NP complement to form a VP modifier), Morrill gives it the category to show that it takes an NP complement to form something that can modify both Ns and VPs. Morrill does not intend for the PP to actually end up modifying both an N and a VP simultaneously—at some point in the derivation, the constructor will be eliminated and the PP will resolve into either N\N or VP\VP. An illustration is shown in (55), where the PP in the moon has category but resolves into an N\N in order to combine with the N man. For better readability, the derivation is done without the term decorations. However, if an adnominal PP is translated as αADN, and an adverbial PP as αADV, the term for in will be The term for the PP in the moon in the second line from the top will be and the term for this below the step will simply be in′ADN(the-moon′).

(55) The conjunction constructor has also been used in cases of neutrality, specifically argument neutrality in cases of functor coordination. Morrill does not mention this possibility, probably because (as noted in Chapter 1) no cases

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Page 49 of category-level argument neutrality have been discussed in the literature. However, the flavor of a conjunctive-type analysis of argument neutrality at the morphosyntactic level can be found in Johnson and Bayer (1995), who take the approach of letting the apply not only to major category, but also to morphosyntactic feature values.9 Thus, an NP like the German Frauen from (8c) in Chapter 1 would be represented as It can be resolved to a plain acc or dat where necessary, but can also participate in sentences such as (8c), repeated below as (56), where Frauen must be both accusative as the object of findet and dative as the object of hilft: (56) Er findet und hilft Frauen. He finds and helps women.ACC.DAT. (Pullum and Zwicky 1986, (40)) What happens is that the accusative-seeking findet is “strengthened” from to the dative-seeking hilft undergoes a similar strengthening. This strengthening step is a theorem dubbed Antecedent Strengthening (ASt) by Bayer (1996), shown here in (57) both with and without the semantic term labels. Similar theorems (not shown here) can derive from A/C, and from either B\A or C\A. All these theorems will be referred to as ASt. The ASt theorems will play a crucial role in many of the derivations in this dissertation. (57) Proof of Antecedent Strengthening (ASt, from Bayer 1996, Fig. 17) a. Syntactic only b. Syntactic and semantic

A derivation of findet und hilft Frauen is shown in (58). 9. Actually, this use of is suggested in Kanazawa (1992), but he does not discuss coordination of unlikes.

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Page 50 (58)Derivation of findet und hilft Frauen (following Johnson and Bayer 1995; Bayer 1996);

It should be noted that the above derivation is shown only to illustrate the mechanics of argument neutrality in a conjunctive-types analysis. There are problems with using conjunctive types for feature neutrality as Johnson and Bayer (and Kanazawa) do, and I do not propose to do so. Heylen (1999:116– 119) illustrates the problems with the German example guten Frau ‘good woman.’ Frau is a 3rd person feminine singular noun, which could be represented in Johnson and Bayer’s system as Guten is a weak genitive adjective, which would be represented as The task is to derive guten Frau as an However, this is impossible. Consider first the failed proof in (59): (59) Failed attempt to derive guten Frau as (Heylen 1999:116)

Even if Frau is represented as only the left side of the above proof would be helped, where instead of having to prove we would now be able to prove But on the right side, it would still be necessary to prove that In order to make the derivation go through, guten would need to be given the result category But the trouble is that guten is NOT always feminine and 3rd person singular: its gender, person and number depend on the noun it

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Page 51 modifies. I suspect that the best treatment of morphosyntactic underspecification (including feature neutrality) will come from work along the lines of Levy and Pollard (2002) or Daniels (2002) in the HPSG literature, and can be incorporated into whatever means one chooses for encoding morphosyntactic information in a TLG. 2.4.2 Disjunction Constructor: The frame semantics for the disjunction constructor and related definitions are provided here only for sake of completeness, since in section 2.4.3 this constructor will be eliminated from the inventory of constructors. The disjunction constructor corresponds to set union. The interpretation is shown in (60): (60) Interpretation of categories of form Extensions to Cat, Typ, Typ and Term are shown in (61): (61) a. If then b. If then c. d. if τ=σ+ρ and e. if τ=σ+ρ and As seen in (61b,c), the type constructor corresponding to is +; types constructed with + are known as SUM TYPES. Terms for expressions of category are members of a set known as the DISJOINT UNION of TermTyp(A) and TermTyp(B). As defined in Morrill (1994:58), the disjoint union of sets X and Y is in other words, special ordered pairs whose first element is 1 if the second element is a member of X, or 2 if the second element is a member of Y. Thus, the semantic term for an expression with a disjunctive category will be a member of can. That is, it will be an ordered pair, the first element of which will be a label (1 or 2) indicating whether the second element’s type is Typ(A) or Typ(B). Just as the projection functions π1 and π2 extract terms from an ordered pair, the injection functions ι1 and ι2 put terms into these special ordered pairs. ι1(α) is equivalent to [1, α]; ι2(α) is equivalent to [2, α]. For example, from the NP Kim, can be derived, with term [1, kim′], where the 1 indicates that the term kim′ is of type Typ(NP). Thus, even though

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Page 52 Kim can be considered as an the fact that its semantics is linked to the NP category is not lost, because the 1 carries that information. The Gentzen sequent presentation of the rules for is given in (62). The rule states that if a C: α can be derived from a sequence “Γ1,…, Γ2” containing an A: x, and if a C: β can be derived from an identical sequence “Γ1,…, Γ2” except with a B: y instead of an A: x, then (considering just the categories) it can be concluded that a C can be derived from the sequence “Γ1,…, Γ2” whether it contains an A or a B. Semantically, the term for the in the conclusion is γ, which will be of form [1, x] or [2, y]. The term for the C in the conclusion is γ→λx.α;λ y.β. This is to be read, “λx.α(a) if γ=[1, a], or λy.β(b ) if γ=[2, b].” The rules state that if an A: α (or B: β) is derivable from sequence Γ, then it can also be concluded that with term [1, α] (or [2, β]) is derivable from sequence Γ. (62) Gentzen sequent rules of inference for

Of the natural deduction rules of inference for the Elimination rule is quite awkward, and therefore, only the rules of Introduction are shown in (63). (For the Elimination rule, see Carpenter 1997:191.) They state that from an A: α (or a B: β) an can be derived, with term [1, α] (or [2, β]). (63) Natural-deduction style Introduction rules for

At this point, linguistic applications for the disjunctive constructor will be considered. Morrill proposes to use disjunctive categories for underspecification of argument categories. One of his examples is the copula be, which can take as its

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Page 53 complement either an NP or an AP.10 Thus, it would be given the category (This analysis is also suggested by Kanazawa 1992, and elaborated in Hendriks 1995:131–133.) Then, if an NP (or an AP) occurs to the right of be, the rules allow it to count as an and combine to form a VP, as seen in the derivations in (64). (64) Derivation of is happy a. Syntactic only

b. Syntactic and semantic

This approach extends naturally to cases of coordination of unlike argument categories (that is, verb neutrality), as Morrill (1994) and Hendriks (1995) note, citing the cases involving coordinated arguments to the copula. Bayer (1996) illustrates this point with a derivation of is a Republican and proud of it, essentially as in (65). Since the semantics of and has not been discussed, and since the constructor is about to be eliminated anyway, this derivation will show only the categories. 10. For purposes of this example, the standard abbreviation AP for adjective phrase will be used, even though a type-logical equivalent has not yet been discussed.

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Page 54 (65) Derivation of is a Republican and proud of it;

Hendriks (1995:133) extends the above analysis to cover the other cases of category neutrality from Sag et al. (1985), such as remember the appointment and that it was important to be on time. To license this VP, remember would have category where Sc is the type-logical category for a complementized S. Now that the conjunctive and disjunctive constructors have been defined, it is time to consider one of the problems that have been noted concerning them, namely the incompleteness of and with respect to the frame semantics. 2.4.3 Incompleteness of and Although and are interpreted as set intersection and union, there are theorems in set theory that are not derivable with the rules of inference for and In other words, is incomplete with respect to the interpretation of and A good example of this incompleteness is that Distributivity, i.e. is not a theorem in the Associative Lambek Calculus, even though as seen in (66):

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< previous page Page 55 (66) Proof that 1. (Interpretation of 2. Since for any 3. 4. 5. 6.

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(Universal instantiation) (1,2, Substitution) (Interpretation of

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(3, 4, Substitution)

(5, Definition of set equality) The usual mitigating factor mentioned by linguists is that there seems to be linguistic need for only the rules of use for and the rules of proof for Morrill (1994:169), for example, says: Although we have presented a logic of both use and proof, it appears that application to linguistic derivation requires just USE of conjunction, and PROOF of disjunction, a fact that seems to originate in the nature of organisation of lexical properties: thus it would be of little use to make a lexical declaration that an element is of type and odd to declare a functor of domain type This means that in sequent derivations conjunctions occur as main [constructors] in antecedents and disjunctions as main [constructors] in succedents. Morrill is right as far as the disjunction constructor is concerned. If one defines a word, presumably the word is known to belong to some category A, and does not need to be declared as an which would indicate that the word is either an A or a B, but the grammar writer does not know which one. Even if a word had two possible categorizations A and B, which were to be captured in a single category, it would not be declared as an but rather as an For example, suppose a single lexical entry covering the transitive and intransitive versions of eat is desired. If it is declared as it can never be simplified to VP/NP or VP, since and (Or in more general terms, ) On the other hand, if it is declared as a it can always be simplified to either VP/NP or VP as needed, since is a subset of both ν(VP/NP) and ν(VP). (In more general terms,

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Page 56 However, Morrill’s remark about the conjunction constructor overlooks some cases. It would indeed be odd to declare a functor with domain type since no functor (to my knowledge, and evidently to Morrill’s, too) is specified in the lexicon to require its argument to have two categories at once. Therefore, there would seem to be no need for a rule of proof to show that a potential argument has category However, the assumption in this passage is that the only reason for having something with category is for it to serve as an argument to some functor. Cases will be encountered in later chapters where this is not the case. For example, in Chapter 3, it will prove necessary to take eat as a and derive the phrase you eat as an In such a derivation, eat neither resolves into VP/NP or VP, nor is it consumed as an argument for some functor; rather, it projects its multiple categorization to the phrasal level. This will require the rule of proof for Consequently, the idea of limiting oneself to the rules of use for will not be feasible. As an alternative to using only the rules of use for and only the rules of proof for I propose to eliminate entirely. This can be done, because is needed only for argument categories, as noted by Morrill, and any category of form is equivalent to as noted in Moortgat (1997:149). This equivalence is demonstrated in (67), with semantics omitted. (67) Equivalence of and a. Derivation of from

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With the elimination of completeness is achieved. This may not seem possible at first, since set intersection and set union are so often considered as a pair. Even if is eliminated, one could argue, set union still exists, and for any sets ν(A) and ν(B), the set is defined. Pursuing this line of thought, one can observe that Without how can there be a corresponding result with The answer: There can’t, and it doesn’t matter. All that is necessary for completeness is that for any categories X and Y, if ν(X) ν(Y), then X Y. The observation that is simply irrelevant here, because there is no longer any category Y such that 2.4.4 The “Type Raising plus Antecedent Strengthening” Theorem Elimination of makes the derivation of is a Republican and proud of it a bit different from the one shown in (65). Instead of the category for is will now be To coordinate the NP a Republican and the AP proud of it, a theorem I refer to as Type Raising plus Antecedent Strengthening (TR+ASt) will be used. TR was presented in (17) and (30); ASt was presented in (57). Applying ASt after TR, the following derivation is obtained: (68) Proof of Type Raising plus Antecedent Strengthening (TR+ASt) a. Syntactic only b. Syntactic and semantic

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Page 58 In the ASt step, it is possible to strengthen (C/A)\C to any category of form but the most useful one for our purposes will be In the case of is a Republican and proud of it, C is instantiated as VP; A as NP, and B as AP. Thus, applying TR+ASt to a Republican and to proud of it will convert each expression to category At this point, they can be conjoined, and take the is as an argument. This is illustrated in (69). The semantic portion of the derivation is suppressed so that the basic syntactic operations can be seen better, and also because the TR+ASt procedure will be used in derivations in Chapters 4 and 5, where semantics will be included. (69) Derivation of a Republican and proud of it via TR+ASt;

Because both TR and (by this point) ASt are familiar theorems, TR+ASt is a convenient name for a derivation in which an item of category A is converted to category in order to be coordinated with a B, as was done with a Republican and proud of it above. It should be noted, however, that this conversion does not have to be written as two separate steps in a derivation. It can simply be seen as a theorem almost like TR, except that instead of hypothesizing a C/A, a is hypothesized, as illustrated in (70). This will be the procedure followed in subsequent derivations; however, for convenience the abbreviation TR+ASt will be used to refer to this theorem.

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Syntactic and semantic

The TR+ASt theorem allows one to have the effect of a disjunctive category without an actual disjunction constructor, enabling one to avoid the logical incompleteness that comes with having both conjunctive and disjunctive categories in a grammar. However, there is a more significant issue than incompleteness, even when only one of the conjunctive or disjunctive type constructors is employed. This is the problem of how to formally distinguish between category neutrality and ambiguity, which will be discussed in the next section. 2.5 Lexical Issues Given the focus on neutrality and ambiguity in this dissertation, and the different status of ambiguous and neutral words in the lexicon, a clear definition of the lexicon is needed in order to discuss ambiguity and neutrality with respect to it. Section 2.5.1 defines a categorial lexicon and discusses the problem of formally distinguishing ambiguity from neutrality in it. Section 2.5.2 covers lexical rules (rules expressing generalizations about the lexicon). 2.5.1 Ambiguity and Neutrality in the Lexicon The introduction of conjunctive categories raises a troubling question about the nature of lexical ambiguity and neutrality. To understand this question, it will first be necessary to define what a lexicon is in a type-logical system. Given the sets Cat and Term as defined in sections 2.2 and 2.3, and the set V of all words in language L, the lexicon will be defined as in (71), following Carpenter (1997:115).

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In other words, Lex is a set of triples consisting of a word, a category, and an appropriately typed semantic term. The lexicon is assumed to be a subset of language L, which is defined as in (72): (72) L is the relation such that for any expression e, if then In other words, Lang is a set of triples like Lex, except that the first element of each triple can be a string of words (i.e. a member of V+) instead of just a single word.11 By decree, so any triple that is in Lex will also be in Lang. Under these definitions of Lex and Lang, the frame semantics can be stated more precisely. Before, for any category A, ν(A) was defined as “the set of expressions in L that are assigned category A.” Now, this definition can be stated thus: For any expression e and category A, iff for some α, Lang. Therefore, for any word w, if then since . This fact has interesting consequences when conjunctive categories are considered. Suppose that a word w appears in two triples in Lex: and Then by the frame semantics, and Consequently, or in other words, by the frame semantics for conjunctive categories in (51), And by the new definition of This situation is illustrated in Figure 3a. Conversely, suppose that a word w appears in only one triple in Lex: Then which means that and which in turn means that and This situation is illustrated in Figure 3b. 11. Sometimes, for convenience of notation, semantic terms will be ignored, and it will be said that an ordered pair is a member of Lex or Lang.

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Figure 3 Two possible situations in which w has category The situation illustrated in Figure 3b reflects the way conjunctive categories are intended to be used, as envisioned by linguists such as Morrill (1994). On the other hand, the situation illustrated in Figure 3a is the reason behind some linguists’ rejection of conjunctive categories (or more specifically, conjunctive categories whose component categories are of different semantic types). Bayer (1996:606–7) uses can as an example to explain: Even though can as a modal auxiliary and can as a transitive verb have radically different meanings, if conjunctive categories are part of the grammar, then can will have the category in Lang, with the paired modal auxiliary and transitive meanings as its meaning. Consequently, there will be no way syntactically to rule out the following sentence from Pullum and Zwicky (1986) (also mentioned in Chapter 1): (73) *I can tuna for a living and get a new job tomorrow if I want. (Pullum and Zwicky 1986, (42c)) The problem is not just that there is still no definitive way to determine whether a word is ambiguous or neutral. The problem is that even if there were a definitive way to do this, it is still IMPOSSIBLE TO DISTINGUISH AMBIGUITY FROM NEUTRALITY in the system as currently defined. To use the can example, one cannot escape Bayer’s observation by simply saying that the two usages of can are clearly homophones, and decreeing that Lex contains them as and Even if one excludes from Lex, this ordered pair will still be a member of Lang. The situations illustrated in Figure 3a and Figure 3b were described by referring to the definition of the frame semantics. However, one possibly significant difference between these two situations is that only one of them can also be proven via the rules of inference. Concerning Figure 3b, if a word w has

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Page 62 conjunctive category then the rules of use for guarantee that w has category A, and category B. In contrast, concerning Figure 3a, if a word w has category A and category B, the rule of proof for does NOT guarantee that w has category To see why, the rule of proof for is repeated below: (74) To prove that an expression has category it must be shown that both A and B are derivable from the identical sequence Γ. If Γ is A: α, then the premise can be proven, but not the premise Parallel remarks hold if Γ is B: β. These are the only two options for Γ if Figure 3a holds. If Γ is then and can be proven, but in this case, it is Figure 3b that holds, not Figure 3a. At first glance, this state of affairs would seem to be another case of incompleteness of with respect to the frame semantics: A result that can be proven in the frame semantics cannot be proven with the rules of inference. However, a closer look reveals that this is not incompleteness. For to be complete with respect to the frame semantics, it must be true that for any A and B, if then In the discussion of Figure 3a, though, nothing was said about any category interpretation being a subset of another—only that if an expression w is a member of both ν(A) and ν(B), then it also a member of As there is no starting premise of the form nothing needs to be proven involving At this point, there are two alternative logical conclusions: One is that TLG as currently defined is not an adequate model of natural language with respect to ambiguity and neutrality. The other is that TLG as currently defined IS an adequate model of natural language with respect to ambiguity and neutrality—in other words, that there is no difference between the two. If one takes the former stance, then some means of formally distinguishing ambiguity from neutrality must be created. However, without a radical change in the foundations of TLG, such a means would probably not be well-motivated. To continue with the can example, to maintain its ambiguity, the means that most readily comes to mind is to introduce subscripts, and declare that Lex contains the pairs This step would exclude any conjunctive category for can from membership in Lang, but there is a problem with the formal status of the subscripts. Clearly, they are not to be pronounced, yet they are in the phonological component of the sign. Instead of signs being ordered triples of phonology, syntactic category, and semantic term, they would have to be ordered quadruples, with one element being a natural

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Page 63 number. Even if this step were taken, however, there is still the question of what the subscripts actually represent. One might take them to represent different memory locations for the lexical entries, different synapses that fire when a speaker uses an ambiguous word with one categorization or the other. However, such speculation is ad hoc, and would most likely not even be entertained if not for the problem of distinguishing lexical ambiguity from neutrality. Aside from the basic question of whether subscripts could be justified, such a solution would require a rethinking of the relationship between ambiguity and multiple lexical entries. If a lexical entry is defined as any member of Lex, and neutral words can constitute more than one member of Lex, then the existence of multiple lexical entries for a word can no longer be equated with lexical ambiguity, unless one revises the definition of lexical entry. To illustrate, if one wanted to represent eat as neutral between its VP and VP/NP categories, one way to do it would be to have the following two members of Lex: and Comparing with the two versions of can above, we have an ambiguous word (can) and a neutral word (eat) both represented as multiple members of Lex. To define ambiguity as a single phonological form with multiple lexical entries, and neutrality as a single phonological form with a single lexical entry, one would have to define a lexical entry as a subset of Lex, each of whose elements had the same phonology and same subscript, like eat above. Returning to the choice stated three paragraphs above, if one takes the stance that TLG as currently defined IS an accurate model of natural language with respect to ambiguity and neutrality, then there is no distinction between the two. In other words, Bayer (1996) is right about the overgeneration possible when conjunctive categories are allowed, but the ungrammatical strings are ruled out for reasons other than ambiguity of the relevant word. This is a much more difficult position to defend, as these “other reasons than ambiguity” need to be identified. In spite of the current theoretical impossibility of formally distinguishing ambiguity from neutrality in a TLG, the investigation in subsequent chapters will proceed as if a distinction could be formalized, in the interest of not allowing the theory to determine the facts. 2.5.2 Lexical Rules Lexical rules are often used as a means of structuring a lexicon. The traditional view of lexical rules is that they state a relationship between two classes of words in the lexicon (see for example, Jackendoff 1975). Specifically, such a rule states that if a word satisfying some description is in the lexicon, then so is

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Page 64 a word satisfying some other description. Under this view, lexical rules are sometimes known as lexical REDUNDANCY RULES. A schematic lexical rule is written in (75), and is to be read, “if then (75) Less formally, this rule states that if a word with phonology ph, category A, and meaning α is in the lexicon, then so is a word with phonology ph′, category B, and meaning β. Even though lexical rules are interpreted as declarative statements under the traditional view (rather than rules that actually derive one word from another), the left-hand side of the rule is often referred to as the INPUT, and the righthand side as the OUTPUT; in addition, the rule is often said to APPLY to an input word. In the literature, lexical rules have been proposed for handling derivational or inflectional morphology (for example, pluralization rules, or rules for the formation of causatives in other languages), and rules that express different categorizations of a single phonological form (sometimes known as CONVERSION or ZERO-DERIVATION rules). The latter kind are the ones of interest here, since they give rise to cases of category neutrality—that is, they state that a single phonological form is assigned to multiple categories. As an example of such a lexical rule, there are the verbs participating in the “unspecified object alternation” (Levin 1993), such as eat, with transitive meaning eat′, and intransitive If one assumes that this is a general rule for transitive verbs in English, a lexical rule could be written as in (76): (76) Sample lexical rule: unspecified object alternation in English verbs In this rule, the like phonology of the input and output words is indicated by the unchanged ph on the left- and right-hand sides of the rule. (Henceforth, the phonological component of a lexical rule will be suppressed, since the input and output phonology are always the same in the rules of interest here.) The rule operates as illustrated in (77) when applied to eat: (77) Unspecified object alternation lexical rule applied to eat Recall from section 2.5.1 that if for some word w, Lex contains both and then Lang is guaranteed to contain One question that now arises is whether the lexicon should

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Page 65 have any conjunctive categories at all, since they don’t seem to be needed in order to guarantee that triples of form can be in Lang. One possible reason to retain the constructor in the lexical component of a grammar could be to narrow the domain of application for a lexical rule. To illustrate, suppose there is a lexical rule that applies to words of category A, but not all of them—only those that also belong to category B. If a word w is assigned to both categories, but is represented in Lex as and then the lexical rule cannot apply to it, even though is a member of Lang. On the other hand, if is itself a member of Lex, then the lexical rule can apply. Just such a lexical rule will be proposed in Chapter 6 for adverbial nouns. Under the traditional view of lexical rules as relations holding between items in the lexicon, lexical rules are different from syntactic rules. Not only do they operate only on words instead of both words and phrases, but also they are part of a separate, lexical component of the grammar. There are a number of reasons for taking this stance; for an overview of them, see Chapter 4 of Dowty (1979). Most significant is the fact that lexical rules are only semiproductive; that is, not every conceivable output of a lexical rule is actually in a speaker’s lexicon. An example with a derivational lexical rule would be the non-word *comfortableness . An example with a conversion rule could be the (to my knowledge) nonexistent intransitive use of like as an output of the lexical rule in (76). Syntactic rules, by contrast, are in theory exceptionless. For instance, any transitive verb can combine with an NP complement and produce a well-formed VP. Also significant is the fact that the output semantics of lexical rules does not completely determine the actual semantics of the words. A common example involving a morphological lexical rule is the fact that readable does not simply mean “capable of being read,” but something more like “easy and/or pleasant to read.” And as with eat, there is an intransitive version of drink, but instead of meaning “drink something,” it usually means, “drink something alcoholic.” On the other hand, syntactic rules are again exceptionless: The rules of inference for the various connectives completely determine the syntax and semantics of any phrase derived by these rules. In recent years, however, the traditional view of lexical rules has been challenged, especially in some of the computational and HPSG literature on lexical rules. Specifically, it has been argued that lexical rules are no different from other constraints in the grammar (except that they apply exclusively to words and not phrases).12 Meurers (1995, 1999) argues for this position, coining 12. Some have gone so far as to remove even the lexical restriction on lexical rules, turning them instead into “unary phrasal rules.” For example, Stanford University’s LinGO system takes this route.

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Page 66 the term DESCRIPTION-LEVEL lexical rules (or DLRs) for his implementation of lexical rules. The name reflects the fact that an HPSG grammar is a set of descriptions, so any constraint on words will be a description, too. And these lexical rules are indeed constraints on words, in the same way as phrasestructure schemata in HPSG are constraints on phrases. This position can be seen as a continuation of a trend in which lexical rules take on more and more of what are usually seen as syntactic phenomena. For example, Pollard and Sag (1994) have lexical rules for subject and complement extraction, and van Noord and Bouma (1994) propose a lexical rule to allow for modification of VPs. In response to Meurers, the traditional view of lexical rules has been defended by Calcagno and Pollard (1995) and Calcagno (1995), who argue for META-LEVEL lexical rules—i.e., lexical rules that operate in a separate, lexical component of the grammar, relating descriptions of words. In light of this debate, the view of lexical rules that will be taken here needs to be stated unambiguously: Lexical rules are taken to be part of a lexical component of a grammar, separate from the syntactic/semantic rules of inference. This position is taken not only because of the semiproductivity and idiosyncratic semantics of lexical rules mentioned earlier, but because if lexical rules are part of the syntax, then the grammar is no longer a type-logical grammar (at least, as TLG is generally defined). To illustrate, consider the “unspecified object” lexical rule in (76), which relates the transitive and intransitive versions of verbs such as eat. If this lexical rule were encoded as part of the syntax, it would look something like (78) in Gentzen sequent style: (78) This rule is stated like the Axiom: From no premises at all, it can be concluded that To cover the lesser problems first, there is the problem of how to restrict this rule to apply only to words, instead of to entire phrases like all the syntactic rules. Assuming that some means of doing this can be found, another point of contention about this rule is that it applies only to one category, namely VP/NP, instead of any category of form A/B. In this respect, this rule is more like a rule in a CCG than one in a TLG. A more serious objection to having lexical rules on a par with the rules of inference is that a fundamental property of type-logical grammars is lost: Cut Elimination. To illustrate how Cut Elimination is no longer guaranteed, suppose that the phrase Kim eats is to be derived as an S, with eats as a VP/NP. To indicate more clearly the necessity of using Cut, the derivation is given in (79)

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Page 67 in Gentzen sequent style. At the bottom level, the only rule other than Cut that can be applied is /L, which would quickly fail. Therefore, Cut has to be used, in order to allow the VP/NP to be parsed as a VP. (79) Cut-requiring derivation of Kim eats as S

Laying aside the specific objections above, the most serious problem with having lexical rules as part of the syntax in a type-LOGICAL grammar is simply that they are NONLOGICAL. To use (78) as an example, it is not a rule of use or a rule of proof for any connective. One could possibly call it a rule of use for /, since it states that from a VP/NP, a VP can be derived, but to do this would displace the true rule of use for /. The rule is different from the Axiom as well. For any category A, it is true that just from the principles of set theory, and the Axiom reflects this truth. However, the principles of set theory do not require that If one defined the frame semantics such that by fiat, then the lexical rule in (78) would be reflecting the frame semantics, but then the question becomes why such a decree is a natural one to place on the frame semantics. One could argue that the principles of set theory do not require that either, but there is a mathematical basis for this rule, which is not the case for Introducing a nonlogical rule into the rules of inference defeats the primary aim of attempting to use a TLG for linguistic inference. As Moortgat (1997:98) puts it in his overview of categorial grammar, “The central objective of the typelogical approach is to develop a uniform deductive account of the composition of form and meaning in natural language….” The view of lexical rules taken in this dissertation, then, is the traditional view, or in HPSG terms, the MLR view.13 13. In fact, there is one area in which lexical rules as defined here differ from MLRs in HPSG. Meurers (1999:132ff) points out that in HPSG, an input to an MLR need not be a member of the lexicon itself. He goes on to demonstrate that this disadvantage does not exist with DLRs. In the system described here, though, a lexical rule is a relation holding between objects in Lex, and therefore, any input is required to be a member of Lex.

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Page 68 2.6 Other Background 2.6.1 The Semantics of Coordination Since most of the search for category neutrality will involve coordination, a discussion of the categories and terms for coordinating conjunctions will be useful. We follow the presentation in Carpenter (1997:178–180). Carpenter first defines a function Coorσ for coordination of any elements with a Boolean semantic type—that is, either the type Bool (or in our system, Prop), or any type σ→τ, where τ is a Boolean type. His definition for Coorσ is shown in (80): (80) Definition for Coorσ (adapted from Carpenter 1997:180) a. (base case) b. (recursive case) With this definition in place, Carpenter defines and with the polymorphic category (X\X)/X, as shown in (81a), with or implied to be as in (81b): (81) a. and: (X\X)/X: Coorσ(and), where and abbreviates b. or: (X\X)/X: Coorσ(or), where or abbreviates This definition is appropriate for coordination of expressions whose ultimate result type is Prop.14 To illustrate how (80) works, consider the coordination walks and sleeps. Walks will have the translation walk′, while sleeps will have sleep′. What is needed for walks and sleeps is so some way of ensuring the same variable assignments for the interpretations of walks and sleeps is needed. The recursive clause (80b) is what makes this possible, taking CoorInd→Prop(and′)(walk′)(sleep′) and returning λx.CoorProp(and)(walk′(x))(sleep′(x)). The base clause (80a) then allows the CoorProp to drop out, leaving just λx.(and)(walk′(x))(sleep′(x)). The final step is just to replace the abbreviation and with and do the λ,-conversion to obtain To allow for coordinations of interrogatives (under the assumption that the denotation of an interrogative is a set of propositions), a second base case will be to be introduced for CoorProp→Bool. More will be said about this clause in Chapter 3. The revised definition of Coor is shown in (82): 14. This definition, in other words, is for Boolean coordination only, and will not handle coordinations such as Kim and Robin met, or Bill and Ted’s Excellent Adventure .

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Page 69 (82) Coorσ revised for proposition coordination a. CoorProp(α)(β1)(β2)=α(β1)(β2) (base case) b. CoorProp→Bool(α)(β1)(β2)=α(β1)(β2) (recursive case) c. Coorσ→τ(α)(β1)(β2)=λ xσ.Coorτ(α)(β1(x))(β2(x)) (recursive case) In deriving coordinate structures, it will sometimes be useful to abbreviate the two steps of functional application that are needed to get from X\(X/X) to X, and to this end, the Conj(unction) theorem is proven in (83): (83) Proof of Conjunction (Conj) a. Syntactic only

b.

Syntactic and semantic

The abbreviation Conj will be used when the semantics is not shown or are straightforward; when there are complications, the derivations will be written out fully. 2.6.2 Scoping Constructor: One more constructor that will be used in Chapters 5 and 6 is the quantifierscoping constructor introduced by Moortgat (1996); the presentation here is based on Carpenter (1997:220–227). Given a category its type is given by the following definition: (84) Thus, if a quantifier phrase such as every cat is assigned category then its type will be (Typ(NP)→Typ(S))→Typ(S), or (Ind→Prop)→Prop. Notice that

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Page 70 this is the very same type as one would have if every cat had category S/(NP\S) or (S/NP)\S. The reason for having a different category with this same type is that the deduction scheme for allows for the to take scope over an S, whereas the other categories would require in situ scoping. The schema is as follows: (85) Elimination rule for (from Carpenter 1997:225)

This schema says that a with meaning α should be treated as a B, with a variable for a semantic term, until a phrase of category A has been derived. At this point, the variable for the B is abstracted, and the resulting term is given as an argument to the original a term. In this way, a quantified NP acts as a simple variable until an S is derived, at which point the meaning of the S is incorporated into the quantificational meaning of the NP. To illustrate, the sentence Every cat meows is derived below: (86) Derivation of Every cat meows

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Page 71 In this derivation, the generalized determine every is translated as every′, equivalent to λPλQ .every ′ (P)(Q), where every′ (P)(Q) is equivalent to 1 iff (in other words, if “every P Q ’s”). The quantified NP Every cat has category and meaning every′(cat′). After the step, the phrase acts semantically as a referential NP, having simply a variable x for its semantics—until an S is derived in the next line, with semantics meow′(x). At this point, the original meaning every′(cat′) is applied to λx.meow′(x), resulting in the meaning every′(cat′)(meow′), which is equivalent to 1 iff 2.7 Conclusions In the first three sections of this chapter, some fundamentals of type-logical grammar were reviewed. In section 2.4 the conjunctive and disjunctive constructors and were defined, and proposed linguistic applications for them were surveyed. It was shown that can be eliminated without loss of coverage, and that derivations formerly done with the rule can still be done via the Type Raising plus Antecedent Strengthening (TR+ASt) theorem, which will be used in many derivations in subsequent chapters. In section 2.5, the interaction of the lexicon and the conjunctive constructor were explored, and it was concluded that Bayer (1996) was right in noting that in the system as currently defined, ambiguity and category neutrality cannot be formally distinguished. In addition, assumptions about lexical rules and their interaction with conjunctive types were made explicit. Finally, section 2.6 briefly defined the semantics for coordinating conjunctions, since many of the possible cases of neutrality to explore involve coordination; it also defined the scoping constructor which will be used in Chapters 5 and 6. At this point, the necessary tools have been introduced, and the investigation of category neutrality can begin.

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Page 73 CHAPTER 3 Category Neutrality and Mixed-Wh Interrogatives 3.1 Introduction The first cases of category neutrality to be addressed are those revealed in MIXED- WH INTERROGATIVES—that is, wh interrogatives headed by a coordination of two or more wh words of different category. For example, there is the interrogative embedded in (87), attested on the Internet. (87) You will learn to become a food detective and control what and when you eat. In this sentence, what needs a clause with an NP gap, but when needs one without an NP gap. Therefore, the coordination what and when requires a clause that can be parsed as both having and not having an NP gap. (Henceforth, the clause that a wh element combines with to form an interrogative will be referred to as the wh element’s complement, or as the body of the interrogative.) For you eat to have an NP gap, eat must be taken as a transitive verb, but for you eat not to have an NP gap, eat must be taken as an intransitive verb. In this sentence, then, since you eat forms an interrogative with what and when, it seems that eat is used simultaneously as a transitive and an intransitive verb—in other words, it is exhibiting category neutrality between its transitive and intransitive usages. Mixed- wh interrogatives (MWIs) like the one in (87) are not grammatical for everyone, but there are speakers for whom they are grammatical to the point of complete unremarkability. For example, when I asked one speaker what her reaction would be upon hearing (87), she said, “I’d want to learn more!” Furthermore, when one sets out to find MWIs, there are plenty of them to find. Simple searches on the Internet yield many attestations, and a surprising number

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Page 74 turn up serendipitously in newspapers and on the radio when one is listening for them. However, even though a good deal has been written about multiple-wh interrogatives (e.g., What did you do when? or When did you do what?), MWIs have received scant attention in the literature. The only mention of them that I have been able to find is in Giannakidou and Merchant (1998), who discuss sentences parallel to (87), noting that there is (p. 239) “variability in judgments,” but sketching an analysis in which they are ungrammatical. As it turns out, apparent cases of category neutrality appear in more than one kind of MWI. The kind exemplified in (87) will be known as an OPTIONAL NP-GAP MIXED- WH INTERROGATIVE, since the body of these interrogatives (that is, the part following the wh coordination) can be parsed with or without an NP gap. Another kind of MWI is that seen in (88), also attested on the Internet. (88) How does CM control when and whose transmissions occur? In this example, the wh-determiner whose seeks as its complement a noun followed by a sentence with an NP gap; when seeks as its complement a sentence without an NP gap. The phrase transmissions occur can be parsed as both, if transmissions is taken to be both a noun and a bare-plural NP. If it is a noun, then occur is the sentence with an NP gap that whose seeks after combining with its N argument; if it is a bare-plural NP, then transmissions occur is the sentence without an NP gap that when seeks. Thus, such a sentence suggests N vs. NP neutrality for this plural noun; similar attestations involve mass nouns such as legislation. This kind of MWI will be referred to as a PLURAL-NOUN MIXED- WH INTERROGATIVE. The discussion of each of these kinds of MWI will proceed in three parts: the results of a corpus search; psycholinguistic experimental results; and a type-logical analysis. The corpus search was performed because attestations of MWIs needed to be found in greater numbers than they would be by simply watching and listening for them in day-to-day activities, for several reasons. First, MWIs are ungrammatical in my idiolect, rendering introspection useless for analysis. Second, just a few attestations will not be sufficient; they need to be found in quantity in order for one to conclude that they are not (all) just instances of speaker error. Finally, many attestations are needed in order for one to see the range of the phenomenon, and be able to observe patterns that may occur. The corpus that was used was the Internet, since it is easily accessible, and large—larger than some corpora specifically made for linguistic research. One drawback to using the Internet as a corpus is that it is not annotated with part-of-speech tags, but since the set of wh words is small, searching for coordinations of them with Internet search engines is quite easy, even without tags.

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Page 75 Although the corpus search yielded many examples of optional NP-gap and plural-noun MWIs, it also revealed some other kinds of MWIs. It will be shown (in sections 3.2.1 and 3.3.1) that these other interrogatives resemble optional NP-gap and plural-noun MWIs, except that they do not involve transitive-intransitive verbs (e.g. eat), or plural or mass nouns. Therefore, an analysis of optional NPgap and plural-noun MWIs that hinges on neutrality for transitive-intransitive verbs, or neutrality for plural or mass nouns, cannot be extended (in any natural or straightforward way) to cover the full range of data. Consequently, a neutrality-based analysis should be rejected, unless there is evidence that the subset of the data that it covers needs to be analyzed in a different way from the rest of the data. Such evidence is found in the psycholinguistic experimental results for optional NP-gap MWIs (in section 3.2.2), but not for plural-NP MWIs (section 3.3.2). For the former case, there is a statistically significant difference in grammaticality judgments between optional NP-gap MWIs and the other kinds, justifying a separate (neutrality-based) analysis for them. But for the latter case, there is no statistically significant difference in grammaticality judgments between plural-NP MWIs and the other kinds, and therefore the evidence does not point to a separate (neutrality-based) analysis for these. Despite the different experimental results for optional NP-gap and plural-noun MWIs, each receives a type-logical analysis (in sections 3.2.3 and 3.3.3), in the event that future evidence shows a need for both. Following these sections on optional NP-gap and plural-noun MWIs, section 3.4 discusses cases of coordinated- wh interrogatives in which category neutrality arises even when no individual word exhibits it. Section 3.5 presents conclusions. 3.2 Optional NP-Gap Mixed-Wh Interrogatives Optional NP-gap mixed- wh interrogatives were introduced informally in the preceding section. Formally, they will be defined as interrogatives headed by a coordination of a nominal wh word or phrase and an adverbial one. The nominal wh words comprise what and who(m), as well as the determiners whose and which when they appear without an accompanying noun (as in Which do you prefer? or Whose is it?). As stated earlier, these words require their complements to have an NP gap. The adverbial wh words comprise where, when, how, and why.15 There are two possible viewpoints on what kind of gap these words require in their 15. Archaic forms such as whither and whence are ignored.

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Page 76 complements. One is that their complements do not need to contain a gap. To illustrate, since the phrase Kim left by itself is a grammatical sentence (that is, it can be parsed as a sentence in which nothing is missing), and why Kim left is also grammatical, it can be concluded that why does not need its complement to contain a gap. The other view, which will be taken here, is that the complements to adverbial wh words contain an adverbial gap. This is certainly true in a few cases, such as how Kim phrased the letter, since the phrase *Kim phrased the letter is incomplete without a manner adverbial (as observed by McConnell-Ginet 1982)—that is, it contains an adverbial gap. It also seems to be true in the general case. One reason is crosslinguistic morphological evidence for the unity of complement and adjunct extraction, presented in Hukari and Levine (1995). The other reason is based on semantics, and specifically on the two readings possible in a phrase such as why Robin said Kim left . In one reading, why asks about Robin’s saying something (i.e. why scopes over say ); in the other, why asks about Kim’s leaving (i.e. why scopes over left ). In a type-logical grammar, Robin said Kim left can be derived as an S with an adverbial gap in two different ways, one with semantics λA. A(say′(leave′(k′)))(r′), and one with semantics λA.say′( A(leave′)(k′))(r′) . The first term gives A scope over say, and the second gives it scope over left . When combined with the semantics for why, the two different scopes for A naturally give rise to the corresponding different readings of the why Robin said Kim left . However, if Robin said Kim left is parsed as an S with no gap at all, the only semantics for it is say′(leave′(k′))(r ′), with no clear means of generating the different scopings of why. Therefore, the position taken in this dissertation is that adverbial wh words take complements with an adverbial gap. In addition to where, when, how, and why, for purposes of this chapter, the embedded question markers whether and if will also be referred to as adverbial wh words. Even though they take as their complements sentences with no gap at all, for the most part these are the same as those which can be parsed as having an adverbial gap,16 and it will be more convenient to refer to “adverbial wh words” than “ wh words whose complement does not contain an NP gap.” Two Internet-attested examples of optional NP-gap MWIs are shown in (89), with the transitiveintransitive verbs eat and teach . 16. Sentences with no gap and sentences with an adverbial gap are not entirely the same set, since a phrase such as Kim phrased the letter contains an adverbial gap, but does not qualify as a complete sentence.

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Page 77 (89)Examples of optional NP-gap mixed- wh interrogatives a.You will learn to become a food detective and control what and when you eat. (repeated from (87)) b.The Standards don’t tell teachers how or what to teach. Now that optional NP-gap MWIs have been defined, the corpus search for them can be described; the psycholinguistic evidence presented; and the type-logical analysis developed. 3.2.1 Corpus Search The search for optional NP-gap MWIs wa s conducted as follows. Between October 2000 and February 2001, the Internet search engine AltaVista was used to search for strings in the following sets:17

These two sets contain 108 strings (6*2*4+5*2*6). of Every cat meows Though it is possible to search for all these strings at once by using Boolean operators, the strings were searched for individually. The reasoning behind this choice was as follows: The all-at-once search might return hundreds of hits, and inspecting each of them for the entire set of wh coordinations would be prohibitive. But if not all of them were inspected, and one of the wh coordinations was much more frequent than 17. Thanks go to Chris Barker (2000) for suggesting that whether/if be included in the search.

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Page 78 the others, MWIs involving other wh coordinations could be missed. On the other hand, with individual searches, the same maximum number of hits can be inspected for each wh coordination, decreasing the likelihood of more frequent wh coordinations hiding the less frequent ones. Therefore, the searches were performed individually. To ensure that all strings were eventually searched for in the available time, only the first ten hits for each search were inspected; in other words, breadth was favored over depth. For each hit, the “view source” feature was used to see the page’s source text, which was then searched for the relevant string by using the search feature in the Edit menu. Sometimes it happened that the string was not part of a MWI; for example, what and when might occur in Something happened, but I don’t know what. And when I found out. …Also, sometimes the strings were parts of elliptical titles, as in The why, what, and when of motorcycle maintenance. And in some cases, for whatever reason, the string could not be found in the source text at all. Even when true MWIs were found, not all of them were collected. Attestations from sites that seemed to be written by nonnative English speakers were discarded. Also discarded were the MWIs in which the wh words were separated by commas, dashes, or parentheses, for example, We want to know what (and when) they eat. This was done because material that would otherwise be ungrammatical can sometimes be inserted parenthetically into a larger phrase, and the aim was to find MWIs that were not obviously parenthetical phrasings. However, when a qualifying sentence was found, it was added to the list of attestations. Finally, several attestations seen in the newspaper or heard on the radio during this time were also included. The results were surprising, because in addition to many attestations of optional NP-gap mixed- wh interrogatives (such as those shown in (89)), in which each of the wh words was separately construable with the body of the interrogative, there were also MWIs in which one or the other of the wh words was not construable with the body of the interrogative. Examples of each are shown in (90), with the earlier examples of optional NP-gap MWIs repeated in (90a) for easier comparison. In some cases, the body of the interrogative had to be parsed as having an NP gap. This might be an object gap following an exclusively transitive verb (as in (90b.i)) or a stranded preposition (as in (90b.ii)), or it might be a subject gap (as in (90c)). In these cases, it is the adverbial wh word that does not seem to fit, indicated by the underlining. These kinds of MWI will be referred to as OBLIGATORY NP-GAP MIXED- WH INTERROGATIVES. In other cases, the body of the interrogative could not be parsed as having an NP gap at all, as in (90d). In these cases, the nominal wh word is the odd one, indicated by the underlining. These kinds of MWI will be referred to as MISSING NP-GAP MIXED- WH INTERROGATIVES. A complete list of attestations resulting from the above search appears in Appendix A, with

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Page 79 Optional NP-gap MWIs in section A.1, obligatory NP-gap MWIs in section A.2, and missing NP-gap MWIs in sections A.3. (90)Different kinds of MWIs, attested on the Internet a. Optional NP-gap (repeated from (89)) i. You will learn to become a food detective and control what and when you eat. ii.The Standards don’t tell teachers how or what to teach. b.Obligatory NP-gap (object gap) i. She was very concerned that she didn’t know how or what to say. ii.You find out everything about someone: who their friends are, what their opinion is on a wide range of matters, whether and who they are having sex with, the full range of som[e]one’s activities and emotions. c. Obligatory NP-gap (subject gap) i. Does anyone have any idea where or who would be able to locate parts? ii.It is not known exactly why or who burned the village. d.Missing NP-gap i. So who or why would you even need this thing. ii.However, due to the nature of dating historical facts, there are opinions and disagreements as to who or when the actual event took place. Before going further, some remarks about missing NP-gap MWIs are in order. Most of the people who have seen these attestations are convinced that the missing NP-gap MWIs are errors, pure and simple. Even if they find optional and obligatory NP-gap MWIs not fully grammatical, they find the missing NPgap MWIs much worse. One could also cite as corroborating evidence the fact that whereas the meaning of optional and obligatory NP-gap MWIs is predictable, the meaning of missing NP-gap MWIs often depends much more on context (see discussion in section 3.2.3.5). In fact, the prescriptivist in me is quite sympathetic to the idea of missing NP-gap MWIs as errors. Nevertheless, since missing NP-gap MWIs were found in comparable numbers to the other kinds, it will be assumed that they are grammatical for at least some speakers. These three kinds of MWI are schematized in the templates in (91). The wh coordinations in the schemata are represented by a sample coordination in each template, with what standing for nominal wh words, when for adverbial wh words, and and for coordinating conjunctions. Type-logical categories have

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Page 80 been used for compactness of representation in showing the gap categories in the bodies of the interrogatives. (91) Templates for different kinds of mixed- wh interrogative a. Optional NP-gap i. {what and when, when and what} Example: what and when you eat ii. {what and whether, whether and what} Example: whether and what you eat b. Obligatory NP-gap (object) i. when and what +(S/NP) Example: when and what you take ii. whether and what +(S/NP) Example: whether and what you take c. Obligatory NP-gap (subject) i. when and what+(NP\S) Example: when and what scared Kim ii. whether and what +(NP\S) Example: whether and what scared Kim d. Missing NP-gap i. what and when+(S/(S\S)) Example: what and when you need this ii. what and whether +S Example: what and whether you need this In addition to the above three kinds of MWI, there were also MWIs involving the copula, as in Who and where are you? These can be found in section A.5 of Appendix A. However, it can be argued (and will be, in Chapter 5) that in such a sentence, who and where actually have the same category, and that the sentence is therefore not a MWI. For this reason, these COPULAR MIXED- WH INTERROGATlVES are not discussed in this chapter. The existence of obligatory NP-gap and missing NP-gap MWIs calls into question the need for a neutrality-based analysis of optional NP-gap MWIs. It was claimed earlier that an analysis of (87) would have to hinge on the fact that eat could be both transitive and intransitive; otherwise, the phrase you eat would not be able to combine with both when and what . Implicit in this claim was the assumption that the interrogative would be well-formed only if each of the wh conjuncts individually could combine with the factor you eat into a well-formed sentence, an instantiation of what Pullum and Zwicky (1986) have dubbed Wasow’s Generalization. (Recall that the factor in a coordinate structure is the material that does not appear in the conjuncts.) However, the interrogatives in

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Page 81 (90) show that Wasow’s Generalization is subject to exception with regard to wh interrogatives. In fact, a neutrality-based analysis of optional NP-gap MWIs is at a tremendous disadvantage now, accounting as it does for only one out of three classes of MWI under discussion. By contrast, without referring to neutrality at all, one could neatly summarize the data thus far just by noting that the odd wh words in (90) are never adjacent to the body of the interrogative, and positing a rule stating that any wh word can be coordinated with a well-formed wh interrogative to yield another well-formed wh interrogative. Such an analysis is similar to the one proposed by Giannakidou and Merchant (1998) for obligatory NPgap mixed- wh interrogatives in Greek; they take them to be generated by a rule similar to the one that licenses sluicing. That is, in their analysis, a Greek sentence parallel to why or who burned the village would be analyzed in much the same way as who burned the village, or why. For this reason, they propose the name REVERSE SLUICING for this kind of construction.18 Though they assume that obligatory NP-gap mixed- wh interrogatives like this one are ungrammatical in English, their analysis could probably be altered to allow English grammars to license them. Under the reverse sluicing analysis outlined above, in an obligatory NP-gap MWI, the nominal wh word appears adjacent to the body of the interrogative, while the odd adverbial wh word is nonadjacent to it. This can be seen in those with an object gap: how or what to say in (90a.i), and whether and who they are having sex with in (90a.ii). It also holds true in those with a subject gap: where or who would be able to locate parts in (90b.i), and why or who burned the village in (90b.ii). Conversely, in a missing NP-gap MWI, the adverbial wh word appears adjacent to the body of the interrogative, while the odd nominal wh word is nonadjacent. This pattern can be observed in who or when the actual event took place in (90c.i), and who or why would you even need this thing in (90c.ii). In an optional NP-gap MWI, either a nominal or an adverbial wh word works equally well adjacent to the body of the interrogative, which can be 18. Reverse sluicing is not entirely parallel to ordinary sluicing, as seen in the following contrast: (a) I don’t know whether or who they are having sex with. (reverse sluicing) (b) *I don’t know who they are having sex with, or whether. (ordinary sluicing) Overall, though, the name is intuitively clear.

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Page 82 parsed both with and without an NP gap. Thus, it would be expected that nominal or adverbial wh words would appear adjacent to the body of the interrogative in approximately equal numbers. An example of each was seen in (89); in (89a), what and when you eat has the adverbial wh adjacent to the body of the interrogative, while in (89b), how or what to teach has the nominal what in that position. The pattern seen in the selected examples is true for the set of attestations as a whole. Table 1 shows that among optional NP-gap MWIs, the nominal and adverbial wh words appear adjacent to the body of the interrogative in approximately equal numbers, while for obligatory NP-gap MWIs, the nominal wh word is adjacent 39 out of 43 times, and for missing NP-gap MWIs, the adverbial wh word is adjacent 35 out of 35 times.19 Kind of mixed- wh interrogative Total attestations wh word adjacent to body of interrogative nominal adverbial Optional NP-gap 51 28 23 Obligatory NP-gap 43 39 4 Missing NP-gap 31 0 31 Table 1 Ordering of wh words in three kinds of mixed-wh interrogatives Thus, the data are mostly consistent with the reverse sluicing analysis, in which any well-formed wh interrogative is coordinated with another wh word, which appears in front of it. Why should such a pattern exist? It might be that MWIs are actually not generated by the grammar, but when the odd wh word appears farther away from the body of the interrogative, it has been forgotten by the time the rest of the interrogative has been parsed; in other words, the acceptability of MWIs is a performance effect. Such a hypothesis is supported 19. Not counted in these totals are the attestations in the “supplementary” sections, in which a wh phrase (e.g. which things) appears instead of what or who(m). This is because, given the way the search was conducted, all such phrases that are found will never be the first wh conjunct—for instance, the phrase where and which things would be found in a search for the string “where and which,” but which things and where would never be found in a search for the string “which and where.”

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Page 83 by existing psycholinguistic evidence showing that speakers tend to remember the content of an utterance while forgetting the actual words spoken. In any case, since the reverse sluicing analysis captures almost all the data instead of just the cases of optional NP-gap, it should be favored, unless there is some other reason to believe that optional NP-gap MWIs require an analysis different from that for MWIs in general. Such evidence will be shown in the next section, where results from the psycholinguistic experiment are discussed. 3.2.2 Psycholinguistic Experimental Data If optional NP-gap and other mixed- wh interrogatives are generated by the same grammar rule, then (all other things equal) speakers’ grammaticality judgments for the two kinds of sentences should be approximately the same. However, experimental results to be discussed in this section show that this is not the case. 3.2.2.1 Procedure Questionnaires were constructed, in accordance with guidelines given in Chapter 9 of Cowart (1997), to test the difference between speakers’ grammaticality judgments of optional NP-gap MWIs and similar obligatory NP-gap MWIs. Each questionnaire consisted of 40 sentences, eight of which were the experimental items, and the other 32 of which were fillers of varying grammaticality (including nine that were straightforwardly grammatical). The experimental items were (or contained) MWIs introduced by a binary coordination of nominal wh word and adverbial wh word (either where, when, how, or why). Four of these eight were (or contained) optional NP-gap MWIs; four of them were (or contained) obligatory NP-gap MWIs. Within each of these sets of four, two items had the adverbial wh word as the first conjunct, and two items had the adverbial wh word as the second conjunct. Thus, there were four kinds of experimental item, each of which appeared twice per questionnaire: optional vs. obligatory NP-gap, adverbial wh first vs. second. A sample token set illustrating the four possibilities is given in (92), in which the template [_] can I [_]? is filled out with either When and what or What and when, and the verb eat or do. Since the (optional) gap in optional NP-gap MWIs is always an object gap, the parallel obligatory NP-gap MWIs have only object gaps.

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Page 84 (92) Sample token set for mixed- wh questionnaire a. When and what can I eat? (optional NP-gap, nominal adjacent) b. What and when can I eat? (optional NP-gap, adverbial adjacent) c. When and what can I do? (obligatory NP-gap, nominal adjacent) d. What and when can I do? (obligatory NP-gap, adverbial adjacent) Eight such token sets were constructed with different verbs, and shuffled and distributed into four “preliminary scripts” (i.e. sets of experimental items). Each preliminary script was combined with the 32 filler items to form a script, and each script was put into two orders, so that there were eight versions of the questionnaire. The token sets, preliminary scripts, and filler items are listed in Appendix B. Each version of each questionnaire was filled out by at least two informants, so that N ≥16. (In actuality, N =18.) Informants were native English speakers in undergraduate linguistics classes at Ohio State University during the fall quarter 2001. They were instructed to rate each item, as quickly and accurately as possible, on a scale of 1 through 5, with 5 indicating an item was “completely normal and acceptable,” and 1 indicating an item was “very odd, awkward, or difficult for you to understand.” Before results are discussed, it should be noted that the questionnaires did not contain any missing NPgap MWIs. The reasoning behind this exclusion was as follows: If it is not the case that a single grammar rule generates all three kinds of MWIs, then there are four possible groupings, illustrated in Figure 4. In these diagrams, the different kinds of MWIs are abbreviated as “optional,” “obligatory,” and “missing,” and the kinds within the same circle are generated by the same rule. If two kinds of MWI are generated by the same rule, then a speaker’s grammar should license one iff it licenses the other. If not, then a speaker’s grammar may license one kind without licensing the other, or it may license both kinds or neither kind, depending on which of the rules (if any) are in the speaker’s grammar.

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Figure 4 Possible groupings of different kinds of mixed-wh interrogatives Figures 4c and 4d do not represent plausible groupings. Turning first to Figure 4c, the question is what kind of rule would generate both optional and obligatory NP-gap MWIs while excluding missing NP-gap ones. The rule cannot be to conjoin any wh word with a well-formed wh interrogative, as this is the very rule proposed to cover all three kinds of MWIs, and would fail to exclude missing NP-gap interrogatives. The rule cannot be to conjoin any adverbial wh word with a well-formed wh interrogative, as this rule would predict that in optional NP-gap MWIs, only the adverbial wh could come first. Optional and obligatory NP-gap MWIs simply do not form natural class, as far as I can see. Similarly, the optional and missing NP-gap grouping in Figure 4d does not form any apparent natural class. At this point, only Figures 4a and 4b are left, and in each of them, the optional NP-gap MWIs are generated by a different rule than the one that generates obligatory NP-gap MWIs. If either of these diagrams accurately reflects the status of the three kinds of MWIs, then we can predict that there will be speakers whose grammars license optional NP-gap MWIs while rejecting obligatory NP-gap ones. (It further predicts that speakers with both rules will have two ways of parsing optional NP-gap MWIs, one via the rule specific to optional NP-gap cases, and the other via the rule for obligatory or missing NPgap MWIs.) Which of these two cases is more likely is not of concern in this dissertation; what is of concern is whether optional NP-gap MWIs need a separate analysis. Therefore, it will not be necessary to compare grammaticality judgments for optional NP-gap interrogatives with judgments for both obligatory and missing NP-gap interrogatives: Proving a significant difference between optional NP-gap interrogatives and either of the two others will be

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Page 86 sufficient to show that optional NP-gap MWIs should be analyzed separately from other kinds. Which class of MWIs is chosen for comparison makes no difference; for this experiment, obligatory NP-gap MWIs were chosen because of their apparently higher acceptability, as mentioned earlier. 3.2.2.2 Result: Optional NP-Gap MWIS Clearly Distinguished Results of the questionnaires are shown in Figure 5, in which higher scores indicate higher acceptability. Scores have been converted to z-scores (standardized scores), so that the mean rating for each informant is 0, and the standard deviation for each informant is 1.

Figure 5 Different acceptability of optional NP-gap and obligatory NP-gap mixed-wh interrogatives The most obvious effect seen here is the effect of the ordering of the nominal and adverbial wh in obligatory NP-gap MWIs: These interrogatives are much less acceptable when the nominal wh word is not adjacent to the body of the interrogative, with a mean acceptability rating of −0.25. This finding accords well with the pattern seen in the Internet attestations, where the nominal wh word was adjacent to the body of the interrogative 39 out of 43 times. On the other hand, it can be seen that the ordering of the nominal and adverbial wh has no significant effect on acceptability in optional NP-gap MWIs. This finding,

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Page 87 too, mirrors the pattern seen in the Internet attestations, where 27 attestations had one order, and 31 had the other. However, the most important finding is one that the corpus data do not show: When the nominal wh word is adjacent to the body of the interrogative, obligatory NP-gap MWIs are still less grammatical (0.29) than optional NP-gap ones (0.68). To calculate the significance of this difference, a repeatedmeasures by-subject analysis of variance (ANOVA) was performed on just the adverbialfirst items using SPSS software, and p (the probability that this difference could happen by chance if optional NP-gap MWIs were only a special case of obligatory NP-gap ones) was found to be .001. A similar univariate byitem ANOVA also yielded a probability of .001. Therefore, experimental results strongly support the hypothesis that optional NP-gap and NP-gap MWIs are different phenomena. Nonetheless, the fact that optional NP-gap MWIs have a higher mean score than NP-gap ones does not necessarily mean they are grammatical. That is, a given speaker may find all MWIs ungrammatical, but nevertheless like optional NP-gap ones better than obligatory NP-gap ones. This could well be the case, since the mean score for the completely grammatical filler sentences was 1.29, far above 0.68 or 0.70. The question that arises, then, is how wide a distribution this score for optional NP-gap MWIs has. Do all speakers have approximately this rating, or are there some for whom these interrogatives are completely grammatical? To judge whether a given speaker’s mean score for optional NP-gap MWIs indicated that they were grammatical in his/her grammar, it was compared to his/her mean score for the grammatical filler sentences. Specifically, if it was within one standard deviation of the mean score for grammatical fillers, I concluded that the speaker found optional NP-gap MWIs to be grammatical. The results of this comparison are shown in Table 2. The mean scores for optional NP-gap MWIs are given in the second column; mean scores for the grammatical fillers, in the third. The standard deviation for the grammatical fillers appears in the fourth column; the difference between it and the mean score for the grammatical fillers is shown in the column labeled “threshold.” If the mean score for the optional NP-gap MWIs meets or exceeds this threshold (i.e., if it is within one standard deviation of the mean score for grammatical fillers), a “yes” appears in the last column. Among the 18 informants, there were four (3, 36, 32, 6) whose mean score for MWIs fell within one standard deviation for their scores for the grammatical filler items. In fact, one informant’s mean scores for the two kinds of items were identical (1.14 for informant 3). Looking further down the table, there are four informants (9, 19, 11, 1) whose scores for the grammatical fillers were so uniform (i.e., all 5’s) that

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Page 88 the standard deviation is 0.20 With such little leeway, the only chance for optional NP-gap MWIs to meet the threshold was for each of them to receive the same score as all the grammatical fillers received. However, each of these four informants gave three out of four of the optional NP-gap MWIs they saw a 5; in other words, there was a clear mode that met the threshold requirement, even though the mean score did not. Therefore, these four informants deserve to be included with the previous four whose scores met the threshold. Overall, then, almost half of the informants seemed to find optional NP-gap MWIs grammatical. To the extent that the sample here represents the population at large, there is a significant population of speakers for whom optional NP-gap MWIs are grammatical. 20. Informant 40 is asterisked because one of his/her filler sentence scores was thrown out. All eight other grammatical fillers were rated 5, while one of them was rated 2. This single result, so different from the other grammatical fillers, on a filler that was rated highly by all other informants, was deemed an anomaly.

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Page 89 informant mean for optional NP-gap mean for grammatical σ for grammatical threshold threshold MWI fillers fillers met? 3 1.14 1.14 0 1.14 yes 36 1.08 1.27 0.33 0.95 yes 32 1.03 1.28 0.42 0.86 yes 6 0.71 1.25 0.57 0.68 yes 9 19 11 1

1.27 0.97 0.91 0.91

1.41 1.4 1.06 1.08

0 0 0 0

1.41 1.4 1.06 1.08

no no no no

30 0.84 1.37 0.2 1.17 no 13 0.72 1.21 0 1.21 no 40* 0.52 1.3 0 1.3 no 5 0.48 1.24 0.32 0.91 no 37 0.47 1.6 0.28 1.32 no 33 0.42 1.48 0.45 1.03 no 28 0.37 1.32 0.23 1.09 no 14 0.37 1.29 0 1.29 no 31 0.19 1.17 0.35 0.83 no 29 0.06 1.62 0.41 1.21 no Table 2 Comparison of mean scores for optional NP-gap mixed-wh interrogatives and grammatical filler sentences The next question to consider is whether there are (as predicted) any speakers who accept optional NPgap MWIs but reject obligatory NP-gap ones. To determine the answer, speakers’ mean scores for obligatory NP-gap MWIs (with the nominal wh adjacent to the body of the interrogative) were compared with their mean scores for the grammatical fillers. The comparison was done in precisely the same way as the previous one; results are shown in Table 3. It can be seen here that only one informant (number 11) found obligatory NP-gap MWIs grammatical. (Unlike in Table 2, the informants with a standard deviation of zero for the grammatical fillers in this table did not have a clear mode that met the threshold.) As can be verified with reference to Table 2, this informant

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Page 90 also found optional NP-gap MWIs grammatical; therefore, there were seven informants (3, 36, 32, 6, 9, 19, 1) who found optional NP-gap MWIs grammatical, but found obligatory NP-gap ones ungrammatical, or at least less grammatical. informant mean for obligatory NP-gap mean for grammatical a for grammatical threshold threshold MWI fillers fillers met? 11 1.06 1.06 0 1.06 yes 5 0.81 1.24 0.32 0.91 no 1 0.74 1.08 0 1.08 no 40* 0.68 1.3 0 1.3 no 13 0.56 1.21 0 1.21 no 14 0.55 1.29 0 1.29 no 19 0.54 1.4 0 1.4 no 3 0.39 1.14 0 1.14 no 28 0.37 1.32 0.23 1.09 no 36 0.31 1.27 0.33 0.95 no 29 0.22 1.62 0.41 1.21 no 6 0.12 1.25 0.57 0.68 no 33 0.1 1.48 0.45 1.03 no 31 0.02 1.17 0.35 0.83 no 32 0 1.28 0.21 1.07 no 30 –0.06 1.37 0.2 1.17 no 37 –0.47 1.6 0.28 1.32 no 9 –0.74 1.41 0 1.41 no Table 3 Comparison of mean scores for obligatory NP-gap mixed-wh interrogatives (with nominal wh word adjacent to body of interrogative) and grammatical filler sentences If the seven informants who found optional (but not obligatory) NP-gap MWIs grammatical had a means of licensing the former that did not license the latter, the patterns seen in the data are neatly explained. Thus, motivation seems to exist for a separate analysis of optional NP-gap MWIs, based on native speaker grammaticality judgments. In the next section, such an analysis will be developed.

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Page 91 3.2.3 Analysis of Optional NP-Gap Mixed-Wh Interrogatives The first part of the analysis of optional NP-gap mixed- wh interrogatives will be to specify the semantics of interrogatives in general. In this dissertation, the denotation of an interrogative will be taken to be a set of propositions that could answer the question the interrogative asks. Thus, the denotation of an interrogative will have type Prop→Bool. Following Carpenter (1997), the category S y will be used for yes/no questions, and S w for wh questions; Typ(Sy)=Typ(Sw)=Prop→Bool. Embedded questions will map to the same type, but will be labeled with the category S eq (mnemonic for embedded question). Optional NP-gap MWIs will be analyzed in the same way as interrogatives with coordinated wh elements of like categories, such as where and when did this happen?, or what or whom did you see? The only difference is that the neutral categories for certain verbs will allow coordinations of wh words that have unlike categories, such as where and what, or whether and who. However, before the semantics of wh coordinations can be discussed, the semantics of conjoined interrogatives needs to be specified. Therefore, section 3.2.3.1 will cover the semantics of conjoined interrogatives; section 3.2.3.2 will present the derivation of an ordinary conjoined- wh interrogative; and section 3.2.3.3 will show how this analysis extends naturally to license optional NP-gap MWIs when verbs are allowed to exhibit category neutrality. Section 3.2.3.4 gives a lexical rule that will allow the relevant verbs to have this category neutrality; section 3.2.3.5 presents further thoughts on the semantics of MWIs. 3.2.3.1 Semantics of Conjoined Interrogatives Recall that to allow for conjoined interrogatives, the following clause was included in the definition of Coorσ, the polymorphic function introduced in Chapter 2 as the semantics for coordinating conjunctions: (93) CoorProp→Bool(α)(β1)(β2)=α(β1)(β2) This clause allows the semantics of a conjoined interrogative such as When did Kim arrive and where did she go?, shown in (94a), to be rewritten as (94b). The question now is how to get from (94b), where and applies to two sets of propositions, to (94c), a single set of propositions. The substitution used for the simple case of coordinated propositions (i.e., cannot be used here, since the logical connective is appropriate only for propositions, not for sets of propositions.

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Page 92 (94) Semantics for When did Kim arrive and where did she sit? a. CoorProp→Bool(and) b. (and) c. (DESIRED) To get an interpretation for conjoined interrogatives, the strategy stated in Groenendijk and Stokhof (1997:1008) will be followed: “By simply conjoining the possible answers to two interrogatives, we obtain the propositions that answer their conjunction.” This interpretation is formalized for and in (95). In (96), it is shown how this definition of and converts (94b) into the desired (94c). (95)Definition of and: (Prop→Bool)→(Prop→Bool)→(Prop→Bool)

(96) The interpretation of interrogatives conjoined by or will be somewhat different. Instead of a conjoined proposition, in which one conjunct is a possible answer to one of the two interrogatives, and the other is a possible answer to the other interrogative, the interpretation will be taken to be the union of the possible answers to both interrogatives. Thus, for example, the interpretation of when Kim arrived or where she sat (disregarding the side conditions on x and y) would be This interpretation is formalized in (97). (97) Definition of or: (Prop→Bool)→(Prop→Bool)→(Prop→Bool) With these definitions in place, ordinary conjoined- wh interrogatives can be derived, as will be demonstrated in the next section.

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Page 93 3.2.3.2 Derivation of an Ordinary Conjoined- Wh Interrogative For simplicity’s sake, the conjoined- wh interrogative to be derived will be one without subject-auxiliary inversion: where and when this happened . This embedded (noninverted) interrogative has been chosen in order to simplify the derivation. To begin, categories and terms will be required for where and when; these are shown in (98). The argument category for each is S/(S\S), a sentence containing an adverbial gap. The result category for each is S eq, since the categories needed here are those that project an embedded question. (Similar definitions can be written for wh words that introduce nonembedded interrogatives.) (98) Categories and terms for where and when where: when: At this point, where and when this happened can be derived. The first step will be to conjoin where and when, as seen in (99). In this derivation, the terms for where and when have been simplified by omitting the place′(y) and time′(y) subterms. The logical equivalencies at the bottom of the derivation come from the revised definition of and in (95). (99) Coordinating where and when; X=Seq/(S/(S\S));

The final step is to combine where and when with this happened, as is done below.

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Combining where and when with this happened

The ultimate term that is derived for where and when this happened is the same as would be derived for where this happened and when this happened, as can be seen in the derivation in (101). This result is in line with my semantic judgments of the two interrogatives. (101) Coordinating where this happened and when this happened; X= Seq

The same kind of derivation that licenses where and when this happened will also license optional NPgap MWIs such as what and when you eat, the only further assumption being that eat can have category Such derivations are the focus of the next section. 3.2.3.3 Derivation of Two Optional NP-Gap MWIs The first optional NP-gap mixed- wh interrogative to be derived will be what and when you eat. The categories and terms for what and when will be as in (102). (Here, the category given for what is appropriate for nonsubject extraction.)

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Page 95 (102)

Categories and terms for what and when what: when: The next step is to coordinate what and when. This is done in much the same way as coordinating where and when earlier. In this derivation, however, both what and when are assigned the category via Antecedent Strengthening (ASt, discussed in Chapter 2) before they are coordinated. (103) Coordinating what and when; a. Syntactic only

b. Syntactic and semantic;

The phrase you eat will need to be derived as category so that it can serve as the argument to what and when. This can be done if eat is assigned the category and term in (104). The derivation of you eat is shown in (105); as it makes use of the rule of introduction (or rule of proof) for the

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Page 96 conjunction constructor introduced in Chapter 2, it is presented in Gentzen sequent style. (104) eat: (105) Deriving you eat as category

The final step is to combine what and when with you eat, as done below. (106) Combining what and when with you eat

The ultimate term that is derived for what and when you eat is the same as would be derived for what you eat and when you eat, as can be seen in the derivation in (107), in just the same way as where and when this happened was semantically equivalent to where this happened and when this happened in the preceding section.

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Page 97 (107) Coordinating what you eat and when you eat; X=S eq

In addition to the reading just derived, there is at least one other possible reading for optional NP-gap MWIs for some speakers. Specifically, this is the reading paraphrasable as what you eat and when you eat IT . However, discussion of this other reading will be deferred until section 3.2.3.5. At this point, the second example of an optional NP-gap MWI will be derived. Instead of containing an adverbial wh, this one contains the polar-interrogative complementizer if: (108) [I] don’t know if or who she married. (Internet attestation) To derive (108), married will be given a category with the appropriate ordered-pair semantic term; and if will be defined as in (109). The term is the set of all propositions p such that p is either the proposition or its negation—the two possible answers to a polar interrogative. (109) whether/if: The coordination if or who will be derived as having category in the same way as when and what was derived; the derivation is shown in (110). (As with what in the earlier derivation, who appears here with a category appropriate for nonsubject extraction.)

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Coordinating if and who; a. Syntactic only

b. Syntactic and semantic;

She married will be derived as having category in the same way as you eat was derived as except that no adverbial argument will need to be introduced. If or who and she married are combined in the derivation in (111). The final term is the set of all propositions p such that p is an answer to if she married (i.e. or or an answer to who she married (i.e., p =marry′(x)(she′)).

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Combining if or who with she married

For each of the two optional NP-gap MWIs just derived, the only assumption was that the verb was assigned to multiple categories, namely VP/NP and VP, with an ordered-pair semantic term. Everything else followed from the Lambek calculus and an extension of the interpretations of and and or suitable for interrogatives, which was necessary in any case. 3.2.3.4 Lexical Rules for Verbs in Optional NP-Gap MWIs In the derivations of the previous section, the verbs eat and marry were summarily given the category This category will need to be given to many other verbs exhibiting this very productive alternation (referred to as the unspecified object alternation in Levin (1993)), and all of them will have a term of form However, it is undesirable to give so many verbs the same conjoined category in the lexicon, with the same semantic relation holding between the elements of their orderedpair terms, without stating some kind of rule about it. To do so would be essentially to say that this similarity in categories and terms is a coincidence, and would miss a generalization. In fact, the unspecifled object alternation is usually described by a lexical rule, and this is the approach that will be used here. Such a rule was given in (76) in Chapter 2, and applied to eat in (77), which is repeated below as (112): (112) Lexical rule for unspecified object alternation applied to eat At this point, the issue of ambiguity vs. neutrality arises. If, as discussed in Chapter 2, there is no formal distinction between the two, then nothing further need be said about eat. If the triples and are each members of Lex, then the frame semantics guarantees that is a member of Lang, the desired state of affairs. On the other hand, if a formal distinction

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Page 100 between ambiguity and neutrality is maintained, then some means will have to be found whereby the two separate lexical entries for eat described by this lexical rule can give rise to a category-neutral form of eat. No such means will be proposed here, but the problem will need to be addressed if ambiguity and neutrality are to be formally distinguished in a TLG. 3.2.3.5 More on the Semantics of MWIs In section 3.2.3.3, what and when you eat was derived to have the same semantics as what you eat and when you eat. Under this reading, an answer to what and when you eat could be thought of as two lists, one of them a list of things that you eat, and the other a list of times when you habitually take your meals. (These times and things correspond to the x and y variables in the final term in the derivation.) There would not necessarily be any mapping between these lists, such that particular items of food correspond to particular times; the lists would be independent of each other. (In other words, this reading is not a pair-list reading.) For this reason, this reading of an optional NP-gap MWI will be referred to as an INDEPENDENT QUESTIONS (IQ) reading. However, it was mentioned in section 3.2.3.3 that at least one other reading is possible for optional NPgap MWIs. For some speakers, a more accurate expansion of what and when you eat would be what you eat and when you eat IT (or when you eat something, and what IT is). In this way, this interrogative is closer semantically to the analogous multiple-wh interrogative what you eat when, or sluiced interrogative what you eat, and when. In fact, this is the reading that Giannakidou and Merchant (1998) have for the reverse sluicing interrogatives in Greek. This reading is a pair-list reading: An answer could be thought of as a list of pairs, each of which contains an item y that you eat, and a time x at which you eat y. This reading will be referred to as a DEPENDENT QUESTIONS (DQ) reading. The IQ and DQ readings are compared in (113). Notice that in (113b), the y appears in both conjuncts of the proposition p, indicating the semantic dependency between them. (113) IQ and DQ readings for what and when you eat a. IQ reading b.

DQ reading

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Page 101 The type-logical analysis for optional NP-gap MWIs will not generate a DQ reading for them. Nor will it generate a DQ reading for obligatory NP-gap MWIs, since the analysis does not cover these at all. Though further investigation needs to be done for confirmation, I suspect that the DQ reading of an optional NP-gap MWI exists only because optional NP-gap MWIs look on the surface like a special case of obligatory NP-gap MWIs. That is, a speaker whose grammar licenses obligatory NP-gap MWIs will have DQ readings for them, as well as for optional NP-gap MWIs, since are structurally ambiguous between the two kinds of MWI. Moreover, if a speaker also has a separate rule generating optional NPgap MWIs, then s/he will have IQ readings for them in addition to the DQ readings. On the other hand, if a speaker’s grammar licenses only optional NP-gap MWIs, then s/he should have only an IQ reading for them. These predictions have not been tested, but have some tentative anecdotal support. For example, one speaker who accepted what and when you eat as completely normal while rejecting obligatory NP-gap MWIs emphatically judged it to have an IQ reading, and dismissed the DQ reading entirely when asked about it. Further research on this issue will have to carefully control for pragmatic influences, since even if there is a built-in IQ semantics for optional NP-gap MWIs, and a built-in DQ reading for sluiced interrogatives, context can sometimes force a DQ reading for an optional NP-gap MWI, or an IQ reading for a sluiced interrogative. For an example of the former, in the context of a discussion of a diet, it would be quite natural to assume that the items eaten and the times are linked, since many diets recommend eating particular things at particular times of the day. For an example of the latter, Carl Pollard (p.c.) notes that an IQ reading is more plausible for (114) in a context in which the speaker is commenting on a coworker who never seems to leave the office: (114) I don’t know what he eats, or when. Semantics also point to a difference between obligatory NP-gap MWIs and missing NP-gap MWIs. Whereas obligatory NP-gap MWIs (judging from the context of the attestations) always seem to be paraphrasable as multiple- wh interrogatives or sluiced interrogatives, this is not always the case for missing NP-gap interrogatives. In some cases, a DQ reading seems reasonable if the nominal wh is understood to replace some NP in the factor; for example, the most plausible reading in (115a) seems to be, “who would need this, and why would s/he need it?” That is, the who replaces the you, and the sentence is in essence recast as an obligatory NP-gap MWI: Why or who would need this thing? In other cases, though, a sensible reading depends much more on the

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Page 102 context. For example, in (115b), my best guess is that the meaning is “who was involved, and when the actual event took place.” (115)Missing NP-gap mixed- wh interrogatives with different readings (repeated from (90d)) a.So who or why would you even need this thing. b.However, due to the nature of dating historical facts, there are opinions and disagreements as to who or when the actual event took place. It seems, then, that missing NP-gap MWIs are not interpreted in the same way as optional OR obligatory NP-gap MWIs. How best to interpret them is left as an open question. 3.2.4 Other Issues Optional NP-gap mixed- wh interrogatives offer strong evidence of category neutrality for certain kinds of verbs. The kind that has received most attention in this chapter has been verbs participating in the unspecified object transitivity alternation. The verbs exhibiting this alternation which can be found in section 1 of Appendix A are: buy, call back, celebrate, eat, foolproof, hire, immunize, judge, learn, love, marry, pack, pay, play, read, recycle, remember, report, ride, teach, test, think, write, and possibly speak. In addition, there are verbs exhibiting essentially the same understood object alternation, except that instead of involving strictly VP/NP and VP, the categories are of form (VP/ wNP)/NP prep21 and VP/NPprep, where prep indicates a prepositional marking, such as about, with, or for. These verbs are: know (about), negotiate (with), pay (for), and ditransitive pay (i.e., pay someone something vs. pay someone). However, in all the attestations that were found, was an unspecified object transitivity alternation the only kind of alternation that seemed to exhibit neutrality? There are other transitivity alternations—for instance, instead of an unspecified object, there could be an understood definite object (Levin 1993; also referred to as “pragmatically controlled zero anaphora” in Fillmore 1986). Giannakidou and Merchant (1998) create some optional NP-gap MWIs involving this alternation (specifically, in the verbs win and approve ), and label them as ungrammatical: 21. The /w constructor indicates a wrapping modality, which will be discussed further in Chapter 4.

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Page 103 (116) (from Giannakidou and Merchant 1998, (23)) a. *The runner was unsure if and what leg of the race he would win. b. *It’s anyone’s guess if and what the censors will approve. However, this alternation is attested in the corpus data, with the verbs ask, believe, call, join, resign, and win, as seen in (117). (117)Optional NP-gap mixed- wh interrogatives involving understood definite object, attested on the Internet a.How many such questions aren’t being asked by our students because, at those hours and under those deadlines, they simple don’t know how or whom to ask? b.I admitted then that I wasn’t sure what or whether I believed, or whether that even mattered. c. You never know who or when we may call. d.There is a new RC5 project competing with Bovine in Finland. I haven’t decided IF or WHICH I’ll join yet. e.In its simplest form, you just date the letter, say when and what you’re resigning, sign it, hand it over, and that’s about it. f. We will notify you if and which award you have won as well as include you on our Winners Circle. Another transitivity alternation is the understood reflexive object alternation (Levin 1993) exhibited by verbs such as shave or bathe. Giannakidou and Merchant construct an optional NP-gap MWI with these verbs, and judge them to be ungrammatical: (118) *I can’t remember whether or which patient he had bathed/shaved. (Giannakidou and Merchant 1998, (23c)) There are no attestations of these verbs in the corpus data in Appendix A, so the judgment above may indeed be true for all speakers. There are still other transitivity alternations, including causative alternations, and the middle alternation (as in Kim frightens easily ). None of the attestations involve these kinds of alternations, either. Moreover, transitivity alternations are not the only kind of argument alternations; others include the dative alternation (“Dative Shift”), the spray/load alternation, and the alternation between subjectless and specified-subject infinitives for verbs such as want . There is in fact one attestation for the dative alternation in the corpus data, with the verb send. In this example, who requires that send be parsed with its double-object subcategorization, while

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Page 104 where requires that it be parsed with its direct object-plus-oblique object subcategorization. (119) Who or where to send Songs? (Internet attestation) As for the spray/load alternation, an MWI would resemble the one in (120). Such attestations were not found, though, since with what and onto what was not one of the strings that was searched for. Judgments vary as to whether (120) is actually grammatical. (120) ?With what and onto what did they load the crates? The MWI in (121), suggested by Carl Pollard (p.c.) the who requires that want be parsed as taking an NP plus an infinitive as its complements, while the when requires that it be parsed as taking just an infinitive as its complement. No such attestations were found in the corpus search, although whom and when was one of the strings that was searched for. (121) ?Whom and when do you want to go? Finally, aside from the question of which argument alternations might appear in MWIs, there is the question of how neutrality of verb subcategorizations extends to declarative sentences. Even verbs participating in the understood object transitivity alternation, so widely attested in optional NP-gap MWIs, can sound horrible in a declarative, as illustrated in (122): (122) *John ate quickly and a grilled cheese sandwich. (Schachter 1977, (4)) These issues will be given the attention they deserve in Chapter 4, which is devoted entirely to neutrality and verbal argument alternations. For now, the conclusion is that category neutrality is definitely part of some speakers’ grammars when certain verb subcategorizations are considered. This concludes the discussion of optional NP-gap MWIs; the focus will now shift to plural-noun MWIs, the other main kind introduced at the beginning of this chapter. 3.3 Plural-Noun Mixed-Wh Interrogatives Plural-noun mixed- wh interrogatives are interrogatives headed by a coordination of an adverbial wh word or phrase and a wh determiner, as in the attested example in (123), repeated from (88).

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Page 105 (123) How does CM control when and whose transmissions occur? The adverbial wh words are where, when, how, and why, which require their complements to have an adverbial gap, as well as whether and if (as was done in the previous section). The wh determiners are what, which, and whose . These MWIs get their name from the fact that in many of the attestations, a plural noun, acting simultaneously as an N and an NP, seems to be what allows this kind of wh coordination to be viable. This can be seen with transmissions in the example above. At this point, the corpus search, psycholinguistic data, and type-logical analysis of plural-noun MWIs can be discussed. 3.3.1 Corpus Search The search for plural-noun MWIs was done concurrently with the search for optional NP-gap ones, with procedure as described in section 3.2.1. Sample attestations are shown in (124). It can be seen that mass nouns, such as work and legislation in (124b), exploit the same N-vs.-NP duality seen in plural nouns to form MWIs. The term PLURAL-NOUN MWI should be understood to refer to these mass-noun interrogatives as well. The full list of attestations of plural-noun interrogatives discovered in the search can be found in section A.4 of Appendix A.

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Page 106 (124)Examples of plural-noun MWIs, attested on the Internet a.With plural nouns i. How does CM control when and whose transmissions occur? ii.Senators Patty Murray (D-Wash) and Robert Toricelli (D-NJ) recently introduced the “School Environment Protection Act,” which among other things would require schools to notify parents when and which pesticides are being used at school. b.With mass nouns i. The final draft must be approved by the teacher who will also decide when, where and whose work will be displayed. ii.It is for Congress in the first instance to determin[e] whether and what legislation is needed to secure the guarantees of the Fourteenth Amendment; and its conclusions are entitled to much deference. c. With both Likewise, managed care organizations often make choices about whether and what equipment or prescription drugs will included in its plan benefits. Not all plural-NP MWIs are actually interrogatives. For example, (125) contains a relative clause instead of an interrogative.22 22. This example is particularly interesting on two counts, which are possibly related. First, this is the only attestation of a mixed- wh relative clause that was found. Second, the coordinated relativizers seem to correspond to the coordinated head nouns: where to areas, and whose to people. In other words, it is almost as if an understood respectively follows the phrase areas and people where and whose . Therefore, it is reminiscent of the phrase people who and robots which…from Dowty (1988), except that the relativizers have been separated from the head nouns to form their own coordination. Whether these two facts are coincidental or not is left for further research. Also, this relative clause does not have to have this “respectively” reading; it can also be parsed so that where needs are greater modifies both areas and people, and whose needs are greater modifies both areas and people.

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Page 107 (125)But certainly it will mean shift of available resources for health care to areas and people where and whose needs are greater; it will mean less to the already privileged and more to the underprivileged, the vulnerable, the weak and the poor. Nevertheless, since the majority of attestations are in fact interrogatives, this name will be retained. Plural-noun MWIs are schematized in the templates in (126). As with the templates in section 3.2.1, when stands for any adverbial wh word; similarly, which stands for any wh determiner. Type-logical categories are used to represent the body of the interrogatives. In particular, the product constructor • (defined in Chapter 2) is used in the category N pl•VP; this simply means a plural N immediately in front of a VP (e.g. reportsN are-dueVP), which is what which is looking for. (126) Templates for plural-noun mixed- wh interrogatives a. With adverbial gap {which and when, when and which} Examples: which and when reports are due, when and which reports are due b. Without adverbial gap {which and whether, whether and which} Examples: which and whether reports are due, whether and which reports are due As with the other search, though, the existence of obligatory NP-gap MWIs suggests an analysis for plural-noun MWIs that does not require neutrality, namely the reverse sluicing analysis described in section 3.2.1. This analysis begins with the fact that obligatory NP-gap MWIs are attested in which the nominal wh is a phrase instead of a word, such as what information, which cows, which person, or what connection in (127). (These and other attestations appear in section 2.7 of Appendix A.) (127)Obligatory NP-gap MWIs with phrasal nominal wh, attested on the Internet a.Object gap i. The important point is to know WHEN and [WHICH cows] to float, not to know that you CAN float a cow. ii.Why and [which one] do I choose?

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Page 108 b.Subject gap i. They have no way to know when and [which person] is busy, out of office or in the meeting. ii.As of now, they are still not sure if or [what connection] exists. Just as optional NP-gap MWIs could be seen as a special case of obligatory-NP gap MWIs, so can pluralnoun MWIs. Specifically, they are the obligatory NP-gap MWIs in which the following conditions hold: 1. The nominal wh is a phrase. 2. The NP gap is a subject gap. 3. The interrogative is embedded (i.e., there is no subject-auxiliary inversion). 4. The noun contained in the nominal wh phrase is a plural or mass noun. Each attestation in (124) meets each of these conditions, and each attestation in (127) fails to meet at least one of them. Though the nominal wh is a phrase in each example in (127), the NP gap is a nonsubject gap in (127a.i, ii); there is subject-auxiliary inversion in (127a.ii); the noun is singular in (127a.ii) and (127b.i, ii). Under the reverse sluicing hypothesis that described the data for the MWIs in section 3.2.1—to wit, that any wh word can be coordinated with a well-formed wh sentence—the data seen here would be accounted for as follows. Considering first the obligatory NP-gap MWIs in (127), the object-gap examples when and which cows to float and Why and which one do I choose? in (127a) are grammatical because which cows to float and which one do I choose? by themselves are well-formed wh interrogatives. Similarly, the subject-gap examples when and which person is busy and if or what connection exists in (127b.i) are grammatical because which person is busy and what connection exists by themselves are well-formed wh interrogatives. The plural-noun MWIs are accounted for in the same way: To give just one example, when and whose transmissions occur in (124a.i) is grammatical because whose transmissions occur by itself is a well-formed wh interrogative. If the reverse sluicing analysis is the correct one, it is predicted that the nominal wh phrase will always appear adjacent to the body of the interrogative. For example, *which cows and when to float is predicted to be ungrammatical, since *when to float is an ill-formed wh interrogative (if float is taken to be transitive). Similarly, *which person and when is busy is predicted to be ungrammatical, since *when is busy is an ill-formed wh interrogative. Unfortunately, it was guaranteed that if any falsifying evidence existed for this

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Page 109 prediction, it would not be found in the corpus search: Which cows and when and which person and when are not members of the string sets that were searched for. In an attempt to overcome this obstacle, a search was conducted using AltaVista’s NEAR operator, to find attestations of (for example) which NEAR and when. The results were of little use, though, since this operator looked for the desired words within 20 words of each other, and there seemed to be no means of narrowing the text window. In another attempt to find falsifying evidence, the Wall Street Journal and Brown corpora were searched using the tgrep command. No falsifying attestations were found; therefore, whether they exist is an open question, and the reverse sluicing hypothesis is still tenable. Another prediction made by the reverse sluicing analysis is that when the noun is not plural or not a subject, the determiner cannot be separated from it. For an example with a singular subject, *which and when person is busy would be ungrammatical, since *when person is busy is an ill-formed wh interrogative. For an example with a plural nonsubject, *which and when cows to float would be ungrammatical, since *when cows to float is an ill-formed wh interrogative. This prediction is consistent with the data. On the one hand, 20 obligatory NP-gap MWIs were found like those in (127), containing nominal wh phrases but failing to meet the criteria to be classified as plural-noun MWIs, with the wh determiner adjacent to the noun. (These attestations are listed in section A.2.7 of Appendix A.) On the other hand, there were no examples following the *which and when person is busy or *which and when cows to float patterns above. This can be verified by checking all the sections in Appendix A that list attestations with the adverbial wh occurring as the last conjunct in the coordination. In none of them is there a wh determiner. By contrast, two out of the 40 plural-noun MWI attestations (in section A.4 of Appendix A) have a wh determiner separated from its noun: (128)Plural-noun MWIs with wh determiner separated from noun a.The public’s perspective in whose and where individual names are commemorated should be taken into account. b.It provides an encrypted filesystem that stores more than one piece of information in the same partition in such a way that it is computationally infeasible to prove what and if data exists. So far, then, the predictions made by the reverse sluicing hypothesis are consistent with the data. There is also a prediction specific to plural-noun MWIs, made by both the reverse sluicing hypothesis and the neutrality-based hypothesis: In a plural-noun MWI, the wh determiner can be separated from the plural subject noun. For example, not only will when and which pesticides are being used be grammatical, but so will which and when pesticides are being

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Page 110 used. Under the reverse sluicing hypothesis, this is because when pesticides are being used is a wellformed wh interrogative. Under the neutrality-based hypothesis, this is because both which and when can individually be construed with the factor pesticides can be used. Based on the corpus data, it seems that plural-noun MWIs can be analyzed as a special case of obligatory NP-gap MWIs, and therefore should be, in absence of compelling evidence that they require a separate analysis. Such evidence was sought, but (as will be seen) not found in psycholinguistic experimental data. 3.3.2 Psycholinguistic Experimental Data If plural-noun and obligatory NP-gap MWIs are the same phenomenon, then speakers’ grammaticality judgments for the two kinds of sentences should be approximately the same. In fact, this seems to be the case. 3.3.2.1 Procedure The experiment was done in the same way as the one described in section 3.2.2.1, except that the experimental items contained MWIs introduced by a binary coordination of an adverbial wh word (either where, when, how, or why) and a wh determiner (which or whose ). Within each of these sets of four, two items had the wh determiner adjacent to the body of the interrogative, and two items had the adverbial wh word adjacent. Thus, there were four kinds of experimental item, each of which appeared twice per questionnaire. Four of these eight contained plural-noun MWIs; four of them contained obligatory NP-gap MWIs that did not qualify as plural-noun MWIs. A sample token set illustrating the four possibilities is given in (129), in which the template I don’t know___ ___ need(s) to be filed is filled out with either when or which or which or when, and the noun report as a plural or a singular. (Alternating between singular and plural NPs was the simplest way of turning a plural-noun MWI into an obligatory NP-gap MWI, since it did not require any other alteration of the sentence.)

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Page 111 (129) Sample token set for mixed- wh questionnaire a. I don’t know when or which reports need to be filed. (plural-noun, wh determiner adjacent) b. I don’t know which or when reports need to be filed. (plural-noun, wh adverbial adjacent) c. I don’t know when or which report needs to be filed. (oblig. NP-gap, wh determiner adjacent) d. I don’t know which or when report needs to be filed. (oblig. NP-gap, wh adverbial adjacent) Eight such token sets were constructed, distributed into four preliminary scripts, and integrated into a questionnaire script, as described in section 3.2.2.1 for the optional and obligatory NP-gap MWIs. As with the other experiment, each script was put into two orders, so that there were eight versions of the questionnaire. Token sets, preliminary scripts, and filler items can be found in Appendix B. 3.3.2.2 Results: Plural-Noun MWIs Not Clearly Distinguished Results of the questionnaire are shown in Figure 6, where higher scores indicate higher grammaticality. Scores have been converted to z-scores (standardized scores), so that the mean rating for each informant is 0, and the standard deviation for each is 1. The first fact to notice is the near-identical mean scores (0.41 and 0.47) for plural-noun and obligatory NP-gap MWIs when the wh adverbial appears adjacent to the body of the interrogative. Thus, pluralnoun MWIs still seem to be the same phenomenon as obligatory NP-gap ones. Second, notice the decrease in acceptability for both kinds of MWI when the wh determiner is not adjacent to the body of the interrogative (.19 for plural-noun MWIs; -0.35 for obligatory NP-gap MWIs). This is predicted for obligatory NP-gap MWIs, as such a sentence does not contain a well-formed wh interrogative; this can be verified by referring to (129d), in which *when report needs to be filed is illformed. However, this difference is not predicted for the plural-noun MWIs, as such a sentence would contain a well-formed wh interrogative. For example, in (129c), when reports need to be filed is perfectly well-formed. This difference is statistically significant: A repeated-measures by-subject ANOVA was performed on just the plural-noun MWIs showed p to be .001.

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Page 112

Figure 6 Different acceptability of plural-noun and obligatory NP-gap mixed-wh interrogatives Nevertheless, such a result does not indicate one way or the other the distinctness of plural-noun MWIs from obligatory NP-gap ones. First of all, this result is not predicted by a neutrality-based analysis for plural-noun MWIs. Second, the fact that English determiners in general are not separable from their nouns is likely a confounding factor. As for the even lower ratings for obligatory NP-gap MWIs with the determiner first (–0.35, compared to 0.19), the fact that these MWIs do not contain a well-formed wh interrogative (as illustrated in which and when report is filed ) could easily explain the difference. So far, then, the evidence is consistent with plural-noun MWIs as a special case of obligatory NP-gap MWIs. What needs to be determined now is whether there are (as predicted) any speakers who accept pluralnoun MWIs while rejecting obligatory NP-gap ones. Though the mean scores are almost identical, it may be the case that all speakers rate the obligatory NP-gap sentences at approximately 0.47, while there are some speakers who rate the plural-noun sentences as much higher (and some who rate them much lower) than 0.41. To judge whether a given speaker’s mean score for plural-NP MWIs indicated that they were grammatical in his/her grammar, it was compared to his/her mean score for the grammatical filler sentences in the same way as

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Page 113 optional NP-gap MWI scores were checked in section 3.2.2.2. One difference, however, is that instead of comparing mean scores for all plural-noun MWIs, only the mean scores for plural-noun MWIs with the determiner adjacent to the body of the interrogative were compared; this was done to eliminate the effect of wh ordering in plural-noun MWIs. The standard deviation for this speaker’s ratings for just the grammatical fillers was calculated, and subtracted from the mean score for just the grammatical fillers. If the mean score for the plural-NP MWIs was greater than or equal to this number, it was concluded that the speaker found optional NP-gap MWIs to be grammatical. The results of this comparison are shown in Table 4.23 The mean scores for determiner-adjacent pluralNP MWIs are given in the second column; mean scores for the grammatical fillers, in the third. The standard deviation for the grammatical fillers appears in the fourth column; the difference between it and the mean score for the grammatical fillers is shown in the column labeled “threshold.” If the mean score for the optional NP-gap MWIs meets or exceeds this threshold (i.e., if it is within one standard deviation of the mean score for grammatical fillers), a “yes” appears in the last column. Among the 18 informants, there were three (12, 17, 39) whose mean score for determiner-adjacent plural-noun MWIs fell within the standard deviation for (indeed, was identical to) their mean scores for the grammatical filler items. Thus, one-sixth of the informants overall seemed to find determiner-adjacent plural-noun MWIs grammatical. To the extent that the sample here represents the population at large, there is a significant population of speakers who find plural-noun MWIs to be grammatical. 23. Informants 21, 26, and 10 are asterisked because for each one, one of the grammatical filler items was thrown out because of an anomalous low rating.

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Page 114 informant mean for plural-noun mixed- wh, wh mean for σ for grammatical thresholdthreshold det. adjac’t grammatical fillers fillers met? 12 1.09 1.09 0 1.09 yes 17 1.08 1.08 0 1.08 yes 39 0.88 0.88 0 0.88 yes 21* 1.05 1.29 0.21 1.08 no 2 0.75 1.32 0.2 1.12 no 7 0.74 1.4 0 1.4 no 26* 0.69 0.99 0 0.99 no 4 0.61 .35 0 1.35 no 24 0.58 .18 0 1.18 no 22 0.55 1.34 0.26 1.08 no 35 0.54 1.42 0 1.42 no 23 0.4 1.27 0 1.27 no 25 0.33 1.48 0 1.48 no 20 0.07 1.35 0 1.35 no 10* –0.24 1.34 0.36 0.98 no 8 –0.31 1.41 0 1.41 no 16 –0.34 1.31 0.6 0.71 no 34 –0.89 1.38 0 1.38 no Table 4 Comparison of mean scores for plural-noun mixed-wh interrogatives with wh adverbial first and grammatical filler sentences A similar comparison was done for the obligatory NP-gap MWIs and grammatical fillers; results are shown in Table 5. It can be seen here that five informants (22, 12, 17, 26, 39) found obligatory NP-gap MWIs grammatical. As can be verified with reference to Table 5, there were no speakers who accepted plural-noun MWIs while rejecting obligatory NP-gap ones: All the informants

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Page 115 who accept plural-noun MWIs (12, 17, 39) also accept obligatory NP-gap MWIs.24 informant mean for plural-noun mixed- wh, wh mean for σ for grammatical thresholdthreshold det. adjac’t grammatical fillers fillers met? 22 1.15 1.34 0.26 1.08 yes 12 1.09 1.09 0 1.09 yes 17 1.08 1.08 0 1.08 yes 26* 0.99 0.99 0 0.99 yes 39 0.88 0.88 0 0.88 yes 21* 1.05 1.29 0.21 1.08 no 24 0.88 1.18 0 1.18 no 10* 0.85 1.34 0.36 0.98 no 23 0.69 1.27 0 1.27 no 35 0.54 1.42 0 1.42 no 20 0.28 1.35 0 1.35 no 4 0.24 1.35 0 1.35 no 2 0.11 1.32 0.2 1.12 no 25 0.04 1.48 0 1.48 no 16 0 1.31 0.6 0.71 no 7 –0.25 1.4 0 1.4 no 34 –0.51 1.38 0 1.38 no 8 –0.66 1.41 0 1.41 no Table 5 Comparison of mean scores for obligatory NP-gap mixed-wh interrogatives (with nominal wh phrase adjacent to body of interrogative) and grammatical filler sentences Although the experimental results cannot disprove that plural-noun MWIs need a separate analysis from obligatory NP-gap MWIs in some speakers’ grammars, they have shown little evidence in support of such a conclusion. 24. Interestingly, though, there are two informants (22, 26) who accept obligatory NP-gap MWIs, but reject plural-noun MWIs, which should not happen if the latter are a special case of the former. I am not sure what to conclude from these results.

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Page 116 Therefore, the safest conclusion for now is that plural-noun MWIs are a special case of obligatory NPgap MWIs. Nevertheless, an analysis specific to plural-noun MWIs will be presented in the next section, in the event that further evidence from English or other languages suggests a need for it. 3.3.3 Possible Analysis of Plural-Noun Mixed-Wh Interrogatives In this section, a possible type-logical analysis of plural-noun mixed- wh interrogatives is presented. This analysis is like the analysis of optional NP-gap MWIs, in that the same interpretations of wh words and conjoined interrogatives are used, with only the assumption that some family of words (in this case, plural and mass nouns) has category neutrality that makes the MWIs possible. It should be emphasized that this analysis is presented only so that it can be referred to if evidence of this kind of plural-noun neutrality should be discovered in the future, as conclusive evidence has not been found in the corpus search or the psycholinguistic experiment from the preceding sections. Section 3.3.3.1 will present a sample derivation, and section 3.3.3.2 will discuss independent questions (IQ) and dependent questions (DQ) readings for plural-noun MWIs. 3.3.3.1 Derivation of a Plural-Noun MWI In this section, the plural-noun mixed- Wh interrogative when and which pesticides are used will be derived assuming that pesticides is neutral between its N and NP categories. In this derivation, which and when will have categories and terms as shown in (130); which is given a category appropriate for interrogatives with a wh subject. (130) Categories and terms for which and when which: when: The first step in the derivation is to coordinate when and which by using the ASt theorem to strengthen both their categories to This step is shown in (131):

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Page 117 (131) Coordinating when and which, a. Syntactic only

b. Syntactic and semantic; σ=Typ(N•VP); τ=Typ(Seq)=Prop→Bool

Next, pesticides are used must be derived as an in order to serve as the argument to when and which. The neutral entry for pesticides given in (132) makes such a derivation possible. The derivation itself is shown in (133); because it involves the rule of proof for it will be presented in Gentzen sequent style, with the semantics shown only on the bottom line. In this

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Page 118 derivation, the phrase are used is taken to be a VP, with semantics (132) pesticides: pesticide′ pl, GEN25(pesticide′) (133) Sequent-style derivation of pesticides are used as

Finally, when and which can be put together with pesticides are used to yield the phrase, category and term seen in (134). The semantics for this interrogative is the same as generated for the conjoined interrogative when (any) pesticides are used, and which pesticides are used. (134) Combining when and which and pesticides are used

In some attestations, the wh determiner is not immediately followed by a noun, but by the phrase type(s) of or kind(s) of, as in (135). Such an interrogative can be derived in much the same way as other plural-noun MWIs, with the 25. GEN is the “generic” semantic function, which takes a plural N and returns an NP.

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Page 119 entire phrase what type of (instead of just the word what ) having category S eq/(N•VP). (135)All pulls are random, Clyde, and the number of coins played has absolutely no effect on determining when or what type of winning symbols will appear on the machine. What type of can be derived as Seq/(N•VP) by use of the Curry and UnCurry theorems, discussed in Chapter 2. A syntactic derivation of what type of as S eq(N•VP) is shown in (136). (136) Deriving the category Seq /(N•VP) for what type of

From this point, the derivation proceeds exactly as the one involving which and when pesticides . 3.3.3.2 Readings for Plural-Noun MWIs The semantics for when and which pesticides are used derived in the preceding section was equivalent to that for when (any) pesticides are used, and which pesticides are used. This is an independent questions (IQ) reading, under which an answer could be thought of as two independent lists, one of them a list of times when any pesticides are used, and the other a list of kinds of pesticides that are used. This would not be a pair-list reading, with particular times corresponding to particular pesticides. If, however, plural-noun MWIs are a special case of obligatory NP-gap MWIs (as seems likely), then instead of an IQ reading, they should have a dependent questions (DQ) reading like any other obligatory NP-gap MWI. Thus,

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Page 120 the semantics for when and which pesticides are used should be the same as those for which pesticides are used when, or which pesticides are used, and when (THEY are used) . Under such a reading, the answer would indeed be a pair-list, each pair consisting of a particular kind of pesticide y, and a time x when y is used. The IQ and DQ readings are compared in (137). (137) IQ and DQ readings for when and which pesticides are used a. IQ reading b.

DQ reading

If it turns out that there are speakers who have only an IQ reading for plural-noun MWIs, this would be evidence in favor of the analysis proposed here. However, as with the optional and obligatory NP-gap MWIs, any research into this question would have to control for pragmatic influences. For instance, even if a speaker had an IQ reading for when and which pesticides are used, since the answer under a DQ reading is so much more useful and informative than an answer under an IQ reading, there could well be a tendency for the speaker to infer a DQ reading. 3.4 Mixed-Wh Interrogatives Without Lexical Neutrality The type-logical analysis of both optional NP-gap and plural-noun mixed- wh interrogatives depended on there being a word in the body of the interrogative that had multiple categorizations: both VP/NP and VP for the optional NP-gap MWIs; both NP and N for the plural-noun MWIs. However, category neutrality can arise in coordinated- wh interrogatives even when there is no single word that is assigned to multiple categories; these will be referred to as MWIS WITHOUT LEXICAL NEUTRALITY. One such MWI involves the coordination of whether with an adverbial wh element. Up until now, whether has been put in a class with adverbial wh words, since neither it nor they require an NP gap in their complement. Nevertheless, they do take different categories of complements, and for whether and (for example) how to be coordinated, their complement must be both an S with no gap, and an S with an adverbial gap. Thus, in an interrogative such as the one embedded in (138), the phrase Saddam Hussein’s regime in Iraq can be changed

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Page 121 would have category even without assuming any kind of neutrality for any word contained in it. (138)Decide whether and how Saddam Hussein’s regime in Iraq can be changed, and whether the United States should undertake a risky military effort alone. (Trudy Rubin, “‘Axis of evil’ rhetoric hurts world stability,” Philadelphia Inquirer, 10 Feb. 2002) The following MWI was written by Chris Brew, who sent it to me once he realized what he had done. In this sentence, the factor must be parsed as S/(S\S) for the how, and as S eq/(NP•(NP\S)) for the which of . (139)The clustering result shows a good match to the manually defined semantic verb classes, and in many cases it is clear which of and how the frames are influential in the creation of which clusters. In another kind of MWI without lexical neutrality, the two categories for the body of the interrogative are actually the same: S/(S\S). This is necessary in a sentence such as (140), where the intended reading has how scoping over the downstairs could have done clause, and why scoping over the upstairs think clause—so that an appropriate answer might be, “With a crowbar and because I’ve always been suspicious of Kim.” (140) How and why do you think Kim could have done this? For this differential scoping to occur, the body of the interrogative must have two meanings, one that allows an adverb to take wide scope, and one that allows an adverb to take narrow scope. As with MWIs, the first step is to strengthen the wh words to have like categories, as shown in (141): (141) Coordinating how and why; a. Syntactic only

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Page 122 b. Syntactic and semantic; σ=Typ(S/(S\S)); τ=Typ(S eq)=Prop→Bool

The next step is to derive you think Kim could have done this as an as done in (142). In this derivation, the phrase you think appears as the S/S with semantics In order to make the derivation fit on the page, ψ is used to abbreviate the term could-have-done′(this′)(kim′) . (142) Deriving you think Kim could have done this as category

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Page 123 The final step is to combine how and why with you think Kim could have done this, as shown in (143). (143) Combining how and why with you think Kim could have done this

MWIs, then, are also a productive (if less apparent) searching ground for category neutrality, in particular, category neutrality that does not arise in the lexicon. 3.5 Conclusions In this chapter, mixed- wh interrogatives taken from the Internet have provided evidence of category neutrality for at least some verbal argument alternations, most clearly the understood object alternation seen in verbs such as eat. However, they provided no firm evidence for neutrality between the N and NP categories for plural and mass nouns. Consequently, later chapters in this dissertation will explore the issue of neutrality in verbal argument alternations, and have little more to say about neutrality and plural nouns. In the course of providing type-logical analyses for the MWIs in this chapter, a type-logical formalization of the semantics of coordinated- wh interrogatives was developed (based on the work of Groenendijk and Stokhof 1997 and Carpenter 1997), which has not to my knowledge been done elsewhere.

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Page 125 CHAPTER 4 Category Neutrality and Verbal Argument Alternations 4.1 Introduction In Chapter 3, it was shown that there exists in English at least one class of cases of category neutrality, specifically, verbs that are both transitive and intransitive with an understood object. This particular argument alternation is typified by eat, and the neutrality was seen in mixed- wh interrogatives, such as this one, in which eat is used simultaneously as a transitive and an intransitive: (144) What and when can I eat? (Internet attestation) This kind of data alone makes untenable the position (espoused by Bayer 1996, and Heylen 1996, 1999) that category neutrality does not occur in natural language. As a result, however, the question of where category neutrality can and cannot occur now becomes unavoidable. In particular, a reasonable question to ask is whether verbs participating in other argument alternations exhibit category neutrality. It was also noted in Chapter 3 that the apparent neutrality of verbs such as eat in sentences such as (144) was at odds with the ungrammaticality of sentences such as (145): (145) *John ate quickly and a grilled cheese sandwich. (Schachter 1977, (4)) Under the assumption that a phonological form with different syntactic categories had to be ambiguous, the ungrammaticality of sentences like this one was predicted: Since the transitive and intransitive versions of eat have different

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Page 126 categories, they must exist in separate lexical entries, only one of which can be used at a time. Since eat is being used both ways at once in (145), the reasoning goes, the sentence is ungrammatical. If eat is neutral, though, then appealing to ambiguity is no longer a valid explanation for this ungrammaticality. The truth is, even if ambiguity were an option for explaining the ungrammaticality of (145), it would only address one corner of a larger issue: When, in general, are coordinations involving verbal complements or adjuncts grammatical? Adopting the term VERBAL DEPENDENTS as a cover term for verbal complements and adjuncts, we can identify three possible classes of verbal dependent coordinations: adjunct with adjunct, complement with complement, and adjunct with complement. Ambiguity might rule out the above coordination of an adjunct (quickly) with a complement (a grilled cheese sandwich), but what about the coordination of adjunct with adjunct in (146)? In this sentence, only one category for eat and see is in play, namely VP, so an ambiguity-based explanation has nothing to say here. (146) a. *John ate with his mother and with good appetite. (Schachter 1977, (10)) b. *I saw John yesterday and in the Coop. (Bechhofer 1976, (70)) Appealing to ambiguity not only fails to rule out apparently ungrammatical adjunct-adjunct coordinations; it also wrongly predicts that various complement-complement coordinations will be ungrammatical. In the often-discussed example in (147), two subcategorizations of is are needed, one taking an NP complement (a Republican), and the other taking an AP complement (proud of it). If is is ambiguous between these two categories, then the grammaticality of (147) is unexpected. (147) Pat is a Republican and proud of it. (Sag et al. 1985, (2b)) Even if it is possible to create a single category for is that will allow for either NP or AP complements,26 and thus license (147), what about other complement-complement coordinations such as those in (148)? In this sentence, two subcategorizations for remember are needed, one taking an NP complement and the other taking an S′. If remember must be ambiguous between these two subcategorizations, then the grammaticality of (148) is unexpected. 26. See Chapter 5 for more on such a possibility.

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Page 127 (148) Pat remembered the appointment and that it was important to be on time. (Sag et al. 1985, (123a)) In short, although ambiguity correctly predicts the ungrammaticality of adjunct-complement coordinations such as the one in (145), it is completely irrelevant in accounting for the ungrammaticality of adjunct-adjunct coordinations such as the one in (146), and worse, incorrectly predicts that complement-complement coordinations such as those in (148) and (149) are ungrammatical. An analysis that makes correct predictions about all three kinds of verbal dependent coordinations should be preferred over one that fits the data for at best only one of them. The groundwork for such an analysis is laid in this chapter, giving support to the thesis that category neutrality is possible for verbs that have more than one subcategorization. Section 4.2 reviews the analyses that have attempted to cover this ground. In section 4.3, a semantic and pragmatic analysis is developed for adjunct-adjunct coordinations. In sections 4.4 and 4.5, this analysis is extended to complement-complement and adjunct-complement coordinations, respectively. Section 4.6 presents a derivation of one particular complement coordination, in a multimodal type-logical framework. Section 4.7 discusses some miscellaneous alternations that did not fit into the earlier sections, and section 4.8 presents conclusions. A final note about terminology is in order before proceeding. The term GRAMMATICALITY is usually taken by linguists to mean whether a phrase is generated by a grammar, while the term ACCEPTABILITY is taken to mean how acceptable a grammatical phrase is to a hearer. A good example of the distinction can be seen in center-embedded constructions such as The rat the cat chased is under the couch, where the relative clause intervenes between the subject and the verb. This sentence is clearly grammatical English. Therefore, so is The rat the cat the dog bit chased is under the couch, since the same rules that generate the first sentence will generate this one. Nevertheless, this sentence is scarcely parsable, and is unacceptable to many (perhaps most) speakers. In the examples to come, the primary question is whether they are ungrammatical, or merely unacceptable because of processing or pragmatic issues. Since there needs to be a way of referring to an example’s status before such a determination has been made, the term UNGRAMMATICAL in this chapter is to be taken to mean “ungrammatical or unacceptable,” except when it is specifically being contrasted with UNACCEPTABLE.

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Page 128 4.2 Previous Analyses of Verbal Dependent Coordinations Since Chomsky (1957), a general assumption has been that two or more elements can be coordinated if and only if they have the same syntactic category, a constraint that Williams (1981) names the Law of Coordination of Likes (LCL). The LCL would rule out (145) directly, since quickly and a grilled cheese sandwich have different syntactic categories. However, it has been recognized that there are empirical problems with both the “if’ and the “only if’ part of the LCL: Likeness of conjuncts’ syntactic categories is neither sufficient nor necessary for a coordination to be acceptable. That likeness of conjuncts’ syntactic categories is not sufficient for acceptability is apparent in cases such as (146), where two (or more) elements have like syntactic categories, but nevertheless do not seem to be coordinable.27 This insufficiency can also be seen in complement-complement coordinations such as the one in (149), which takes advantage of the two transitive alternants of the verb serve . Although this sentence could be grammatical, the brackets around the * indicate that this is the case only for the bizarre readings, in which both the guests and the desserts are the food items, or both the guests and the desserts are the recipients. (149) [*]Robin served the guests and the desserts. That likeness of conjuncts’ syntactic categories is not necessary for grammaticality is apparent in the examples of “coordination of unlikes” seen earlier in (147) and (148). In addition to the above shortcomings, the LCL also fails to explain two other facts. First, it has been noted (by Bechhofer 1976, Schachter 1977, Bolinger 1978, and others) that coordination of wh-adjuncts is much more consistently grammatical than the coordination of non- wh adjuncts, as illustrated by the contrast in (150): (150) a. *I saw John yesterday and in the Coop. (Bechhofer 1976, (70)) b. When and where did you see John? (Bechhofer 1976, (88a)) 27. One could argue that in (146b), yesterday and in the Coop have different categories: yesterday could be NP, or AdvP (depending on how one chooses to analyze adverbial NPs), and in the Coop, PP. However, the assumption here is that yesterday is an AdvP (see Chapter 6 for further discussion), and in any case, declaring in the Coop to have some category other than AdvP or NP raises the question of why more intuitively temporal PPs CAN be coordinated with yesterday —for example, yesterday and on Friday.

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Page 129 This pattern extends to wh adjunct-complement coordination, as seen earlier in (144) and (145). Second, there is the fact that coordinations that are problematic with and sometimes improve with a different conjunction, as seen in the following adjunct-adjunct coordinations: (151) a. *John ate with his mother and with good appetite. (Schachter 1977, (10)) b. John ate with his mother but with good appetite. c. John ate with his mother or with good appetite (but not both). To my knowledge, this contrast has not been discussed or noted in the literature, but it should be covered in a satisfactory analysis of coordination. Also, in a type-logical grammar in which conjunctive categories are allowed, coordination of seemingly unlike categories is still possible. Recall the derivation of is a Republican and proud of it from Sag et al. (1985) in Chapter 2, repeated in (152). Here, the coordination of the seemingly unlike NP and AP categories turns out to be a coordination of like categories after all, specifically, two phrases of category (152)

Derivation of a Republican and proud of it via TR+ASt;

To overcome the limitations of a strictly syntactic constraint, Schachter (1977:90) proposes the Coordinate Constituent Constraint (CCC), which augments the syntactic requirement of like categories with a semantic0 component: “The [conjuncts] of a coordinate construction must belong to the same syntactic category and have the same semantic function.” For the syntactic part of the CCC, the problems noted above still hold. As for the semantic part, Schachter argues that coordinations such as (146) *John ate with his mother and

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Page 130 with good appetite are ungrammatical because “functional differences” between the two adverb phrases (i.e., an adverb of accompaniment vs. an adverb of manner) lead to a violation of his CCC. However, Schachter (p. 90) admits the vagueness of what it means to have the same semantic function: “Just what is meant by ‘same semantic function’? This is not a question to which I can pretend to give a definitive answer.” Overall, then, an explanation for the grammaticality or ungrammaticality of coordinations of verbal dependents will need to look beyond the syntax and compositional semantics. 4.3 Coordination of Verbal Adjuncts 4.3.1 Background and Questions to Be Addressed In discussing when coordination of adverb phrases is and is not allowed, it will be necessary to talk about the alternative to coordinating adverb phrases—that is, simply putting them adjacent to each other. The two options are illustrated in Figure 7, with the option of placing the adverb phrases adjacent to each other labeled as NESTING, because of the nesting of a smaller VP inside a larger one. Of course, a third option in English is to put one or more adverb phrases in front of the VP, and the other(s) after it. For simplicity’s sake, this option will not be considered, since (i) not every adverb in English can appear before the VP; (ii) those that do sometimes have subtle meaning differences from those appearing after the VP; and (iii) those that do not can be treated as another variety of nesting as far as the analysis below is concerned.

Figure 7 Coordination or nesting of adverb phrases Below is a list of questions that a theory of adverbial coordination should be able to answer, in the approximate order in which they will be addressed:

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Page 131 1. Why coordination sometimes seems OBLIGATORY for semantically “similar” adjuncts, or at least much more acceptable than nesting: quickly and carefully vs. ?quickly carefully, or yesterday and today vs. ? yesterday today . 2. Why coordination of wh adjuncts is much easier to do than coordination of non- wh adjuncts: When and where did it happen? vs. ?It happened yesterday and at noon . 3. Why coordination sometimes seems FORBIDDEN for semantically “different” adjuncts, or at least much less acceptable than nesting: ?in the shower and at night vs. in the shower at night, or ?with his mother and with good appetite vs. with his mother with good appetite. 4. Why coordination sometimes seems FORBIDDEN even for semantically “similar” adjuncts, or at least much less acceptable than nesting: ?yesterday and at noon vs. yesterday at noon . 5. Why coordinations with or or but sometimes differ from similar coordinations with and in level of acceptability: ?with his mother and with good appetite vs. with his mother but with good appetite. The overall argument in this section is that in some cases, coordination is obligatory because of the semantics of the adverb phrases and the conjunctions. In other cases, the semantics is such that either coordination or nesting can be employed based on the intended meaning. And in cases where there is minimal difference between the semantics of a coordinated or nested adverb phrase, the neo-Gricean Q and R Principles affect the acceptability of the different options. In section 4.3.2, the semantic part of the analysis is developed, which addresses Question 1, and lays the groundwork for the pragmatic part to come. Section 4.3.3 discusses the semantics of multiple wh interrogatives in English, and shows why the easier coordinability of wh adjuncts should not be surprising (Question 2). The pragmatic part of the analysis, which addresses Questions 3, 4, and 5, is developed in section 4.3.4. 4.3.2 Semantics of Coordination and Nesting The different semantics of coordinated vs. nested adverb phrases can explain some of the grammaticality patterns discussed in sections 4.1 and 4.2, as well as the apparent obligatoriness or optionality of coordinating certain adverb phrases (Questions 1 and 2 above). For convenience, I adopt Schachter’s terminology of “functionally similar” or “functionally different” adverb phrases, but in no way does the analysis rely on such a taxonomy of adverb phrases.

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Page 132 For the discussion to follow, it is necessary to introduce events into the semantic system. In order to take event semantics into account, every formula is now decreed to have type Event→Prop, rather than Prop. Thus, is now equivalent to Existential closure is assumed to occur when a proposition is interpreted, so that is interpreted as (This approach is taken from Hinrichs 1985.) With this redefinition of the semantic type for formulas, Carpenter’s definition of Coorσ, given in (80) in Chapter 2, will need to be revised, so that the base case is now CoorEvent→Prop instead of CoorProp. This revision is shown in (153): (153) Revised definition for Coorσ a. CoorEvent→Prop(α)(β1)(β2)=α(β1)(β2) (base case) b. Coorσ→τ(α)(β1)(β2)=λxσ.Coorτ(α)(β1(x))(β2(x)) (recursive case) The definitions of and and or will still be as given in (81) in Chapter 2, but and and or are now taken to abbreviate the semantic terms in (154): (154) a. b. The above definition for and takes two formulas and ψ, declares an event variable for each of them, and declares that each of these events e1 and e2is contained in the larger event e that is abstracted for the entire compound formula. The distinct event variables are necessary, since two different events may be referred to in a conjoined proposition—for example, Kim was born in Texas, and Robin was born in Ohio. It is also necessary to have the single event e that subsumes these separate events, since two separate events may be lumped together as a single event and subjected to further adverbial modification, as in In 1980, Kim was born in Texas and Robin was born in Ohio. Similarly, the definition for or allows for two event variables e1 and e2. The different variables are necessary in this case in order to allow for the non-exclusive- or reading, as in Kim went dancing or saw a movie (maybe both). And since the entire VP may be further modified, as in Last night, Kim went dancing or saw a movie, the single event subsuming e1 and e2 is necessary. To illustrate how these definitions work together, a derivation of Kim walked and talked is given in (155):

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Page 133 (155) VPs coordinated by and: Kim walked and talked; X=VP

Notice that the existence of these separate event variables e1 and e2 allows for two readings of Kim walked and talked: one in which the walking and the talking are distinct events (i.e., e1≠e2,, as made explicit in a sentence such as Kim walked in the morning and talked in the afternoon ), and one in which the walking and the talking are the same event (i.e., e1=e2, as made explicit in a sentence such as Kim walked and talked at the same time). A derivation of Kim walked or talked (not shown) proceeds in exactly the same way as (155), with final category and term as in (156). (156) VPs coordinated by or: Kim walked or talked In this case, the existence of these separate event variables e1 and e2 allows for three readings of Kim walked or talked: the exclusive-or reading, in which Kim walked or talked, but not both; plus the two readings obtained for Kim walked and talked —Kim walked and talked on separate occasions (i.e., e1≠e2, one of the “inclusive or” possibilities), and Kim walked and talked on the same occasion (i.e., e1=e2). At this point, the semantics of a VP modified by coordinated adverb phrases can be calculated. A schematic derivation of a VP modified by two adverb phrases coordinated by and is shown in (157). The Conj theorem from (83) in Chapter 2 combines the two adverb phrases, and the resulting phrase combines with the VP.

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Page 134 (157) Semantics of a VP modified by and-coordinated adverb phrases; X=VP\VP; σ=τ=Typ(VP)=(Ind→(Event→Prop))

Notice that after existential closure for e, the formula will refer to two subevents, e1 and e2. Thus, in a sentence such as I saw a movie yesterday and today, the desired meaning that there were two moviewatching events is obtained. Of course, multiple events are not necessary: As a special case, e1 and e2 could be identical, just as in the Kim walked and talked example. So in a sentence such as Kim worked quickly and efficiently, the more plausible interpretation is possible, in which there is only one event of working. A similar derivation for a VP modified by adverb phrases coordinated by or (not shown) has the following final category and semantic term: (158) Semantics of a VP modified by or-coordinated adverb phrases With the semantics of adverb phrases coordinated by and and or established, we can move on to the semantics of nested adverb phrases. A derivation of one is shown in (159). In this derivation, a VP with meaning P is modified by two adverb phrases with meanings α and β. The first adverb phrase combines with the VP in the first \E step; the second adverb combines with the resulting VP in the second \E step.

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Page 135 (159) Semantics of a VP modified by nested adverb phrases

The nested adverb phrases give rise to a nested-scope reading, in which α is within the scope of β. In contrast, with the coordinated adverb phrases given in (157) and (158), each adverb phrase scopes separately over the VP. Also, the final term in (159) has just one event variable abstracted, indicating that when existential closure occurs at the sentence level, the proposition will refer to a single event e. It has been shown that the semantics of nested adverb phrases leads to a single-event reading, while the semantics of adverb phrases coordinated by and and or leads to multiple-event readings (with single-event readings as a special case). An immediate prediction that can be made is that when a single-event reading is impossible, the adverb phrases will have to be coordinated rather than nested, since nesting forces a single-event reading. An easy (and perhaps the only) way to make a single-event reading impossible is to have the different adverb phrases contribute information that is contradictory when associated with a single event. Furthermore, adverb phrases that are “functionally similar” are more likely to contribute this kind of contradictory information, since they are not contributing complementary information, as functionally different adverb phrases would. In this way, the contrast between (160a) and (160b) below falls immediately into line, and matches the intuitive explanation behind the unacceptability of (160b): that to do something “yesterday today” is impossible. In fact, the event semantics of adverb phrases also predicts that (160b) should improve if a context can be imagined in which it is possible for a single event occur during two disjoint intervals of time, and this is indeed the case: If I have a time machine, and used it this morning to go back in time to yesterday afternoon and see Kim, then I saw Kim yesterday today begins to make more sense. (160) a. I saw Kim yesterday {and, or} today b. ?I saw Kim yesterday today Similar remarks about inconsistent information can be made about the following locative example:

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Page 136 (161)

a. I saw Kim here {and, or} there. b. ?I saw Kim here there. The nested adverb phrase here there results in a contradiction when associated with a single event, since here is defined to exclude there . But when the semantics allows for a multiple-events reading, as in (161a), the coordination is fine. The preceding discussion answers to some extent Question 1 (why coordination is sometimes obligatory for functionally similar adjuncts), using temporal and locative adverb phrases to illustrate. However, manner adverb phrases do not yield to the above explanation, and the contrast in (162) is still unexplained. Specifically, if Kim did something quickly and carefully at the same time, there is no apparent reason so far why nesting the adverbs in (162b) should sound as strange as it does. (Issues pertaining to or-coordinations such as quickly or carefully are deferred to section 4.3.4) (162) a. Kim did it quickly and carefully. b. ?Kim did it quickly carefully. A possible explanation for this contrast is based not on the different event structures of nested vs. andcoordinated adverb phrases, but on the difference between the separate scopings and nested scoping of adverb phrases. In the nested adverb phrase, one adverb is within the scope of another, whereas in a coordinated adverb phrase, each adverb scopes individually over the VP. For temporal and locative adverb phrases, the only difference this makes is the difference in event structure discussed above, but for other adverb phrases, the differences are more significant. To illustrate, the semantics of two temporal adverbs will first be explored in more detail, followed by a discussion of scoping effects of other adverb phrases. Consider the sentence I saw Kim yesterday today . This means the same thing as “I saw Kim yesterday and I saw Kim today,” with the stipulation that there is (impossibly) only one event of me seeing Kim. To see how this is so, let us translate this sentence initially as λe.(yesterday′(today′(saw′(kim′)(i ′))))(e). The terms yesterday′and today′are taken to be defined as follows: (163) a. b. With these definitions for yesterday and today substituted into the above translation, the more fully written out translation for I saw Kim yesterday today is which is a special

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Page 137 case of the separate-scope reading

specifically, it is the case in which e1=e2 =e. The only difference between the readings is that the nested-scope reading requires (impossibly, given the laws of physics) that there be a single event, while the separate-scope reading allows for multiple events. To put it another way, even though yesterday is technically within the scope of today, today essentially looks right through the semantically transparent yesterday to modify only saw Kim . However, this is not in general the case: Very often, wider-scoping adverb phrases do have a nontrivial effect on the adverb phrases within their scope, and when this is the case, nesting or and-coordination is used depending on the desired scoping. For example, consider the pair of sentences in (164), where coordination and nesting are both viable. Sentence (164a) means that neither plagiarism nor being hated by Dr. Jones would ordinarily be enough to cause me to fail, but that in conjunction, they are. On the other hand, (164b) means that either plagiarism or being hated by Dr. Jones can cause me to fail, though (in the and case) it just so happens that both were in effect. (164) a. Dr. Jones flunked me because I plagiarized my essay because he hates me. b. Dr. Jones flunked me because I plagiarized my essay {and, or} because he hates me. Similar effects can be seen in the coordinations of adverb phrases shown in (165). In both cases, the nesting is somewhat strange out of context, but can be sensibly interpreted in the proper context. To illustrate, I could say (165a) if I did a job happily, but was at the same time sad that I was doing it happily—for example, if I were “burying an evil or hated family member” (suggested by Brian Joseph). It does not mean that I did the job sadly, as it would if sadly scoped individually over did the job. Likewise, (165b) means that I fixed the bicycle with a wrench, and that in some way I used a hammer to do this, perhaps banging the hammer on the wrench to turn it—not the same reading as would obtain if with a hammer scoped individually over fixed the bicycle . If this action, unusual as it is, is truly what I want to convey, then (165b) is not only acceptable, but in fact the only suitable choice between nesting and coordination. (165) a. ?I did the job happily sadly. b. ?I fixed the bicycle with a wrench with a hammer.

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Page 138 Returning to the case of ?quickly carefully, I submit that there are similar, but more subtle, scoping differences at work, such that doing something quickly and carefully is not the same as doing it quickly carefully or carefully quickly. That is, if I did a job quickly and carefully, then I did it quickly, and I did with some degree of care—say between 7 and 10 on a scale of 1 to 10. However, if I did a job quickly carefully, it is true that I did it quickly, but (depending on the job) one can be only so careful if quickness is a given. So if quickly includes carefully in its scope, then my degree of care might be between, say, 5 and 8, not between 7 and 10. Before such an explanation can be fully accepted, the formal semantics of manner adverbials must be worked out more thoroughly, a task that is not taken up here. In its favor, however, this explanation is based on the undeniable fact of the scoping differences between nested and and-coordinated adverb phrases, and the fact that only in special cases (i.e., temporal and locative) are these scoping differences truth-conditionally trivial. In light of these facts, it would be surprising if these differences did NOT have an effect on the choice between nesting and and-coordination in general. So far, then, the analysis is that sometimes, semantic differences between nesting adverb phrases and coordinating them results in seeming obligatoriness of coordination. 4.3.3 Coordination of Wh -Adjuncts As noted earlier, wh adverbial coordinations are often better than analogous non- wh adverbial coordinations, an observation that forms the basis of Question 2. The following pair from Bechhofer (1976), repeated from (150), illustrates the point well: (166) a. *I saw John yesterday and in the Coop. (Bechhofer 1976, (70)) b. When and where did you see John? (Bechhofer 1976, (88a)) This difference in grammaticality is usually explained by declaring that wh phrases count, in some relevant aspect, as being similar enough to be coordinated. Schachter (p. 91) notes their semantic similarity: “Evidently, the function that [two adverbial wh words] share, that of requesting information, takes priority over the function that distinguishes them…” Bechhofer and Bolinger simply appeal to the words’ similarity in being wh words without stating whether they have in mind semantic similarity, or (less likely) phonetic or even orthographic similarity. Bechhofer (p. 119) ventures: “Perhaps the very fact that the conjoined constituents [in a conjoined- wh interrogative] are wh

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Page 139 words makes them more similar, and thus more easily conjoined.” Bolinger (p. 139) is more confident: “If the rule for coordinating with and is some form of equal status on the part of the elements coordinated, then we must conclude that it is their equal status as wh words that entitles how-why, when-how, etc. to this treatment….” However, it is not necessary to stipulate that wh words are inherently semantically parallel in order to explain the improved grammaticality of adverbial wh coordinations. When the different means of incorporating more than one wh adverb into an English interrogative are considered, coordination ties with one other method as the most natural one to use. The two other means of deploying more than one wh adverb are multiple- wh interrogatives, and sluiced interrogatives. All three methods are illustrated in (167). (167) Three ways of having more than one wh-adverb in an interrogative a. Wh coordination When and where did you see John? Where and when did you see John? b. Multiple-wh When did you see John where? Where did you see John when? c. Sluicing When did you see John, and where? Where did you see John, and when? The relevant semantic difference between the different patterns above seems to be that multiple- wh interrogatives in English expect a (non-singleton) pair-list answer, while coordinated and sluiced wh interrogatives do not. Thus, a natural answer to (167b) would be a list of time-place pairs (for example at school yesterday and in the mall today ), whereas a single time-place pair would usually be an unexpected answer. Although a multiple- wh interrogative does not always expect a pair-list answer, there must be a special context for this to be the case. The main example of such a context is what Ginzburg and Sag (2000) call DISJUNCTIVE RESOLUTION CONTEXTS, as exemplified in (168): (168) [Context: It is known that Robin phoned Dale or Dale phoned Robin.] Who phoned whom? (Ginzburg and Sag 2000:141) However, as far as adjunct-adjunct coordinations are concerned, disjunctive resolution contexts are irrelevant, since they exist only for wh NPs, as in Ginzburg and Sag’s example.

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Page 140 Since multiple- wh interrogatives carry an expectation of a pair-list answer, they are not the optimal way to incorporate more than one wh adverb into an interrogative if the asker is not looking for that kind of answer. The remaining choices are sluicing and coordination of the wh adverbs. Neither of these kinds of interrogatives expect a pair-list answer; a natural answer to either (167a) or (167c) could be at school yesterday (although pair-list answer would also be acceptable). Therefore, if a speaker is not expecting a pair-list answer to a question involving more than one wh adverb, sluicing and coordination are equally natural courses to take. The analyses of coordinated and nested wh adjuncts and non- wh adjuncts may seem to be heterogeneous, but they have a common core: When the simpler syntactic choice of nesting the adverbials makes the desired meaning unattainable, then the option of coordination is taken, even if it results in ambiguity. For non- wh adverbials, the desired meanings that are unavailable with nesting are multiple-event readings, or readings in which each adverbial scopes independently over the main VP. For wh adverbials, the desired meanings that are unavailable with nesting are the readings without an expectation of a pair-list answer. 4.3.4 Q- and R-Based Implicature The previous two subsections dealt with Questions 1 and 2: Why are some adjunct-adjunct coordinations are (seemingly) obligatory, and why are wh adjunct-adjunct coordinations generally much more acceptable than their non- wh counterparts? This section takes up first Question 3 (why some coordinations of functionally different adverbials are forbidden), and then Question 4 (the same question for functionally similar adverbials). Question 5 (why the same coordination can have different levels of acceptability depending on choice of conjunction) is addressed in the course of answering Questions 3 and 4. Horn (1984, 1989) refines the Gricean conversation maxims of Quantity, Relation, and Manner into what he names the Q and R Principles. Q is mnemonic for Quantity (in particular Grice’s first Quantity maxim), and R for Relation; the two are summed up in (169):

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Page 141 (169) The Q and R Principles (from Horn 1984:13) a. The Q Principle (Hearer-based): MAKE YOUR CONTRIBUTION SUFFICIENT; SAY AS MUCH AS YOU CAN (given R) b. The R Principle (Speaker-based): MAKE YOUR CONTRIBUTION NECESSARY; SAY NO MORE THAN YOU MUST (given Q) The interaction these principles explains some of the facts about adjunct-adjunct coordinations with or and and. 4.3.4.1 Coordination of Functionally Different Adverb Phrases We begin with the coordination of functionally different adverb phrases, with the following amended version of the earlier sentence from Schachter: (170) ?John ate with his mother or with good appetite. Here, there is an accompaniment adverbial and a manner adverbial. On the one hand, the coordination of these two different adverbials seems to be a non-sequitur, a violation of the R Principle. However, assuming that the speaker truly is following the cooperative principle, it may be that the R Principle is being flouted rather than violated. That is, by seeming to violate the R Principle, the speaker Qimplicates that there is some message to be conveyed by the or -coordination that could not be conveyed otherwise. What might that message be? A well-known type of Q-based inference is the exclusive-or reading; as an example, Horn (1984:2d) gives the sentence Maggie is patriotic or quixotic . Though it is possible that Maggie could be both, the implication is that she is not, or else the speaker would have made the more informative statement Maggie is patriotic and quixotic .28 This exclusive-or effect holds when one considers the event structure of coordinated adverb phrases, discussed in section 4.3.2. In this case, the use of or Q-implicates that the pieces of information apply to mutually exclusive events—in other words, that there was either an event e1 of John eating with his mother, or an event e2 of John eating with good appetite, but not both an e1 and an e2 (not to mention an e1 and an e2 that name the very same event). Put another way, the speaker is implying that John never has a good appetite when he eats with his mother. If the context allows for the hearer to make such an accommodation, this sentence 28. Compare the similar implicature in “Would Zeke be good, or would Zeke be Zeke?” (Cynthia Rylant, Mr. Putter and Tabby Walk the Dog)

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Page 142 improves greatly. And it is virtually impeccable if the speaker emphasizes this point by saying John ate with his mother or with good appetite—not both. It is also impeccable if the speaker acknowledges the implicature by explicitly canceling it, adding or maybe both. A similar interaction of the Q and R Principles can be traced in the original sentence from Schachter: (171) *John ate with his mother and with good appetite. (Schachter 1977, (10)) The complementarity of the information contributed (accompaniment, manner) seems to invite the listener to snap the two pieces together like parts of a jigsaw puzzle, to assemble a fuller picture of a single event. However, if this were the case, then the choice of and instead of nesting would be a violation of the R Principle, since nesting would result in an unambiguous single-event reading, whereas and allows for a single event or multiple events. But if the speaker is flouting rather than violating the R Principle, the Q-implication is that the and is conveying some message that nesting would not. One such message might be that two events are being referred to (an insight due to Bechhofer 1976:92), and indeed, a clear indication of separate events, shown in (172), improves the sentence: (172) John ate with his mother yesterday, and with good appetite today. However, more important than the indication of separate events is the ease of imagining some kind of logical connection between the two conjuncts—in other words, how well they seem to respect the R Principle. This sentence, for example, seems to suggest a causal relation (or at least a correlation) between John eating with his mother and John eating with good appetite: John usually has a poor appetite, but eating with his mother seems to help him to have a good appetite. If one imagines this kind of context, the yesterday and today can be omitted without a problem. A causal relationship can even be uttered explicitly, resulting in a perfectly acceptable coordination: John ate with his mother (yesterday) and therefore with good appetite (today) . In other words, the Q-implicated message that and is sending is not so much that there are separate events, but that the hearer needs to imagine a sensible connection between the two conjuncts. Causation is not the only imaginable logical connection between the conjuncts. Another possibility is that instead of a positive correlation between John eating with his mother and eating with good appetite, there might be a negative one—to wit, the same scenario envisioned for the or -coordination,

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Page 143 where John usually has a poor appetite when he eats with his mother (a context suggested by David Dowty). In that case, when John eats with his mother and has a good appetite, the relation between the two conjuncts is one of contrast, or violated expectations, and (171) is acceptable. In fact, it sounds even better in this scenario when and is replaced by a conjunction (but) that conventionally implicates contrast, as illustrated below: (173) John ate with his mother but with good appetite. Finally, even if neither of these scenarios is part of the common ground, the speaker can induce the hearer to accommodate that there is something noteworthy about John eating with his mother and with good appetite simultaneously, simply by adding simultaneously after the coordination—in other words, explicitly canceling any multiple-events implicature, just as adding or maybe both canceled the exclusive- or implicature earlier.29 The idea of coordinations’ acceptability depending on how well they respect the R Principle meshes well with an analysis by Kehler (2002) of coordinations that violate the Across-the-Board constraint but are nonetheless acceptable. Kehler builds on the work of Lakoff (1986), who enumerated three kinds of these coordinations: those in which the conjuncts formed some kind of natural sequence of events, as in (174a); those in which the conjuncts formed an unexpected sequence of events, as in (174b); and those in which a causal relation was implied between the conjuncts, as in (174c): (174) (from Lakoff 1986) a. What did Harry go to the store and buy—? b. How much can you drink—and still stay sober? c. That’s the stuff that the guys in the Caucasus drink—and live to be a hundred. Kehler analyzes all these cases in terms of “coherence relations” of Result, Violated Expectation, and Contiguity, which are essentially the same kinds of contexts imagined above. To sum up, an and-coordination of functionally different adverb phrases Q-implicates (i) that a multipleevent reading is intended, or (ii) that there is some connection between the conjuncts that nesting would not convey, or (iii) both. 29. Notice that even in this last sentence in the text, with his mother and with good appetite are coordinated, and there is no obvious way of paraphrasing it without a coordination.

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Page 144 When the context can support any of these implications, the coordination is acceptable. A similar analysis can be performed on the locative-temporal coordination in (175): (175) a. ?Kim sings in the shower or at night. b. ?Kim sings in the shower and at night. The choice of or over nesting in (175a) Q-implicates that the events of Kim singing in the shower and the events of Kim singing at night are mutually exclusive, and if it is known (or can be accommodated) that this is true, then (175a) is acceptable. The choice of and over nesting in (175b) Q-implicates either that the events of Kim singing in the shower and Kim singing at night are at least sometimes separate events (since otherwise, nesting the adverb phrases would be the more informative choice), or that there is some other message to be conveyed that nesting would not convey. Turning first to the possibility of separate events, suppose it is known that Kim showers only in the morning. Then clearly Kim singing in the shower and Kim singing at night are separate events, and (175) becomes perfectly sensible. Indeed, in this case, coordinating the adverb phrases is the only choice, since nesting them would result in a falsehood. Even if Kim does not shower exclusively in the morning, as long as it is known that Kim does not shower exclusively at night, the coordination is acceptable, and the Q-implication is that at least some of the events of Kim singing in the shower do not take place at night. Also, the sentence improves if it explicitly notes different time periods for the different conjuncts, as in (176): (176) Kim sings in the shower on the weekends, and at night during the week. And finally, simply adding the qualifier simultaneously, as done in the previous example, makes the coordination of in the shower and at night acceptable by canceling any multiple-events implicature. Turning next to the possibility of some other Q-implication, the possibilities are much the same as with the John ate examples. One possibility is that there is a causal relation (or at least a correlation) between singing in the shower and singing at night. For instance, if a researcher has observed that people who sing in the shower are much more likely than the general population to sing at night, then the speaker making observation (175) about Kim is offering corroborative anecdotal evidence, and obeying the R Principle. The speaker might put it this way: “Well, that’s certainly true in Kim’s case. Kim always sings in the shower,

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Page 145 and showers only at night. So we know for sure that Kim sings in the shower and at night.” The possibility of a negative correlation instead of a positive one also exists, as with the previous example. If a researcher has observed that people who sing in the shower almost never sing at night, then the speaker uttering (175) is providing a surprising counterexample, and still obeying the R Principle. The speaker might put it this way: “Oh yeah? Well, my good friend Kim always sings in the shower, and showers only at night. So, Kim sings in the shower and at night.” (As with the previous example, using but instead of and in this case makes the coordination sound better.) There is even a third possibility for a marked single-event reading. Perhaps in order for some other condition to hold, two things must be true: that Kim sings in the shower, and that Kim sings at night. For example, maybe eligible participants in a psychological experiment are only those who habitually do both of the following: sing in the shower, and sing at night. In that case, even though Kim happens to do both simultaneously, someone might phrase it as (175) in order to emphasize the meeting of both requirements. In fact, phrasing it this way would be more perspicuous, since nesting the adverb phrases might lead the hearer to think that the speaker had misunderstood the eligibility requirements, thinking that participants had to sing in the shower and at night simultaneously.30 4.3.4.2 Coordination of Functionally Similar Adverb Phrases Having considered two examples of coordinations of functionally different adverb phrases, we will now consider coordinations of functionally similar ones. As noted in section 4.3.2, when functionally similar adverb phrases are coordinated, there is a greater chance of their contributing contradictory information than with functionally different adverb phrases. When they contribute contradictory information, then nesting is not an option, as noted earlier with examples such as yesterday {and, or} today, here {and, or} there . I have nothing more to say about such coordinations here. However, discussion of one class of coordinations of functionally similar adverb phrases with contradictory information was deferred to this section, and it is time to revisit them now. They consist of manner adverbials coordinated by or, as in (177): (177) ?Kim worked slowly or quickly. Though this coordination sounds somewhat better than ?slowly quickly, it is still a bit odd, which is not predicted by analyses requiring functional similarity 30. Note once again the naturally occurring in-text coordination of the relevant adverbial phrases in describing a possible context.

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Page 146 of the conjuncts. In contrast, the pragmatic explanation developed thus far does predict the oddness of this sentence. The problem is once again a seeming violation of the R Principle. To see how, suppose that it is known that Kim always works either slowly or quickly, and never at some moderate, inbetween speed. In that case, (177) is uninformative. But in most situations, (177) SHOULD be informative, telling us that Kim worked only at the extremes of the speed continuum, not in the middle. So what is the problem? For whatever reason, mentioning just the extremes has the effect of removing the middle ground, rendering a sentence such as (177) uninformative. Once one makes the information about the excluded middle explicit, as in (178a), the coordination is acceptable. Another way to make (177) satisfy the R Principle is to embed the coordination inside I don’t know whether (which does offer new information, specifically as to the speaker’s ignorance) as in (178b): (178) a. Kim worked slowly or quickly, never at some moderate, in-between speed. b. I don’t know whether Kim worked slowly or quickly. In short, these coordinations are rescued when it is clear that they are obeying the R Principle of being informative. Of course, functionally similar adverb phrases do not always contradict one another, and when they do not, acceptability is sometimes degraded for both and- and or -coordination, as seen in (179): (179) a. ?Kim saw Robin in New York {and, or} in a barbershop. b. ?Kim saw the movie on Saturday {and, or} at noon. The oddness of these coordinations is not predicted by a requirement of functional similarity of conjuncts, but is perfectly in line with the Q and R Principles. Given the functional similarity of these adverb phrases, and the fact that in each example, one is more specific than the other, the tendency is for the hearer to want to snap the two pieces of information together like jigsaw puzzle pieces, into a single event. But if a single-event reading were intended, then nesting would be more appropriate, and using and or or would violate the R Principle. Therefore, one possible Q-implicature is that separate events (for and) or mutually exclusive events (for or ) are intended. In fact, the and coordinations do improve when separate events are explicitly indicated, as in (180), with the addition of in Ohio and today: (180) a. Kim saw Robin in New York and in a barbershop in Ohio. b. Kim saw the movie on Saturday and at noon today.

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Page 147 Even without the in Ohio or today, the sentences can work if one simply imagines that there are no barbershops in New York, or that there were no noon showings of the movie on Saturday. The or coordinations can be rescued in this manner, too. Also, simply adding but not both after the orcoordinations makes them acceptable, just as in example (170). The other possible Q-implicature for the and-coordinations is that there is some connection between the conjuncts that simply nesting them would not convey. The movie example will be used to illustrate. First, suppose the question under discussion is whether on Saturdays, this movie is ever shown at any time other than at noon. In other words, the claim is that a Saturday showing entails a noon showing. Then someone uttering (179b) with an and is offering corroborative evidence (albeit circumstantial). Second, if the claim is that this movie is never shown at noon on Saturdays, a speaker could felicitously declare (179b) to disprove the claim, perhaps substituting but for and as with earlier examples. And finally, if seeing both a Saturday showing and a noon showing of this movie is a necessary condition to, say, win a sweepstakes, a speaker who has met both requirements simultaneously by seeing the show at noon on Saturday could still felicitously utter (179b) with an and to emphasize the meeting of both requirements (a context suggested by Brian Joseph). Next we consider a coordination of non-contradictory manner adverbials, shown in (181). Here, it is only the or -coordination that sounds bad; the and-coordination is acceptable for reasons discussed in section 4.3.2. (181) a. Kim worked slowly and meticulously. b. ?Kim worked slowly or meticulously. Again, the questionability of (181b) is not predicted by a requirement of functional similarity of conjuncts, but falls into place when the Q and R Principles are brought to bear. Since meticulousness usually requires slowness, it is reasonable for a hearer to think Kim might have worked both ways at the same time, in which case it would be more informative to say Kim worked slowly and meticulously . Thus, the speaker seems to be violating the R Principle. However, if the speaker is taken to be flouting the R Principle, forcing an exclusive- or Q-inference, the hearer is invited to conclude that Kim worked slowly or meticulously, but not both. It is difficult to imagine a context that would support this inference, but as with the preceding examples, if the inference is specifically supported (as in Kim worked slowly or meticulously, but not both) then the coordination improves. Lastly, consider the coordination of accompaniment adverb phrases in (182), which are compatible with each other, but are not so closely associated with each other as to lead the hearer to a single-event reading (as slowly and

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Page 148 meticulously do). In this case, no seeming violation of the R Principle leads to the kinds of Q-implicature discussed above, and the coordination is acceptable with no special context required. (182) Kim worked with Robin or with Sandy. To sum up, the Q and R Principles explain why some adverb phrases are difficult to coordinate (Questions 3 and 4 from section 4.3.1). The analysis does not need to resort to intuitively and poorly defined ideas of functional (dis)similarity of adverb phrases, since it applies regardless of the similarity or dissimilarity of the coordinated adverb phrases. 4.3.5 Summary In this section, it has been seen that the semantics of and and or explains to a great extent why coordination is sometimes obligatory for adverb phrases, and that neo-Gricean pragmatic principles explain why it sometimes seems to be forbidden. Though the semantics of manner adverb phrases remains in need of formalization, this analysis covers more of the facts about verbal adjunct-adjunct coordination than any other that I am aware of: coordinations of functionally similar and different adverbs; coordinations of contradictory and non-contradictory adverbs; coordinations of non- wh and wh adverbs; coordinations employing and, or, and but. Furthermore, it does so using well-motivated, independent principles, without resorting to ad hoc distinctions between adverb classes, or between wh and non- wh adjuncts. The next two sections show how the principles that are applied here to adjunctadjunct coordinations can be applied to complement-complement and adjunct-complement coordinations. 4.4 Coordination of Verbal Complements In section 4.3, an analysis of verbal adjunct coordination was developed based on the compositional semantics of conjunction, and on pragmatic principles of conversational implicature. In this section, the analysis is extended to cover coordination of verbal complements. It is intended to cover (trivially) coordinations of complements when only one subcategorization for a verb is required (e.g., I saw Kim and Robin ), as well as some coordinations of complements from different subcategorizations (e.g., He remembered the appointment and that it was important to be on time, from Sag et al 1985). Other coordinations.

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Page 149 In this analysis, considerable reference will be made to LEXICAL ENTAILMENTS of a verb; these are simply the properties that various arguments to a verb must fulfill. For example, the verb drink lexically entails that its direct object is a liquid, and that its subject ingests this liquid through its mouth. Different subcategorizations of a verb impose different entailments on their arguments. For instance, transitive break lexically entails that its direct object undergoes a change of state (specifically, from being whole to being in more than one piece), and that its subject causes this change in the direct object; in contrast, intransitive break lexically entails that its subject undergo this change of state. Section 4.4.1 deals with argument alternations that do not involve a difference in entailments for the verb’s arguments; section 4.4.2 deals with alternations that do. Section 4.4.3 summarizes the findings. 4.4.1 Subcategorizations with Identical Lexical Entailments We will begin with cases of complement-complement coordinations that are uncontestedly grammatical. The semantic and pragmatic analysis from section 4.3 does not need to be extended to cover these cases: There is nothing to rule out, and they are automatically generated if the verbs are allowed to have multiple categorizations. Most of these examples involve verbs of mental action or states. Furthermore, the different subcategorizations of the verb have essentially the same lexical entailments for their arguments. In particular, the subject is always the participant that is performing the mental action or is in the mental state, and the direct object is always what the subject is thinking about during the named action or state. The most obviously and uncontroversially grammatical examples come from alternations whose different syntactic categories still have the same semantic type—namely, the “bridge” verbs such as say that can take either an S or an S c (the type-logical category for complementized sentences) for a complement. An example is given in (183): (183) Mary said [she hated me] and [that she never wanted to see me again]. The next alternations, used by Sag et al. (1985), involve verbs such as remember or frighten, which can take either an NP or an S c for an argument (the direct object for remember; the subject for frighten). Their examples are given in (184), along with an attestation involving forget taking an about -Marked NP. Though NP and S c have different semantic types—specifically, Ind and Prop—the lexical entailments for each verb are the same across the different subcategorizations. First, the subject is always the participant whose memory is

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Page 150 affected. Second, the NP and S c complements are interpreted as propositions. For example, in (184a,b), the NP the appointment and the PP about the Great Valley act as a contextually determined propositions, such as that he had an appointment at 2:00, or that the Great Valley was very important in his personal destiny. Likewise, in (184c), the NP the implications thereof stands for a whole set of propositions involving Himmler’s appointing Hitler. (184) a. Pat remembered [the appointment] and [that it was important to be on time]. (Sag et al. 1985, (123a)) b. Littlefoot forgot [about the Great Valley] and [that he must somehow reach it]. (The Land Before Time, 1988) c. [That Himmler appointed Heydrich] and [the implications thereof] frightened many observers. (Sag et al. 1985, (123b)) The alternations so far have involved propositional arguments, and the category S c for the relevant argument in one subcategorization. The next alternations involve propositional arguments, with an infinitive phrase for the relevant argument in one subcategorization. The first of these is the Object Raising subcategorization of believe, compared with its clausal-complement alternant in (185). In (185a), believe takes two non-subject arguments: the NP Robin, and the infinitival VP to be a spy. In (185b), believe takes the S cthat something should be done about it . (185) a. I believe Robin to be a spy. b. I believe that something should be done about it. The pattern seen in the previous examples still holds for believe. In (186), Robin to be a spy is coordinated with that something should be done about it, and the sentence is grammatical: (186) I believe [Robin to be a spy] and [that something should be done about it]. This coordination is more complex than the previous examples, since one conjunct contains two arguments (Robin and to be a spy),31 while the other contains just one (that something should be done about it). Nevertheless, the lexical entailments for the different alternants of believe are the same: The subject is always the believer, and (since Robin and to be a spy together form a 31. Evidence that Robin to be a spy is actually two constituents comes from the passivizability of the NP, as in Robin is believed to be a spy.

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Page 151 proposition) the complement or complements following the verb are interpreted as the proposition that the subject holds to be true. Written out as lambda expressions, the semantics for believe taking an S c complement would be and the semantics for believe taking the NP and infinitival VP complements would be λP λy.believe′ (P(y)). In both terms, believe′ takes a propositional argument, but in one case it comes from a single argument and in the other from two arguments (P, y). Next under consideration are the Subject Control (Equi) and Object Control alternants of want . The alternation is illustrated in (187). In (187a), want takes the infinitival VP to leave as an argument; in (187b), want takes two non-subject arguments: the NP Robin, and the infinitival VP to leave . (187) a. I want to leave. b. I want Robin to leave. Want breaks the pattern seen up until now. Like the previous alternations, the lexical entailments for the two subcategorizations for want are similar: The subject is always the wanter, and the remaining complement is always interpreted as the proposition that the subject would like to come true (with the infinitival VP identifying its subject with that of the main verb want ). To illustrate, the lambda expressions, the semantic term for want with a VP complement would be λP λx.want′ (P(x))(x), and that for want with an S complement would be want′ —whether or P (x), the argument following want′ is a proposition. Despite these similar entailments, the examples of such a coordination in (188) are questionable, or actually ungrammatical under the desired reading: (188) a. ?I want [to wash the dishes] and [you to dry them]. b. [*]I want [you to wash the dishes] and [to dry them]. (i.e. I want to dry the dishes.) This result is unexplained, though for (188b) one can speculate that the ungrammaticality of the desired reading is due to a garden-path effect, whereby you is parsed as the subject of each infinitive. On the other hand, although (188a) is questionable, my son uttered the sentence in (189), indicating that whether or not such a coordination will be part of his adult grammar, it was part of it at age 3.75: (189) I want [to hide] and [nobody to find me]. (Douglas Whitman, age 3)

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Page 152 Coordinations are also possible with or . One example is given in (190), and in (191) are two attested examples, both from my wife, addressed to our son on separate occasions: (190) I don’t want [to do it myself], or [you to do it for me]. (191) (both from Amanda Whitman) a. Do you want [to walk upstairs], or [me to carry you]? b. Do you want [to brush your teeth first], or [Adam to brush his teeth first]? Therefore, it seems that in some contexts, coordinations of infinitival VP and S after want are permitted. As a final note on this alternation, there is this even more striking attestation involving or: (192)Last week, a Groveport Madison sixth-grader named seven students and two teachers on a list she titled, “People I want to die or kill.” (“4 student threats, 4 different responses,” Ruth E.Sternberg and Mary C.Bridgman, Columbus (Ohio) Dispatch, 10 May 2002, p. A1) This attestation exhibits the same category neutrality for want as is considered above, and is further complicated by the fact that the NP people is extracted, which serves as the subject of die, and the direct object of kill. A derivation of this unusual coordination appears in section 4.6. Another alternant of want takes an NP complement, as in I want a bagel. As with the remember example and related examples above, the NP is interpreted via the lexical semantics of the verb to be a propositional argument; thus the propositional argument for want corresponding to a bagel in (193) would actually be something like “for me to have a bagel.” Therefore, is no conflict in lexical entailments, and coordinations like the one in (193) should be at least as good as the remember examples. Nevertheless, this coordination definitely sounds like a joke: (193) ?I want [one more bagel] and [to leave]. On the other hand, there is the following movie attestation, with want taking both an NP complement and an infinitival clause: (194)Charlotte Dennon wants [a Tiffany engagement ring] and [her boyfriend to stop dragging his feet] …. (Elf, 2003)

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Page 153 In addition, there is the attestation (again from my wife) in (195) with the similar alternation in need: (195) He also needs [a refill on his juice] and [his diaper changed]. (Amanda Whitman) Like want, need can take an NP complement (in this case a refill on his juice ). The other relevant subcategorization of need here is not entirely parallel to want, since it takes not an infinitive complement, but an NP plus a predicative phrase (in this case, his diaper changed). Still, the complement his diaper changed and to leave are both non-finite and essentially propositional complements, with his diaper as the subject of the passive changed in (195), and I as the understood subject of to leave in (193). Consequently, I take the attestations in (194) and (195) to suggest that neutrality for this kind of alternation (between verbs that take an NP complement and a nonfinite propositional complement) is possible for at least some speakers. In this section, several argument alternations were considered in which the different subcategorizations did not impose different lexical entailments on their arguments. More specifically, these alternations all had either implicit or explicit propositional arguments, which all carried the same lexical entailments with respect to the verb. In most of the cases, coordinations of the complements with unlike categories was completely grammatical. Furthermore, even when artificially constructed examples did not seem to be grammatical, this evidence was mitigated by actual attestations in speech. All the alternations so far, then, can exhibit category neutrality. 4.4.2 Subcategorizations with Contrasting Lexical Entailments In this section, argument alternations will be considered in which the different subcategorizations impose contrasting lexical entailments on their arguments. In section 4.4.2.1 are examples that seem quite ungrammatical at first, but which fit neatly into the semantic and pragmatic analysis developed for adjunct-adjunct coordinations in section 4.3. In section 4.4.2.2 are examples that hover on the border between questionability and outright ungrammaticality, and which do not fit into the existing semantic and pragmatic analysis. Some speculation on the patterns of grammaticality for these examples will be offered. In referring to various argument positions for verbs, I will follow a practice established in Dowty (1982), whereby a verb’s subject is defined as the last argument to combine with it to yield an S; the direct object as the second-to-last; indirect and oblique objects as the first. Dowty presents a number of linguistic reasons for such a definition; interested readers are referred to sections 5 and 7

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Page 154 of Dowty (1982). These arguments will be referred to by numbers in subsequent discussions. The last argument to combine with a verb, namely the subject, will be ARG1. The second-to-last argument will be ARG2; the third-to-last will be ARG3, and so on. Thus, for any transitive verb, ARG2 will be the direct object, while for polytransitive verbs, ARG3 will be an oblique object. In this section, it will be convenient to discuss verbs’ lexical entailments in terms of various thematic roles that certain clusters of entailments are commonly known as. This approach is based on the work of Dowty (1989, 1991). Dowty (1991) proposes that there are various PROTO-ROLE (or P-ROLE) entailments that hold for a verb’s arguments. Some of these entailments are PROTO-AGENT entailments, and the argument that has the most of these entailments is the one that will be lexicalized as the subject (ARG1). Other entailments are known as PROTO-PATIENT entailments, and the argument that has the most of these entailments will be lexicalized as the direct object (ARG2). (In case of ties, or near-ties, either or both lexicalizations are possible.) Remaining arguments will be lexicalized as oblique objects. Thus, there are no role names, just sets of p-role entailments, the more frequent combinations of which are known as AGENT, PATIENT, GOAL, etc. The lists of p-role entailments that Dowty uses are as follows: (196) Proto-Agent entailments (from Dowty 1991, (28)) a. volitional involvement in the event or state b. sentience and/or perception c. causing an event or change of state in another participant d. movement (relative to the position of another participant) (197) Proto-Patient entailments (from Dowty 1991, (28)) a. undergoing change of state b. incremental theme32 c. causally affected by another participant d. stationary relative to the movement of another participant One complication that wiil be relevant for some of the argument alternations discussed in the next section is the issue known as WRAPPING. In a phrase such as They gave the book to Kim, since the book appears adjacent to the verb give, it will combine with it before to Kim does so; in other words, the book will be ARG3, while to Kim will be ARG2. However, as evidenced by its 32. As defined in Dowty (1991), the incremental theme is the participant x in the event such that, the closer the event is to completion, the more of x has been affected.

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Page 155 passivizability, the book is the direct object, and therefore should be ARG2. To resolve this conflict, Dowty (1997) presents a “wrapping modality” for type-logical grammar, whereby a verb can combine with its arguments in the desired order, even if their linear order does not match their order of combination. A “wrap” operation appears to be well motivated independently, and was proposed as early as Bach (1981); a summary of the motivations for wrapping can be found in section 2.2 of Dowty’s paper. The mechanics of the wrapping modality will not be important here. All that needs to be recognized is that a category of form (A/ wB)/C indicates that the first argument to be consumed is the C, and the second is the B, even though the C constituent may not be the one that appears adjacent to the functor. For example, the give in the above example would have category (VP/ wNP)/NP to, indicating that the oblique object (ARG3) is the to-marked NP, even though it does not appear adjacent to the verb. 4.4.2.1 Alternations Involving Role Replacement The semantic/pragmatic analysis of adjunct-adjunct coordinations in section 4.3 extends well to some alternations in which the two alternants have the same arity, but different roles filled by ARG2—hence the term ROLE REPLACEMENT. The two alternations to be considered here are serve (with its two transitive usages of serving food, or serving people), and write (its transitive usage as in write a book, and its dative-object usage as in write to Kim ). The alternation seen in serve is illustrated in (198), where in each example, serve has the category VP/NP, but in one case the NP ARG2 is the recipient (the guests) of the theme, while in the other it is the theme itself (the desserts). (198) a. Kim served the guests. b. Kim served the desserts. In fact, as noted in Dowty (1979:405–7), the alternant in (198a) can be related to the double-object alternant of serve (as in served the guests the desserts) by a role-reduction lexical rule: Whereas the double-object alternant has both a recipient and a theme role, the alternant in (198a) has only the recipient role. Similarly, the alternant in (198b) can be related to the dative transitive alternant of serve (as in served the desserts to the guests ) by a different role-reduction lexical rule. These facts will turn out to be significant when the pragmatics of the test coordinations, given in (199), are discussed.

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Page 156 (199) a. [*]Kim served [the guests] and [the desserts]. b. [*]Kim served [the desserts] and [the guests]. c. ?[Who] and [what] did Kim serve? d. ?[What] and [who] did Kim serve? The only possible readings for (199a, b) are the bizarre ones in which the guests and the desserts are both the recipients of some item of food, or are both the theme. The coordinated- wh interrogatives in (199c, d), are somewhat better. Note the similarity between the pattern seen here, and that seen with adverbial coordination from section 4.3. In both cases, the declarative coordinations are ungrammatical, while the interrogative ones sound somewhat better. Concerning the semantics, note that the use of and raises the possibility of multiple events, just as with the adverbial coordinations. To see how this is so, the semantics of both sentences will be compared. The meaning for double-object serve (as in served the guests the desserts), with category (VP/ wNP)/NP, will be translated as serve1′. The semantics generated for Kim served the guests the desserts is shown in (200a). The transitive serve seen in serve the guests will be translated as serve2′, which will be defined as equivalent to The transitive serve seen in serve the desserts will be translated as serve3′, which will be defined as equivalent to When these translations are used, the semantics generated for Kim served the guests and the desserts are as shown in (200b). (200) a. Single-event reading: Kim served the guests the desserts. λe.(serve1′(desserts′)(guests′)(kim′)) (e) b. Multiple-event reading: Kim served the guests and the desserts.

As with the single- and multiple-event readings for the adverbial combinations discussed in section 4.3.2, the single-event reading in (200a) is a special case of the multiple-event reading in (200b). Specifically, it is the case in which e1=e 2, x=desserts′, and y=guests′. On the pragmatic side, note that if one is referring to a single event of serving, then the sentence in (199a) is longer than it needs to be: Given the existence of the (VP/ wNP)/NP subcategorization for serve, it can be more perspicuously stated as Kim served the guests the desserts. Assuming that the speaker is following the Cooperative Principle, it is Q-implicated that something other than an ordinary, single-event reading is intended. One possibility is that

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Page 157 the speaker is referring to multiple events, and indeed, if the context makes it clear that this is the case, the coordination improves, as demonstrated in (201): (201) You’ll be serving [the head table when the food arrives], and [the wedding cake after the cutting ceremony]. Another possibility is that there is some interesting relationship between the conjuncts, such as causation or contrast. For example, suppose that Kim is a server in a restaurant so fancy that (i) the desserts are served by one particular server, and (ii) an exclusive party room for VIPs is attended by specially designated servers. Now imagine that the dessert server calls in sick one night, and asks Kim, who normally attends the VIP room, to take on his duties. Kim agrees, and tells the manager: (202) I’ve agreed to serve the desserts and the VIPs tonight. Coordination with or is also possible, provided that the Q-implicated exclusive- or reading is plausible. Sentence (203) illustrates, continuing the example of the fancy restaurant, this time with a server contemplating his or her assignment for the evening: (203) I don’t know whether I’ll be serving the desserts or the VIPs. As for the improvement seen in the coordinated- wh interrogatives, it is predicted in the same way here as in section 4.3.2: Coordination of the wh elements is the simplest way to ask both who someone was serving and what someone was serving without implying that a pair-list answer is expected. A role replacement alternation similar to that in serve can be seen in write, illustrated in (204): (204) a. I wrote an essay. (VP/NP) b. I wrote to John. (VP/NPto) A similar pattern is seen here as with serve: The declaratives are quite bad, while the interrogatives (one of them, at any rate) are better, but still questionable. (205) a. *I wrote [an essay] and [to John]. (Bechhofer 1976, (73b)). b. *I wrote [to John] and [an essay]. c. ?[What] and [to whom] did I write? d. [*][To whom] and [what] did I write?

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Page 158 The same analysis as for serve applies here. Under an expectation of a single event, a sentence involving a writer, a thing written, and an animate recipient thereof should use the (VP/ wNP)/NP subcategorization of write. As with serve, though, an indication of multiple events improves matters, as seen in (206): (206) a. I wrote [an essay yesterday] and [to John today]. b. I wrote [to John yesterday] and [an essay today]. Other contexts, such as causation or contrast, can also be imagined which would improve the coordination with and. As with serve, coordinations with or are easier to accept, as long as an exclusive- or reading is plausible: (207) a. So, are you writing [an essay], or [to John]? b. ?So, are you writing [to John], or [an essay]? The improved acceptability of the coordinated- wh interrogatives is explained in the same way as it was for serve and the adverbial coordinations: The wh coordination is the easiest way to ask the two desired questions without implying an expectation of a pair-list answer. The ungrammaticality of the desired reading in (205d) is most likely due to a garden-path effect, such that both whom and what are taken as complements of to. Summing up the two cases of argument alternations involving argument replacement, category neutrality is plausible for both, since the seeming ungrammaticality of the test coordinations can be accounted for by the same pragmatic means as many ungrammatical coordinations of adverbials, as discussed in section 4.3. 4.4.2.2 Alternations Involving Role Rearrangement The alternations in this section are those in which two subcategorizations have the same number of arguments with essentially the same roles, but two of the roles occupy different argument positions in the different subcategorizations. For example, in give the dog a bone, ARG2 (the dog) is the recipient, while ARG3 (a bone) is the gift; but in give a bone to the dog, ARG2 (a bone) is the gift, while ARG3 (to the dog) is the recipient. Such exchanging of argument positions is given the name ROLE REARRANGEMENT in Dowty (1982). Two role-rearrangement alternations will be considered here: the dative alternation typified by give, and the locative alternation (also known as the spray/load alternation) seen in load with vs. load onto.

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Page 159 As mentioned at the beginning of section 4.4.2, the coordinations in this section hover between questionable and ungrammatical. The grammaticality of coordinations involving these verbs is not explained by the semantic and pragmatic account developed in section 4.3. Instead, the level of grammaticality seems to be affected more by which arguments are actually coordinated, and which are left in the factor of the coordination. To illustrate with give, first consider sample coordinations in which the conjuncts contain only ARG3, as in (208): (208) a. *Robin gave the dog [a bone] and [to Kim]. b. [*]Robin gave the dog [to Kim] and [a bone]. These sentences are robustly ungrammatical, at least under the desired readings.33 The intended readings for (208) are those in which Robin gives the dog a bone, and gives the dog to Kim. But (208a) is ungrammatical, and in (208b), the only grammatical reading is the one in which to is parsed as part of the factor, and the remaining NPs are taken as conjoined recipients, in a bizarre reading where Robin gives the dog TO an inanimate object (that is, to the bone). At least as far as and coordinations go, the semantic and pragmatic analysis developed for adverb phrases is inapplicable here. The basis of that analysis is that for adverb phrases, either coordination or juxtaposition is possible syntactically, which opens the door to Q-implicatures depending on which option is chosen. In these sentences, however, simply juxtaposing the NP and PP is syntactically illformed (unless the PP can be parsed as modifying the head noun in the NP, in which case there is only one constituent serving as an argument to give ). Coordination is the only option. Even if the above part of the semantic and pragmatic analysis were applicable to these complementcomplement coordinations, there is evidence that something other than pragmatics is influencing their acceptability. Recall that the part of the pragmatic analysis in section 4.3 given for or -coordinations does NOT depend on the possibility of juxtaposing adverb phrases instead of coordinating them. For our purposes, the only implicature going on for or 33. In light of such robust ungrammaticality, it should be emphasized that if one assigns a neutral category to give, then these sentences are generated (as are the load sentences), even given the role rearrangement. The derivation is done in essentially the same way as the derivation of is a Republican and proud of it in (152) in section 4.2.1; the difference is that the give derivation requires that one pay attention to the specific properties of the Wrapping mode mentioned above. For this reason, such a derivation will not be shown here, but interested readers can find a derivation of give the dog a bone and to Kim in section 4.6.

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Page 160 coordinations is the exclusive- or implicature. Therefore, the or part of the earlier analysis IS still applicable here, and we should expect the sentences in (208) to be acceptable as long as the exclusive- or reading is plausible. However, they do not seem to improve when or is substituted for and, even though it is quite easy to imagine that Robin did only one of two things with the dog (give it a bone, or give it to Kim), or that Robin performed only one act of giving (giving the dog a bone, or giving the cat a toy). In fact, for all the example coordinations in this section, there is no appreciable difference in grammaticality between and and or coordinations, and for this reason, only andcoordinations will be discussed in the rest of section 4.4. Another indication that what is going on in these sentences is qualitatively different from the situation with coordinated adverb phrases is that the wh-interrogatives sound just as bad as the declaratives: (209) a. *[What] and [to whom] did Robin give the dog? b. [*][To whom] and [what] did Robin give the dog? If the semantic and pragmatic analysis does not explain the grammaticality patterns here, what does? An interesting fact that may point to an answer is that when both ARG2 and ARG3 are in the conjuncts, the coordination improves. Consider the revised coordinations in (210), and the parallel attestation in (211): (210) a. ?Robin gave [the dog a bone] and [a toy to the cat]. b. ?Robin gave [a toy to the cat] and [the dog a bone]. (211) We’ll give [that to Adam] and [Doug the bookmark]. (Amanda Whitman) A hypothesis that would be consistent with this pattern is that when an a single token of an argument has conflicting lexical entailments placed on it by the verb, the coordination is unacceptable, possibly due to processing difficulty. Consider (208) and (209) again. In these sentences, the single token the dog is in the factor. On the one hand, it must be the recipient of something, and on the other, it must be the theme. In terms of proto-role entailments, there is a Stationary/Motion conflict. In addition, give places a Sentience entailment on the argument filling the recipient role, and an entailment of nonsentience on the argument filling the theme role, which must be nonsentient, or at least not sentient enough for there to be an obstacle to its being given. Thus, there is also a Sentience/Nonsentience entailment placed on the dog. By contrast, in (210c, d), ARG2 is represented by two tokens, the dog and a toy. The dog is the recipient of something; the toy is the theme, and there are no conflicting entailments.

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Page 161 But why is the improvement only partial, as seems to be the case with (210)? At this point, pragmatics does have something to say. There IS a more perspicuous way to state the propositions in (208), illustrated in (212): (212) a. Robin gave [the dog a bone] and [the cat a toy]. b. Robin gave [a toy to the cat] and [a bone to the dog]. Therefore, as in earlier examples, using the more confusing phrasing Q-implicates that there must be some extra information to be conveyed that the simpler option would not convey. The acceptability should improve if the context makes it clear that this is the case. This prediction is in fact borne out with these examples. Suppose that Robin has a toy, which everyone assumes she is going to give to her friend’s dog when she visits. But if Robin surprises everyone by giving the dog something else, and giving the toy to someone else, then the slight alteration of (208a) in (213) sounds much better: (213) [Context: It was assumed that the toy was for the dog.] Guess what? Robin gave the dog a bone, and the toy to the cat! What happens when ARG3, ARG2, and ARG1 are all distributed into the conjuncts? This possibility is illustrated with the gapped sentences below: (214) a. ?Robin gave the dog a bone, and Kim, a toy to the cat. b. ?Kim gave a toy to the cat, and Robin, the dog a bone. Any differences between these sentences and those in (210) are too subtle to call. Furthermore, gapped sentences introduce complications due to intonation and style register that are beyond the scope of this chapter. Therefore, they will not be considered further. Though the processing-based hypothesis is speculation at this point, it has an advantage over saying that give is ambiguous between these two subcategorizations: The improvement seen in (210) is completely unexpected if give is ambiguous. Thus, category neutrality with respect to these two subcategorizations give is plausible, even given the very low acceptability of some of the test coordinations. Does this hypothesis hold up when load is considered? The spray/load alternation is illustrated in (215): (215) a. They loaded the truck with crates. ((VP/wNP)/NP with ) b. They loaded crates onto the truck. ((VP/wNP)/NP)/NPonto)

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Page 162 The test sentences for load are given in (216) and (217). In (216a, b), ARG2 (the crates) is in the factor, and only ARG3 is distributed into the conjuncts. The intended readings are those in which the oranges are put into the crates, and the crates are put onto the truck. Thus, the crates are both recipient and theme; in terms of proto-role entailments, this is another Stationary/Movement conflict. In (216c,d), ARG2 is also included the conjuncts, so that the crates are recipient, the melons are theme, and there is no conflict. In (217), coordinations of wh-interrogatives are shown. (216) a. ?They loaded the crates [with oranges] and then [onto the truck]. b. ?They loaded the crates [onto the truck] and then [with oranges]. c. ?They loaded [the crates with oranges] and [the melons onto the truck]. d. ?They loaded [the melons onto the truck] and [the crates with oranges]. (217) a. ?[With what kind of fruit] and [onto which truck] did they load the crates? b. ?[Onto which truck] and [with what kind of fruit] did they load the crates? Judgments are less definitive here. Though the sentences are marked with question marks, some informants found them awkward but grammatical, others found them questionable, and some found them ungrammatical. As a consequence, any improvement that occurs when both ARG2 and ARG3 are distributed into the conjuncts is too subtle to identify with any confidence. Even though it is hard to tell whether there is improvement in (216c, d), there is one piece of evidence in favor of neutrality. Recall that the give coordinations were improved somewhat by putting ARG2 into the conjuncts, but what brought them to near-unremarkability was placement in a suitable context. In the case of load, even though there is at most a subtle difference when ARG2 is distributed into the conjuncts, the coordination becomes almost unremarkable in the right context. First, note that the information in (217a, b) could be conveyed more perspicuously using just one subcategorization for load, as done in (218): (218) a. They loaded [the crates with oranges] and [the truck with melons]. b. They loaded [the melons onto the truck] and [oranges into the crates].

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Page 163 As with give, it is Q-implicated that there must be some special reason for not using this simpler syntax, and when a context is provided that gives such a reason, the coordination works. For the following sentence, the context is such that the melons and the crates are both more salient than the oranges or the truck: (219) [Context: The melons were supposed to go into the crates.] Those idiots loaded the crates with oranges and the melons onto the truck! Overall, then, category neutrality is plausible with respect to the with and onto subcategorizations of load, as well as the two subcategorizations for give . The primary reason is the improvement in grammaticality of coordinations in context, a fact which is unexplained if one claims that give and load are ambiguous. Furthermore, grammaticality of coordinations also seems to be affected by whether ARG2 is in the factor or in the conjuncts, though psycholinguistic experimentation is needed to determine the strength of this effect. 4.4.3 Summary Cross-subcategorization coordination of complements was undertaken for several verb alternations in section 4.4. Some of the coordinations were quite grammatical, and needed no explanation. Others seemed ungrammatical at first, but were explained by the same semantic/pragmatic analysis developed for adjunct-adjunct coordinations in section 4.3. Still others were either ungrammatical or questionable, and did not fit neatly into the existing semantic/pragmatic analysis. Nevertheless, even these coordinations were improvable when a suitable context was provided, and for a number of alternations there were even attestations of relevant coordinations. Therefore, category neutrality is unquestionable for some verbal valence alternations considered here, and more plausible than ambiguity for the others. 4.5 Coordination of Adjuncts with Complements The alternations examined in this section are some of the transitivity alternations from Levin (1993), coordination tests for which involve coordinating a direct object with an adverb phrase. The same processing and pragmatic effects discussed in sections 4.3. and 4.4 are relevant here. Section 4.5.1 examines

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Page 164 alternations with identical lexical entailments—including the verb eat, the subject of the very first examples in this chapter. Section 4.5.2 examines alternations with contrasting lexical entailments, mainly varieties of causative and middle verbs. Section 4.5.3 summarizes the findings. 4.5.1 Alternations with Identical Lexical Entailments The same semantic and pragmatic analysis developed in section 4.3 and extended in section 4.4 can be extended to cover at least some adjunct-complement coordinations. Two transitivity alternations are considered in this section: the understood indefinite object alternation, and the understood definite object alternation. The understood indefinite object alternation (Levin 1993) is exemplified by the verb eat, as illustrated in (220): (220) a. John ate a grilled cheese sandwich. b. John ate quickly. Adjunct-complement coordinations involving or are given in (221): (221) a. ?John ate quickly or a grilled cheese sandwich. b. ?John ate a grilled cheese sandwich or quickly. The same exclusive-or Q-implicature seen in section 4.3 is in effect here: The or -coordination suggests that John performed only one of the actions, but the complementarity of the complement and adjunct information suggests that he did both, in a single event. But if the context supports the implicature that eating quickly and eating some particular item are mutually exclusive, the coordination improves somewhat. For example, maybe John eats everything fast, except for grilled cheese sandwiches, which he slows down to savor. And a similar attested coordination within the scope of a negation (shown below with brackets added to highlight the relevant conjuncts) is impeccable: (222) Don’t eat [fast food] or [at restaurants, food-service companies or caterers]. (William H.Balson, Jr., Columbus (Ohio) Dispatch letter to the editor, 19 Jan. 2003) Moving on to and-coordinations, sample sentences are given in (223):

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Page 165 (223) a. *John ate quickly and a grilled cheese sandwich.

(Schachter 1977, (4)) b. [*]John ate a grilled cheese sandwich and quickly. (i.e. John ate a sandwich, and John also ate some meal or snack quickly.) As already noted, these sentences are ungrammatical, at least under the desired reading; (223b) is acceptable only with the idiomatic interpretation meaning, “John ate a grilled cheese sandwich, and did so quickly.” Once again, the complementary information contributed by the adjunct and complement invites a single-event interpretation, but the single-event reading could be conveyed simply by juxtaposing the adjunct and the complement, as in ate a sandwich quickly (or in this example, by putting the adjunct before the VP: quickly ate the sandwich). Therefore, if a speaker chooses and-coordination, the Qimplication is that there is some other meaning to be conveyed than the one in a single-event reading. One possibility is that the speaker is actually referring to multiple events; another is that the speaker is referring to a marked, noteworthy single event. The better the context can support either of these possibilities, the better the coordination. To illustrate how the semantics for John ate a sandwich quickly is a special case of the semantics for John ate quickly and a sandwich, the terms are written out in (224). The meaning for transitive eat will be translated as eat1′. Intransitive eat will be translated as eat2′, which will be defined as equivalent to (224) a. Single-event reading: John ate a sandwich quickly. λe.(quickly′(eat1′(a-sandwich′)))(john′) (e) b. Multiple-event reading: John ate quickly and a sandwich.

The single-event reading, then, is the special case in which e1=e2=e, and x=a-sandwich′. In (225), a multiple-event reading for the sentences from (223) is forced by adding the adverbs yesterday and today to the conjuncts, and the sentences show some improvement: (225) a. ?John ate quickly yesterday and a grilled cheese sandwich today. b. ?John ate a grilled cheese sandwich yesterday and quickly today.

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Page 166 However, like the examples of John eating with his mother and with good appetite in section 4.3.4.1, these sentences are still questionable, since whether we are talking about a single event or separate events, the coordination of quickly with a grilled cheese sandwich, absent any context, is a nonsequitur. For the coordinations to be completely acceptable, there has to be some sensible connection between the conjuncts. One such context (for a single-event reading) was suggested earlier: It is understood that a grilled cheese sandwich is something that must be eaten slowly, and therefore eating something quickly when that something is a grilled cheese sandwich is unexpected. Inserting an and, or even better, a but, is acceptable in such a context. Other contexts are harder to envision, but as with earlier examples, simply adding at the same time leads to improvement, leaving it to the hearer to figure out what the relevant context might be. Finally, it happens that some adjunct-complement coordinations involving the understood-object alternation seen in eat and other verbs can be dramatically improved with judicious choice of the adverb and direct object. For example, consider (226): (226) John ate ravenously yesterday but hardly anything today. Here, the adverb ravenously is not merely a manner adverb; it entails that the amount of food John ate is large. Likewise, the direct object hardly anything does not say what John ate, but indicates that the amount is small. In this way, the adverb and the direct object have been chosen so as to carry the same kind of semantic information, and the sentence does not violate the R Principle as those in (225) do. The indication of separate events removes the contradiction of saying that John ate a lot and a little simultaneously, and the sentence makes sense, much more so than the original ate quickly and a grilled cheese sandwich example. Similar adverbs can be chosen for certain other verbs in this class, for example, prolifically with write. Concerning coordination of a wh adjunct and complement, as in (227), the same argument made for wh adjunct-adjunct and complement-complement coordinations can be made here: The wh coordination is the easiest way to ask the two desired questions without conveying an expectation of a pair-list answer. (227) What and when can I eat? Moving on to the understood definite object alternation (Levin 1993, Fillmore 1986), an illustration with the representative verb notice is shown in (228):

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Page 167 (228) a. Kim noticed that Robin had entered the room. b. Robin entered the room. Kim noticed. An ordinary coordination of adjunct and complement is constructed in (229). Only one order is tried, since the understood-object usage needs to immediately follow the utterance of the noticed event. In addition, only and is used, since or results in crashingly bad sentences, a fact for which I have no explanation. (229) John entered the room. ?Mary noticed immediately, and also the lipstick on his collar. The sentences are questionable, but improve when separate events are indicated, as in (230): (230) Mary noticed [immediately when John left], and [the lipstick on his collar when he returned]. Here, not only does the indication of separate events seem to help, but the choice of the adverb phrase when John left in the first conjunct increases the sentence’s acceptability. This phrase is doing the job of identifying what Mary noticed, even though notice is being used intransitively, in much the same way as ravenously provided information about what John ate in (226). Before moving on to wh adjunctcomplement coordinations with notice, it is worth noting that even an or -coordination becomes acceptable, with the conjuncts lengthened as in (231), and embedded under a negation: (231) Mary didn’t notice [at all when John left], or [the lipstick on his collar when he returned]. A wh adjunct-complement coordination with notice is given in (232). In this example, since the when question presupposes that it is common knowledge that Mary noticed something, what else is used instead of what: (232) John entered the room. ?When and what else did Mary notice? This example is much less acceptable than What and when can I eat? above, a fact about notice for which I have no explanation. At the beginning of this chapter, there was conflicting data over the status of the understood definite object alternation, exemplified by eat. Mixed- wh interrogatives involving eat suggested transitiveintransitive neutrality, while the

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Page 168 ungrammaticality of analogous declarative coordinations pointed toward ambiguity. Further investigation has revealed that the ungrammaticality of the declarative coordinations is explained by the same means that is already needed to explain the coordination of adverb phrases. The evidence is now solidly in favor of transitive-intransitive neutrality for verbs participating in this alternation, and somewhat in favor of it for verbs participating in the understood indefinite object alternation. 4.5.2 Alternations with Contrasting Lexical Entailments Transitivity alternations in which the different subcategorizations impose contrasting lexical entailments on their arguments are investigated in this section. They include another understood object alternation (namely, the understood reflexive object alternation), the middle alternation, and two causativity alternations. Coordination tests for these alternations are uniformly ungrammatical, but even here, ambiguity is not necessarily the best explanation. In discussing the alternations in this section, two other possible reasons that do not involve ambiguity will be proposed, namely, that certain kinds of entailment conflicts or conflicts involving ARG1 are more difficult to process than others. The understood reflexive object alternation is illustrated with shave in (233), with test coordinations given in (234): (233) a. John shaved his father. b. John shaved. (234) a. *John shaved [quickly] and [his father]. b. [*]John shaved [his father] and [quickly]. (i.e. John shaved his father, and John shaved himself quickly.) c. *[How] and [whom] did John shave? d. *[Whom] and [how] did John shave? These sentences do not pattern with the alternations in section 4.5.1. Those, like the complementcomplement coordinations in section 4.4.1 (serve, write) and the adjunct-adjunct coordinations in section 4.3, improved when it was made clear that there was a good reason for coordinating the two elements instead of simply juxtaposing them. We might expect that at least (234a, b) could be improved in this way. One way of doing so is by indicating that a multiple-event reading is intended. This is done in (235), with no improvement in grammaticality:

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Page 169 (235) a. *John shaved [quickly yesterday] and [his father today]. b. *John shaved [his father yesterday] and [quickly today]. In contrast, these sentences have several properties in common with the test coordinations for the give and load alternations in section 4.4.2.2. First of all, as indicated in (234), all are less than fully grammatical, even the wh coordinations. Second, it happens that there is no appreciable difference whether the conjunction is or or and (and therefore, as in 4.4.2.2, only and coordinations will be discussed). Third, these alternations place very different proto-role entailments on one of the verb’s arguments, specifically ARG1, the subject. For intransitive shave, the subject (ARG1) fills the patient role; that is, it must satisfy three proto-patient entailments: being causally affected, undergoing a change of state, and being the incremental theme. (It fills the agent role, too, but that is not directly relevant.) For transitive shave, though, it is ARG2, the direct object, that fills this role. I assume that the proto-patient entailments of being causally affected, undergoing a change of state, and being the incremental theme are such that if they are placed upon one argument, the other arguments must NOT satisfy them. Consequently, John is lexically entailed to be both affected and NOT affected by the action; undergo a change of state and NOT undergo a change of state; be the incremental theme and NOT be the incremental theme. In short, contrasting entailments are placed upon the subject in this coordination. The test coordinations for give improved when the argument with conflicting lexical entailments was taken out of the factor and distributed into the conjuncts. If the same is done to the shave coordinations, do they improve? In (236), gapped sentences are shown, in which ARG1 is included in the conjuncts, not in the factor. There is no discernible improvement, though given the differences in intonation and style register of gapped sentences (noted in section 4.4.2.2), it is difficult to draw a conclusion from this lack of improvement. (236) a. *[John shaved quickly yesterday], and [Mary, her father today]. b. *[Mary shaved her father yesterday], and [John, quickly today]. Finally, there is one definite difference between these coordinations and those in section 4.4.2.2. For give and load, when the relevant argument was in the factor instead of the conjuncts, the coordinations hovered between grammatical and ungrammatical. For shave, though, there is no doubt: The coordinations are resoundingly bad. The question remains, then, of why the contrasting lexical entailments for shave are so much more damaging than those encountered earlier with load and give . One possibility is that it is because with shave, it is ARG1 that has the conflicting lexical entailments, whereas with load

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Page 170 and give, it was ARG2. In other words, it is just more difficult to recalculate lexical entailments for ARG1 than for other argument positions, perhaps because ARG1 in English is uttered earlier than the other arguments, and therefore requires more backtracking before its entailments can be recalculated. Another possibility is that contrasts involving the Causally Affected, Change of State, or Incremental Theme proto-role entailments are just more difficult to process than the Stationary/Motion or Sentient/Nonsentient conflicts seen with give and load. The next alternation is the middle alternation, exemplified by frighten in (237), and test coordinations in (238): (237) a. John frightens Marsha. b. John frightens easily. (238) a. *John frightens [easily] and [Marsha]. b. [*]John frightens [Marsha] and [easily]. (i.e. John frightens Marsha, and John himself is easily frightened.) c. *[Whom] and [how easily] does John frighten? d. *[How easily] and [whom] does John frighten? The pattern seen here is similar to the one seen for shave: All sentences, including coordinated- wh interrogatives, are ungrammatical. Also as with shave, there is a contrast imposed on ARG1: The subject of transitive frighten in (237a) is not causally affected and does not undergo a change of state, but the subject of intransitive in (231b) frighten is and does. And as with shave, improvement fails to occur when this argument is distributed into the conjuncts of the coordination, as done in the sentences in (239): (239) a. *[John frightens Marsha], and [Kim, easily]. b. *[Kim frightens easily], and [John, Marsha]. Nor is there improvement with an indication of multiple events of someone being frightened, as shown in (240): (240) a. [*]John frightens [Marsha because he’s mean] and [easily because he’s high-strung]. (i.e. John is easily frightened because he’s high-strung.) b. [*]John frightens [easily because he’s high-strung] and [Marsha because he’s mean]. (i.e. John is easily frightened because he’s high-strung.)

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Page 171 At this point, the possibilities listed for shave can be slightly narrowed down: Either contrasting entailments for ARG1 are more serious than a conflict in some other argument position, or contrasts involving Causally Affected or Change of State (but not Incremental Theme) are more difficult to process than other kinds. The first of the two causative alternations to be considered is the causative-inchoative alternation exemplified by break in (241), with test coordinations in (242): (241) a. The rock broke the scissors. b. The rock broke. (242) a. *The rock broke [the scissors] and (then) [into three pieces]. b. *The rock broke [into three pieces] and [the scissors]. c. *[What] and [into how many pieces] did the rock break? d. *[Into how many pieces] and [what] did the rock break? All test coordinations are ungrammatical, including the coordinated- wh interrogatives, as happened with both shave and frighten. For transitive break, the direct object has the Change of State and Incremental Theme entailments, but for intransitive break, these entailments are placed on the subject. Therefore, as with shave, there is a conflict on the subject argument for these two entailments. For this alternation, however, there is no Affected/Non-affected contrast for the lexical entailments for the subject. Although the direct object for transitive break has this Affected entailment, the subject for intransitive break does not, since it is possible for things to break by themselves, without being causally affected by anything. Still, the pattern of acceptability for the test coordinations for break matches the pattern for shave and frighten very closely, including the lack of improvement in gapped sentences, or when multiple events are indicated, as in (243) and (244): (243) a. *[The rock broke the scissors], and [the statue, into three pieces]. b. *[The statue broke into three pieces], and [the rock, the scissors]. (244) a. *The rock broke [the scissors yesterday] and [into three pieces today]. b. *The rock broke [into three pieces yesterday] and [the scissors today]. Therefore, the possible causes of ungrammaticality that were listed for shave and narrowed down for frighten can be further narrowed: Either coordinations

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Page 172 are ungrammatical because there is a conflict in ARG1, or because a Change of State conflict is more difficult to process than others. Before leaving the causative-inchoative alternation, an attestation involving a similar verb deserves attention. The verb is get, which participates in a causative alternation shown in (245). As can be seen, get has two relevant subcategorizations, VP/Pr and (VP/ wNP)/Pr,34 and is very much analogous to break except that an extra Pr argument is involved. (245) a. Kim got ready. (VP/Pr) b. Kim got everything ready. ((VP/wNP)/Pr) The attestation involving get is from my sister-in-law referring to the difficulties posed by her son’s afternoon karate class. (246) It makes it tough for him to get [his things done] and [to bed on time]. (author’s sister-in-law) A conclusion to draw from this attestation is one that has been noted many times by many linguists: If the context is just right, things that seemed impossible based on introspection are sometimes not only possible, but quite natural. This sentence is also a small piece of supporting evidence for the possible neutrality for verbs such as break . The final transitivity alternation to be considered is the induced action causative alternation seen in walk in (247), with test coordinations shown in (248): (247) a. Kim walked briskly b. Kim walked the dog. (248) a. *Kim walked [briskly] and [the dog]. b. [*]Kim walked [the dog] and [briskly]. c. *[How] and [what] did Kim walk? d. *[What] and [how] did Kim walk? As with shave, frighten and break, the test coordinations are ungrammatical, and there is no improvement in grammaticality in gapped sentences, or when multiple events are indicated, as in (249) and (250): 34. Pr is the category for predicative phrases, with type Prop→Bool, to be further discussed in Chapter 5.

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Page 173 (249) a. *[Kim walked briskly], and [Robin, the dog]. b. *[Robin walked the dog], and [Kim, briskly]. (250) a. *Kim walked [briskly yesterday] and [the dog today]. b. *Kim walked [the dog yesterday] and [briskly today]. For transitive walk, the direct object has the Change of State and Causally Affected entailments. For intransitive walk, the subject has the Change of State entailment. This situation is consistent with the narrowed down possible causes of ungrammaticality given for break: Either coordinations are ungrammatical because there is a conflict in ARG1, or because a Change of State conflict is more difficult to process. For the last four argument alternations that have been considered (shave, frighten, break, walk), one could of course say that every sample coordination has been ungrammatical because the verb in question is ambiguous, and can therefore be used with only one subcategorization at a time. However, this reasoning is even more suspect than it was earlier, when it was shown to be circular. Now that independently motivated semantic and pragmatic analysis has accounted for the seeming ungrammaticality of similar coordinations involving other verbs, to say that the verbs in these particular alternations are really and truly ambiguous is to admit that we just do not know why the coordinations are unacceptable or ungrammatical. Though the possibilities arrived at here are speculative, they are at least as (and maybe more) plausible than an appeal to ambiguity. 4.5.3 Summary In section 4.5.1, it was shown that adjunct-complement coordinations are subject to the same pragmatic influences seen for adjunct coordinations (in section 4.3) and the complement coordinations tested for serve and write (in section 4.4.2.1); specifically, Q- and R-implicature based on the semantics of conjunction. All three of these kinds of coordinations improve in acceptability when there is a clear reason to use coordination instead of simply placing the constituents adjacent to each other, one possible reason being that multiple events are being described. In section 4.5.2, this semantic and pragmatic analysis failed to account for why the test coordinations were uniformly bad. Even here, though, there are at least two possibilities to explore before concluding that ambiguity is indeed the cause—specifically, that lexical entailment conflicts involving ARG1 or involving Change of State are more difficult to process than other such conflicts.

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Page 174 4.6 Excursus: Two Sample Derivations 4.6.1 People I Want to Die or Kill In section 4.4.1, an attestation was presented in which the verb want took both a subjectless infinitive and a specified-subject infinitive as its complement: people I want to die or kill. This phrase was more complicated than a coordination such as I want to go and you to stay, since an NP (people) is extracted from the coordinated infinitival phrase, and furthermore, people fills both the subject argument of die, and the object argument of kill. A derivation of this phrase will be carried out in this section. A basic sketch of the derivation is as follows. First, want to is composed to have category As a VP/VP, it is something that can take a VP argument (such as kill someone) to become a VP (want to kill someone) . As a (VP/VP)/ΔNP, it is something that can take an NP (for example, someone) and a VP (such as die ) to become a VP (want someone to die). The complication is that the NP needs to be able to commute, so that it can come between want and to, while still allowing the chunk want to to be a constituent. To this end, the category ΔNP is used, Δ indicating a commutative modality (as employed in Morrill 1994). The next step is that die and kill are derived to have category in order to be coordinated. Thus, the coordination die or kill will be able to take want to as its argument, and the resulting phrase will have category VP/ΔNP. This is a category indicating a VP lacking an NP somewhere inside it. It is at this point that the derivation stops. The category VP/ΔNP is suitable for combining with people as a relative clause (via whatever analysis one has for relative clauses with no relative pronoun to introduce them). The derivation of want to as is shown in (251), in Gentzen sequent format since the rule of proof for the conjunctive constructor is being used. In this derivation, Comm stands for a structural postulate of Commutativity applicable to categories of form ΔA. There is not room to show the semantic part of the derivation, but the semantic terms for the bottom line of the derivation are given separately in (252).

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Page 175 (251) Deriving want to as category

(252)

Semantic terms for categories in bottom line of above proof a. b.

to: VPinf /VP: λP.P

c. Next, die and kill will each be derived to be able to take the category for want to as an argument, and result in a VP/ΔNP. This derivation is shown in (253).

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Page 176 (253) Strengthening the categories of die and kill to

With like categories, die and kill can be coordinated, as shown in (254):

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Page 177 (254) Coordinating die and kill;

The last two steps are to combine want to with die or kill by functional application, and I with want to die or kill by another step of functional application, as done in (255) and (256): (255) Combining want to and die or kill

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Page 178 (256) Combining I and want to die or kill

The semantics is not quite the desired reading, which would be λx.(want′(kill′ (x)(i′) die′(x))(i′)). That is, the intended reading is “any person x such that I want either of the following to happen: I kill x, or x simply dies.” The generated semantics in the above derivation is, “any person x such that either I want to kill x, or I want x to die.” However, it is a short step by implicature to get to this reading from the actual generated semantics. 4.6.2 How to Give the Dog a Bone and to Kim In section 4.4, on coordination of verbal complements, and more specifically in section 4.4.2.2 on argument alternations that involved role rearrangement, a derivation of *give the dog a bone and to Kim was promised, but postponed to a later section because the derivation would involve multimodal type-logical grammar. The derivation will be presented here, and will make use of the Wrapping modality as defined in Dowty (1997), in particular making use of a structural postulate of Mixed Commutativity. A preliminary step is to specify the categories and semantic terms for each version of give . The doubleobject give (as in give the dog a bone) will have category (VP/ wNP)/NP, and its meaning will be translated as give1′. The dativeshifted give (as in give the dog to Robin ) will have category (VP/ wNP)/NP to, and its meaning will be translated as give2′. In order to compare apples to apples, instead of just translating the verbs as give1′ and give2′, one meaning will need to be given in terms of the other. Therefore, give2′will be defined as shown in (257b); note the reversal of x and y, such that ARG3 for give2′ (i.e., the x) fills in the ARG2 slot for give1′.35 35. Dowty (2000) warns against assuming that the different alternants in an argument alternation are perfectly synonymous. Therefore, translating the meaning

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Page 179 (257) Categories and semantic terms for double-object and dative-shift give a.Double-object give (VP/ wNP)/NP: give1′ b.Dative-shift give A neutral lexical entry for give will have the following category and term: (258) The basic strategy of the derivation will be to move the phrase the dog to the right periphery of the phrase by using Mixed Commutativity; then to lift both a bone and to Kim to a category that takes give as an argument and results in a VP/wNP. This can then combine with the direct object the dog. The lifting of a bone and to Kim is shown in (259); the combined use of TR and ASt is discussed in Chapter 2, section 2.5.4. (259) Strengthening the categories of a bone and to Kim to

The coordination of these two phrases is shown in (260): of dative-shift give as a perfect synonym double-object give except for the different mapping of arguments may be only a crude approximation of its meaning. However, this translation will suffice for purposes here.

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Page 180 (260) Coordinating a bone and to Kim;

With the category for a bone and to Kim established, the derivation can proceed. The permuting of the dog and a bone and to Kim will be carried out by the structural postulate of Mixed Commutativity, shown in (261). (261) Mixed Commutativity (M-Comm) (adapted from Dowty 1997, (56))

The partial derivation is shown in (262). With the dot notation, it is difficult to line up the words with their categories, so they are omitted. The category corresponds to give; NP to the dog; and X to a bone and to Kim, as derived above. Semantic terms are also omitted. (262) Using M-Comm to permute the dog and a bone and to Kim;

Finally, a \E and /wE step suffice to complete the derivation. In the resulting term, the translation for the dog appears in the receiver-linked ARG2 direct object slot in the first conjunct, but in the gift-linked ARG3 oblique slot in the second conjunct, indicated by underlining.

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Page 181 (263) Derivation of VP from permuted give (a bone and to Kim) (the dog);

In short, even though the different subcategorizations of give lexicalize the roles of gift and recipient to different argument positions, if give exhibits category neutrality, phrases such as give the dog a bone and to Kim are in fact derivable. 4.7 Miscellaneous Alternations Although the analysis presented in the preceding sections describes a significant amount of data concerning possible neutrality of various verb argument alternations, it does not currently account for the ungrammaticality of every relevant coordination that can be formulated. For example, the ungrammaticality of the following sentences from Schachter (1977) has not been addressed: (264) (Schachter 1977, (7, 8)) a. *Running and to overeat may be unhealthy. b. *It’s odd for John to be busy and that Helen is idle now. Nor has the ungrammaticality of sentences such as (265) been accounted for: (265) *It seems [that Robin is a spy] and [to be true that no one else knows].

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Page 182 One possibility is that these coordinations are ungrammatical for the same reason as some of the coordinations in section 4.4, based on the Q and R Principles: A simpler way to express the information in these sentences would be to use a single subcategorization for the verbs be and seem, and then coordinate two gerunds or infinitives (in (264a)), or two finite clauses or infinitival phrases (in (264b) and (265). Not to do so violates the R Principle, and therefore these sentences are degraded. However, why do they sound so bad, when the give and load sentences just sound awkward? I do not have an answer to this question. There are also a number of attestations encountered during the writing of this chapter that seemed to involve category neutrality for various verbs, but which did not neatly fit into the organization of the chapter. They are presented in (266). It is hard to tell whether these attestations are intended to have a humorous, zeugmatic effect (indicating that the verbs are ambiguous), or are merely clever turns of phrase—or indeed, whether there is a clear distinction between outright zeugma and more subtle wittiness. (266)a.But the jigging made [Tabby nervous] and [Zeke itch]. (Cynthia Rylant, Mr. Putter and Tabby Toot the Horn, 1998) b.The soldiers did their best to evaluate their resources, but most had little idea of what they were looking [for when they went after it], or [at when they found it], (Bill Bryson, In a Sunburned Country, 2000, p. 73)36 c. From her office window, she could see [debris floating through the air] but not [that the north tower was in flames]. (Columbus (Ohio) Dispatch, 13 Sept. 2001, A4) d.Come on out and see [Dave’s cargo shirt] and [me sweat]. (Jimmy Jamm on WNCI’s Morning Zoo radio program, Columbus, Ohio, 7 June 2002) e. How to Behave so Your Children Will, Too (Sal Severe, PhD, 1999) f. But depending on the day, they’ve already been outside, or it’s pouring and they can’t go out, or it’s [midwinter] and [been dark since five]. (Paula Spencer, “Why I Love TV” Parenting. June/July 2000, p.212) As for the look, make and see attestations, I have no comments to offer at present beyond noting their existence. Concerning the behave attestation, I do not have a type-logical analysis of VP-ellipsis at my disposal, but this title seems 36. Thanks to Elaine Whitman for noticing this example.

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Page 183 to use behave in two senses at once. The most common reading of how to behave is “how to conduct oneself’ (that is, the VP/Adv categorization) but the elliptical end of the title, so your kids will, too definitely favors the “conduct oneself politely or properly” reading (i.e., the VP categorization). Of course, it is possible to read the title as “how to conduct yourself politely so your kids will conduct themselves politely, too,” but a glance at the book’s introduction seems to support the first reading. In the last attestation, it’s is simultaneously a contraction for it is and it has. As the auxiliary has, the ’s contains little semantic information; as is, its semantic contribution depends on whether one has a separate meaning for be for “weather it ” sentences or not. 4.8 Conclusions In this chapter, a limited number of verbal argument alternations were investigated which by and large are consistent with the stance that all verbal argument alternations are potentially neutral if there is no phonological difference in the alternants. This investigation was situated in a larger exploration of coordination of verbal dependents, and it was shown that, in many cases, the same influences on grammaticality of coordinations are in effect regardless of whether the verb in the coordination has one category or two. Therefore, appealing to ambiguity is simply not necessary in order to explain why certain coordinations of verbal dependents are not acceptable. A few objections need to be addressed, however. First, it might be argued that some of the improvement seen when multiple or alternative events are indicated is actually due to the psycholinguistic recency effect. That is, the test coordinations discussed in this chapter are actually ungrammatical, but that by the time the last conjunct has been parsed, the syntactic category of the verb has been forgotten, and as long as the conjunct makes sense, the coordination will be accepted. However, to defend this claim, one would have to explain why this effect fails to improve coordinations with verbs such as break, shave, frighten or walk. A second objection could be that the argument alternations discussed here actually occupy multiple lexical entries, but are just close enough in meaning that one can get away with using a single verb token in two ways at once. However, given the different levels of acceptability in the various test coordinations in this chapter, this just transforms the question into: How different must the senses of an ambiguous word be before it cannot be used with both senses at once? The preliminary picture that seems to be emerging from the survey of verbal argument alternations undertaken here is that instead of trying to pin

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Page 184 down how neutral words differ from ambiguous words, a better motivated view is that there is no fundamental distinction between the two, and that pragmatic and other factors highly influence the acceptability of test coordinations involving the different senses of a given word. This view accords well with the theoretical observation in Chapter 2, that under current definitions, it is impossible to formally distinguish ambiguity from category neutrality.

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Page 185 CHAPTER 5 Category Neutrality and Predicative Phrases 5.1 Introduction Sentences containing predicative complements provide some of the best known examples of coordination of unlike categories in the literature, since no fewer than three kinds of categories can appear in predicative positions: adjective phrases (APs),37 prepositional phrases (PPs), and noun phrases (NPs). These three categories allow for three kinds of unlike coordination (ignoring coordinations of more than two items): AP with PP; PP with NP, and NP with AP. Sag et al. (1985) show examples of all three kinds, some of which are shown in (267): (267) (from Sag et al. 1985, (2), (3)) a. Pat is either [stupid]AP or [a liar]NP. b. Pat is [a Republican]NP and [proud of it]AP. c. That was [a rude remark]NP and [in very bad taste]PP. d. Sandy is either [a lunatic]NP or [under the influence of drugs]PP. e. Pat is either [asleep]AP or [at the office]PP. Attested examples of NP-PP and NP-AP coordinations can also be found in searching the Internet for mixed- wh interrogatives (MWIs) like those discussed in Chapter 3. The Internet search for strings such as what and where, why and what, etc. (discussed in Chapter 3), turned up many instances of mixed- wh interrogatives with the copula as the verb. A sampling is given in (268); other copular MWIs can be found in section A.5 of Appendix A. Sentence (268a) is 37. Including participial phrases.

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Page 186 analogous to an NP-PP coordination, with who expecting an NP answer, and where expecting a PP answer. A similar pairing in seen in (268b), except that the nominal wh is the phrase whose son instead of the word what, and the where appears second instead of first. Sentence (268c) is analogous to an NP-AP coordination, with how expecting an AP answer. (268)Mixed- wh interrogatives involving copula, attested on the Internet a.Who and Where Are Our Children with Cochlear Implants? b.In the case of Saul’s replacement, Samuel knows where and whose son the new king will be, but he does not know which one of the sons of Jesse. c. As long as I am distracted by how or what I SHOULD be, or how or what she SHOULD be, or how or what the marriage or relationship SHOULD be, I will not be able to see her, or myself, clearly, nor will I be able to see ANYTHING as it truly is. Given the grammaticality of the coordinations in (267) and (268), it has been proposed that be and a few other verbs have neutral lexical entries, specifying that they can take more than one type of complement. For instance, the lexical entry for be would indicate that it can take either an NP, AP, or PP argument. However, linguists who argue that category neutrality does not occur (for example, Bayer 1996) take a different view, maintaining that be selects only for a certain semantic type as its complement (specifically, Ind→Bool, or in the system used here, Ind→Prop), and that APs, PPs and noun phrases all have (or can have) this semantic type. The idea of noun phrases being able to have type Ind→Bool goes back at least to Williams (1983), and is also promoted in Partee (1987). In fact, this is the analysis that will be pursued here, but interestingly enough, it does not eliminate category neutrality. With a new type available for APs, PPs and NPs, new possibilities for neutrality are opened up. Regarding APs, if predicative APs now have a different type from attributive APs, the question arises of whether an AP could ever have both types at once. The same question arises for PPs, and moreover, since PPs can be adverbial as well as predicative and attributive, there are two extra cases to consider: predicative-adverbial neutrality, and attributive-adverbial neutrality. As for NPs, if predicative NPs now have a different type from referential NPs (for example, Kim ) and quantificational NPs (for example, every cat ), it is reasonable to ask if an NP ever needs to have more than one of these types at once. These possibilities for neutrality among APs, PPs, and NPs are the focus of this chapter.

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Page 187 Before going further, it will be necessary to shift from the pretheoretical AP, PP, and NP category notation, to the type-logical category names as defined in Chapter 2. Also, the category that will be used for the copula needs to be established. These issues will be addressed in section 5.2. In the remainder of this chapter, section 5.3 covers the possibilities for neutrality in APs and PPs, with the finding that there is a good possibility of neutrality in prepositional phrases. Section 5.4 deals with neutrality in noun phrases, with the finding that and neutrality is a fact of the English language. Section 5.5 explains in detail the choice of the VP/Pr categorization of the copula, including drawbacks that have been noted for this analysis. Section 5.6 summarizes and offers closing comments. 5.2 Categories for the Copula, APs, PPs, and NPs The category that is assigned to the copula be depends on what categories one assigns to APs, PPs, and NPs. First, the categories for these phrases when they are NOT used predicatively need to be established. Attributive APs will usually have either N/N or N\N as their category, depending on whether they appear to the left or the right of the noun they modify. (Tough adjectives and a few others will have slightly different categories.) Attributive PPs will have category N\N; adverbial PPs, the category S\S.38 Incidentally, since AP and PP are not in the inventory of type-logical category names, it will be safe and convenient to use these names when it is necessary to refer to adjectival or prepositional phrases without regard to their type-logical category. As for noun phrases, referential noun phrases will have category NP—and from this point forward, the name NP will be reserved for this type-logical category for referential noun phrases. Quantificational noun phrases will have category as defined in Chapter 2, section 2.6.2. When the need arises to refer to noun phrases without regard to their typelogical category, the name “noun phrase” will be spelled out. With these categories established, the next question to consider is whether to have a separate category for predicative APs and PPs (call it Pr, following Carpenter 1997, with type Ind→Prop). If one decides not to, then a certain set of categories will be needed for the copula. If one does decide to have Pr as a category, the next question is whether it should be given just to predicative APs and PPs, or whether it should be given to predicative noun phrases as well. 38. For simplicity, cases of PP subjects (as in Under the bed is a strange place to hide your beer ) will not be considered, nor will PPs in which the prepositions serve just as case markers, as in rely on someone.

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Page 188 Depending on one’s choice here, the copula again has different possible categories. The choices are summed up in the flowchart in Figure 8:

Figure 8 Categories for copula, depending on categories for APs, PPs and noun phrases The analysis that will be pursued for most of this chapter is the one labeled C, in which the only category for the copula is VP/Pr. However, the other two analyses exist in the literature, and deserve some consideration. Analysis A is essentially that proposed by Morrill (1994:166–8) and Hendriks (1995:130–3), except that the categories have been rewritten so as to avoid using the disjunctive constructor With these categories for the copula, some AP-PP

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Page 189 coordinations cease to be coordinations of unlikes—namely, coordinations of PPs with APs of category N\N (for example, Kim is [in the kitchen]ppand [mad enough to spit]AP ). The semantics for the copula with the categories VP/(N\N) and VP/NP is shown in (269). (The semantics for the copula with category VP/(N/N) would have the same semantics as with category VP/(N/N)). (269) Categories and semantics for be under analysis A a. VP/(N\N): λVN/Nλx. V(λy.y=y) b. VP/NP: λxλy. (x=y) To show how the semantic term in (269a) generates the desired semantics, a sample derivation of Pat is proud of it is given in (270). The key is the supplying of the (ordinarily) attributive adjective, which usually takes an N as its argument, with a property that is always true (i.e. λy.y=y), so that the “core” semantics (i.e., proud′) can combine with the subject of the sentence. (270) Derivation of Pat is proud with copula as VP/(N\N)

The use of the semantic term in (269b) is illustrated in the derivation of Pat is a Republican, given in (271). The resulting term here, some′(repub′) (λx.(x=pat′)),=pat′)), is logically equivalent to repub′ (pat′). (For further discussion on this equivalence, see section 5.4.5).

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Page 190 (271) Derivation of Pat is a Republican with copula as VP/NP

Putting these categories together, be will have the category in order to allow for unlike coordinations such as Pat is a Republican and proud of it . A derivation is given in (272) through (274), similar to (69) in Chapter 2 (section 2.4.4), but this time with the AP for proud of it replaced by N\N, the NP for a Republican replaced by and semantic terms shown. Because of spacing considerations, the derivation is presented in several pieces. In the first part, a Republican and proud of it are derived to have category In this part of the derivation, the step labeled is never discharged, but it will be further down in the derivation in (274). For the TR and ASt theorems, the reader is referred to (30), (47), (57), and (68) in Chapter 2.

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Page 191 (272) Strengthening the categories of a Republican and proud of it to

In the second part of the derivation, a Republican and proud of it are coordinated: (273) Coordinating a Republican and proud of it;

Finally, a Republican and proud of it can be combined with Pat is:

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Page 192 (274) Combining Pat is with a Republican and proud of it

Under analysis A, a copular MWI such as who and where are our children would be derived in the same way as the optional NP-gap MWIs in the previous chapter. That is, who and where would both undergo ASt to be assigned like categories—something like —and our children are would be derived to have category thanks to the conjunctive categorization for the copula. This derivation is not shown here, since the general shape of such a derivation can be found in section 3.2.3.3 in the Chapter 3. Analysis B, with categories VP/Pr and VP/NP for the copula, is favored by Carpenter (1997:197). There is some independent motivation for having separate categories for attributive and predicative APs: First, there is the existence of exclusively predicative adjectives such as asleep . Furthermore, having Pr as a separate category prevents exclusively attributive adjectives (such as former and utter ) from being used as predicatives (as in *That fool is utter ). Under this analysis, the VP/Pr version of the copula would have semantics as in (275), and Pat is proud would be derived as in (276).

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Page 193 (275) Category and semantic term for copula under analysis B a. VP/Pr: λP.P b. VP/NP: λxλy.(x=y) (276) Derivation of Pat is proud of it with copula as VP/Pr

Pat is a Republican and proud of it would be derived as in (277) and (278); the steps are the same as in the earlier derivation of this sentence, but with Pr replacing N\N, and the corresponding semantic changes. (277) Coordinating a Republican and proud of it,

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Page 194 (278) Combining Pat is with a Republican and proud of it

Derivation of copular MWIs under analysis B is similar to their derivation under analysis A, with Pr substituted for N/N. If one chooses analysis A or B, one accepts category neutrality upfront—specifically, verb neutrality for the copula. For this reason, these analyses are not favored by linguists opposed to the idea of category neutrality; rather, an analysis like C is promoted, in which the copula has only one category: VP/Pr. Under this analysis, the category Pr is assumed to be appropriate not only for APs and PPs, but for noun phrases as well. In the type-logical framework, this analysis is closest to that of Bayer (1996:607–8). Various motivations for analysis C have appeared in the literature, in particular in Williams (1983), but not all of them are valid. A critical review of these reasons is presented in section 5.5. The reason that analysis C will be adopted in this dissertation concerns facts about quantification, discussed in section 5.5.1. Under this analysis, a Republican might (by means to be discussed in section 5.4.5) have category and term as in (279), and Pat is a Republican and proud would be derived as in (280). (279) a Republican: Pr: repub′

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Page 195 (280) Derivation of Pat is a Republican and proud of it; X=Pr

Under analysis C, wh-words that can introduce interrogatives headed by the copula (specifically, who, what, where, when, and how) would all need to have category S w/(S/Pr), and semantics Given this category for wh words, copular MWIs are not true MWIs, since there is no need for their wh-words to undergo ASt in order to have like categories. They are derived in the same way as ordinary coordinated- wh interrogatives. Although no category neutrality is needed under analysis C in order to derive unlike coordinations such as Pat is a Republican and proud of it, or copular MWIs such as how or what I should be, all that has been eliminated is verb neutrality for the copula. Still remaining is the possibility of argument neutrality for APs, PPs and noun phrases. In fact, this possibility is heightened, since each kind of phrase now has an additional category (Pr) available to it. These categories are summed up in (281): (281) Categories for APs, PPs and noun phrases a. adjective phrases: Pr, N/N, N\N b. prepositional phrases: Pr, N\N, S\S c. noun phrases: NP, Pr, In the next three sections of this chapter, the possibilities for neutrality across these categories will be explored: for APs and PPs in section 5.3, and for noun phrases in section 5.4.

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Page 196 5.3 Category Neutrality, APs, and PPs In this section, with VP/Pr as the category for the copula, the consequences of letting APs and PPs have category Pr are explored. Specifically, sentences will be constructed in which an AP or PP must have category Pr and some other category simultaneously. Additionally, sentences will be constructed in which a PP has to be both attributive (N\N) and adverbial (S\S) simultaneously. Section 5.3.1 deals with APs; the data presented there do not suggest or neutrality for APs. Section 5.3.2 deals with PPs; the data presented there do not suggest neutrality for PPs, but do show that and neutrality exists. Lexical rules to allow APs and PPs to have their various categories are presented in section 5.3.3. 5.3.1 Examination: Predicative and Attributive APs To search for test cases for neutrality of predicative and attributive APs, coordinations are constructed whose factor must be simultaneously both Pr and N\N. (Coordinations whose factor is simultaneously both Pr and N/N cannot be constructed, since the only position for an N/N is immediately to the left of an N, and Pr never occurs here.) This can be done by coordinating two VPs with final Pr and N\N gaps. To get a VP with a final Pr, verbs such as consider, deem, or make are used, which take a noun phrase plus predicative complement; for example, deemed the photos suitable for framing ends in the Pr phrase suitable for framing. To get a VP with a final N\N, all that is needed is a VP that ends in a noun phrase whose head noun is modified by an N\N. For example, bought the posters suitable for framing also ends with the phrase suitable for framing, which is operating here as an N\N. Without the final suitable for framing, these VPs can be derived as VP/Pr and VP/(N\N), as shown in (282) and (283):

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Derivation of deemed the photos as VP/Pr deemed: the: (VP/Pr)/NP39 NP/N

photos: N

[Pr]1

Derivation of bought the posters as VP/(N\N)

The test coordination for Pr and N\N combines (282) and (283) to yield the ungrammatical (284), where the sentence-final AP suitable for framing, with category serves both as a complement of the S/Pr and the S/(N\N). (The derivation has been shown separately in (285), since it will be relevant again in later examples.) (284) *I deemed the photos and bought the posters suitable for framing. VP/Pr VP/(N\N) 39. If the direct object is always the second to last argument to combine with a verb, then the category for deemed should be (VP/NP)/Pr. However, a verb with such a category would not be able to combine with a nonadjacent Pr. This is a general problem, and the solution (discussed in section 4.2) is to use a Wrapping modality, and assign deemed the category (VP/ wNP)/Pr. As a multimodal derivation would unnecessarily complicate the picture, deemed has been given the category (VP/Pr)/NP.

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Page 198 (285) Derivation of deemed the photos and bought the posters suitable for framing as

Although (284) is decidedly bad, it is unclear whether this is because of predicative-attributive ambiguity of the AP suitable for framing. As a control, coordinations have been constructed in (286) and (287) in which the AP is exclusively Pr or N\N. For the most reliable comparison, these sentences should be as much like (285) as possible. Therefore, the only thing that has changed in these sentences is the choice of verb in one of the conjuncts, so that the coordinated VPs each have a Pr gap, or each have an N\N gap. In (286), then, suitable for framing has only the category Pr, and the VP/NP bought has been replaced with the (VP/Pr)/NP rendered . (286) I deemed the photos and rendered the posters suitable for framing. VP/Pr VP/Pr Pr The result is slightly awkward, but nonetheless seems to be grammatical. Thus, the ambiguity hypothesis can still stand. In parallel fashion, in (287), suitable for framing has the category N\N, and the (VP/Pr)/NP deemed has been replaced with the VP/NP identified . (287) [*]I identified the photos and bought the posters VP/(N\N) VP/(N\N) suitable for framing. This sentence is marked with a [*] to indicate that the desired reading is ungrammatical: The only available reading seems to be one in which identified the photos is a VP instead of a VP/(N\N). However, a significant difference between (287) and (286) is that in (286), suitable for framing is needed as a complement for deemed the photos (which can only be a VP/Pr), while in (287), it is not needed as a complement for identified the photos (which can be parsed as a VP). If the sentence is altered so that there is a preference for suitable for

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Page 199 framing to be taken as a complement to identified the photos, grammaticality of the desired reading improves. This is done in (288) by turning (287) in to a gapped sentence, with coordinated subjects I and Kim . The more prominent parallelism of the subject-verb-object sequences makes it easier for the single AP at the end to be taken as a factor of a conjunction, as indicated by the ? marking. (288) ?I identified the pictures and Kim bought the posters S/(N\N) S/(N\N) suitable for framing. N\N To sum up, the test coordinations do improve when suitable for framing is exclusively a Pr or an N\N, and not a Therefore, the hypothesis that Pr-N\N ambiguity is responsible for the ungrammaticality of (284) can still stand. Although it is still conceivable that a lexical item such as suitable could have a neutral entry in the lexicon (in this case, that for unrelated reasons could never pass a coordination test, the conclusion for now is that the evidence does not point toward neutrality for predicative and attributive APs. 5.3.2 Examination: Predicative, Attributive, and Adverbial PPs Given the three categorial possibilities for PPs—Pr, N\N, and S\S—there are three binary possibilities to investigate for neutrality: and Turning first to in (289) is a sentence parallel to the example in (284), again using deem as the predicative complement-taking verb, but replacing the AP suitable for framing with the PP in danger of collapsing. The derivation proceeds precisely as in (285). Like (284), sentence (289) is ungrammatical. (289) *I deemed the library and condemned a dormitory VP/Pr VP/(N\N) in danger of collapsing. As with the similar coordination with an AP in (284), the ungrammaticality of this sentence may be due to ambiguity of the PP between its Pr and N\N categories: When similar sentences are constructed in which the PP has only the category Pr or N\N, grammaticality is improved. In (290a), in danger of

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Page 200 collapsing is used only as a Pr, and the VP/NP condemned has been replaced with the (VP/Pr)/NP declared. (290) a. ?I deemed the library and declared a dormitory VP/Pr VP/Pr in danger of collapsing. Pr b. I deemed the library and Kim declared a dormitory S/Pr S/Pr in danger of collapsing. Pr In (291), in danger of collapsing is used only as an N\N, and the (VP/Pr)/NP deemed has been replaced with the VP/NP surveyed . Like the sentences in (290), these sound better than the starting sentence in (289). (291) a. I surveyed a library and condemned a dormitory VP/(N\N) VP/(N\N) in danger of collapsing. N\N b. ?I surveyed a library and Kim condemned a dormitory S/(N\N) S/(N\N) in danger of collapsing. N\N As with the AP examples in the previous section, the evidence is consistent with predicative-attributive ambiguity of PPs. Next, a coordination test for neutrality is constructed. Two verb phrases are coordinated, one with a Pr gap, and the other with an S\S gap. The VP/Pr will be the phrase wanted the statue. The VP/(S\S) will be the phrase put the vase.40 The PP that will serve as the complement to both will be on the table . The sentence is shown in (292); the derivation is shown in (293). Like the sentences in (286), (290), and (291), sentence (292) sounds somewhat stilted, 40. Of course, put does not take just any adverbial complement—only locatives. Currently, there is no means in type-logical grammar of expressing this distinction. It might be argued that instead of a S\S complement, put actually takes a Pr complement (again restricted to locatives), by likening put to predicative-complement verbs such as make. However, since put can be followed by definitely adverbial locatives such as PPs headed by into or onto, S\S seems to be the overall most reasonable choice of category.

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Page 201 but not ungrammatical. Thus, it seems that neutrality is possible for PPs. (292) ?I put the vase but wanted the statue on the table. VP/(S\S) VP/Pr (293) Syntactic derivation of put the vase but wanted the statue on the table;

Further evidence for neutrality can be found in data on English where . First, consider interrogative and relative where, in the grammatical coordinations seen in (294). (294) a. Where did you put the vase but actually want the statue? VP/(S\S) VP/Pr b. the table where I put the vase but actually wanted the statue VP/(S\S) VP/Pr As in (292), the categories VP/(S\S) and VP/Pr will have to be strengthened via ASt to before they can be coordinated. The category for the gap will percolate up, so that in (294a), the phrase did you put the vase but actually want the statue will have category 41 and in (294b), I put the vase but actually wanted the statue will have category Here, though, instead of combining with an actual PP of category the gap in the coordinated verb phrases is bound off by where . In order for this to happen, interrogative and relative where will have to have categories as given in (295). (295) Categories for interrogative and relative where a. (nonembedded) interrogative: b. relative: 41. S inv is the category for sentences with subject-auxiliary inversion.

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Page 202 In other words, instead of taking a complement with an S\S gap, such as an S/(S\S), where takes a complement with a gap.42 Thus, although (294) does not show that neutrality exists for PPs, it does show that it exists in argument categories for where, and thus increases the plausibility of such neutrality for PPs. Similar evidence can be found in the free relatives introduced by where that are shown in (296), and parallel to the upstairs-downstairs neutrality seen in (11) in Chapter 2, except at the category level: (296) a. I’m gonna put all your forks where your knives should be. VP/(S\S) VP/Pr (Wild Man Fisher, The Creature from Outer Space ) b. I wanted my knives where Kim put all my forks. VP/Pr VP/(S\S) c. I’m gonna put all your forks where I put your knives. VP/(S\S) VP/(S\S) d. I wanted the knives where Kim wanted the forks. VP/Pr VP/Pr In (296a), where needs to be given category (S\S)/(S/Pr), since it takes a sentence with a Pr gap (your knives should be__) as its argument, and acts as a S\S complement to put. In (296b), on the other hand, where needs to be Pr/(S/(S\S)), since it takes a sentence with an S\S gap (Kim put the book__) and acts as a Pr complement to want . And in (296c) and (296d), where needs to be (S\S)/(S/(S\S)) and Pr/(S/Pr), respectively. Having four entries for free-relative where misses a generalization, especially given the “matching effect” in free relatives (Bresnan and Grimshaw 1978), which essentially states that free relative pronouns have categories of form X/(S/X). It is overall more plausible to assign where the category Again, the sentences in (296) do not prove that neutrality exists for PPs, but they do strongly indicate that this category exists in both the argument and result categories for free relative where, and thus increase the plausibility of neutrality in PPs. 42. Interestingly, the category for where still licenses simple sentences such as Where did you go?, in which only a S\S gap exists. The reason is that for wh adverbs is derivable from S inv/(S\S) via ASt. (For the same reason, still licenses relative adverbials such as the town where I was born, even though I was born has category S/(S\S).)

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Page 203 Lastly, neutrality will be considered for PPs. Sentence (297) is designed to test this possibility; its grammaticality indicates that neutrality is possible. (297) I put the picture and cleaned up the trash in my desk drawer . VP/(S\S) VP/(N\N) To sum up, evidence supports the existence of and neutrality among PPs; as with APs, available evidence does not point toward neutrality. 5.3.3 Lexical Rules for APs and PPs In the preceding sections, three possibilities for neutrality have been explored: for APs and PPs; for PPs; and for PPs. Of these three, only the two involving the category S\S were able to pass coordination tests (and for one of these, corroborating evidence was found in sentences involving free-relative where ). At this point, lexical rules will be introduced to capture these facts. 5.3.3.1 Lexical Rules for Predicative and Attributive APs and PPs Before the cases of category neutrality are addressed, a set of lexical rules that relate predicative and attributive APs and PPs will be presented, since this issue will play a part in later discussions of neutrality. The basic choice to be made for a lexical rule relating predicative and attributive APs and PPs is whether to have the predicatives as input and the attributives as output, or vice versa. Each way has advantages and disadvantages, but overall, deriving attributives from predicatives is the preferable direction. First, it should be noted that either direction allows for overgeneration: since there are exclusively predicative adjectives (asleep, aware, etc.), and exclusively attributive ones (former, utter, etc.), a lexical rule in either direction will theoretically allow exclusively predicative or attributive adjectives to be used in ungrammatical ways. However, as discussed in Chapter 2, a characteristic of lexical rules is their semiproductivity, and given that the majority of adjectives (and all adjectival PPs) can be either predicative or attributive, this lexical overgeneration will be overlooked. A seeming advantage of deriving attributives from predicatives is that it is easier to write a rule converting the predicative meaning a to the attributive meaning than vice versa. Nevertheless, it is possible to write

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Page 204 lexical rules going in the other direction that result in the desired semantics for predicative and attributive APs and PPs, so ease of writing out the semantics cannot be considered a true advantage of deriving attributives from predicatives. A disadvantage to a lexical rule deriving attributives from predicatives is that, since it has been decided that noun phrases can have category Pr, lexical noun phrases can theoretically act as predicatives, licensing phrases such as *the Kim dog. Although such phrases do exist, they seem to be part of a more general conversion of various constituents into adjective phrases, as in her devil-maycare attitude. This lexical overgeneration is not a decisive disadvantage, given the semiproductivity of lexical rules, but still it is not a desirable aspect of such an analysis. However, it will be seen that the predicative-to-attributive has an advantage to offer, while the attributive-to-predicative direction suffers from syntactic (as opposed to lexical) overgeneration. To see this, the actual predicative-to-attributive lexical rule will now be introduced. Carpenter (1992) develops an extensive set of lexical rules concerning the English predicative, and for attributive and predicative adjectives, he proposes a lexical rule along the lines in (298): (298)Predicative-to-attributive lexical rule (from Carpenter 1992, (191)) Pr$ n : The first point that should be explained about this rule is the $n in the categories Pr$ n and (N/N)$n . This is a convention that Carpenter adopts from Ades and Steedman (1982). Under this convention, a category written as A$n stands for any category whose ultimate result category after combining with n arguments is A. The sequence of abstracted variables λx1…λ xn is the semantic analog of the $. For the category Pr$ n in (298), n arguments will need to be supplied before arriving at a Pr, with meaning α. These arguments are the string of variables (x1)…(xn). When a is applied to them, the resulting (α(x1)… (xn)) will have category Pr, and the change in category and semantics specified by the lexical rule can be made. In this case, the category change is from Pr to N\N, and the semantic change is to apply the term adn (to be discussed shortly). The n variables must be re-abstracted (in the λx1…λ xn sequence), so that the category of the output word will be (N\N)$n, instead of just N\N. Using the $ convention, a family of lexical rules can be abbreviated as something that looks like a single lexical rule. In (298), adn (“adnominal”) stands for a semantic term that turns the predicative meaning of an adjective or preposition into an attributive one. A suitable choice for adn would be the term in (299). A sample derivation of an attributive adjective from a predicative is shown in (300); here, the sequence of abstracts λx1…λ xn is empty.

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Page 205 (299) (300) Application of predicative-to-attributive lexical rule: red Carpenter’s formulation of this lexical rule is ingenious, as it not only converts attributive adjectives into predicative adjectives, but also converts modifiers of attributive adjectives into modifiers of predicative adjectives. Even without considering the question of category neutrality, the issue of modifiers of adjectives (and adverbs) has posed a problem. Specifically, since APs can be modified by adverbs, those adverbs will consequently have to be categorized both as Pr/Pr (to modify predicative APs), and (N/N)/(N/N) and (N\N)/(N\N) (to modify attributive APs). Given that adverbs make the same semantic contribution whether they modify predicative or attributive APs, this seems to be an unwarranted multiplicity of categories. Furthermore, adverbs themselves can be modified by other adverbs, which can complicate the situation in some theoretical frameworks. Sadler and Arnold (1994) were the first to point out this problem; Kasper (forthcoming) identifies this as a semantic as well as syntactic issue, and gives it the name RECURSIVE MODIFICATION. To illustrate, in a phrase like apparently available, the adjective available could be either predicative (Pr) or attributive (N/N). As a Pr, available would have the term available′. If apparently is assigned the category Pr/Pr, and the meaning apparent′, then apparently can combine with available to produce a Pr with apparent′(available′) as its semantic term. As an N/N, on the other hand, available will have meaning with the core meaning of available′ buried in the larger term. If apparently is to modify the attributive available, then it will also need to be assigned category (N/N)/(N/N), and the appropriate (and more complex) semantic term. In an HPSG framework, Kasper notes, the semantics works out such the phrase apparently available solution means something that not only might not actually be available, but also might not actually be a solution! Carpenter’s lexical rule, however, solves this problem. (Carpenter does not note this fact, as his paper was published in 1992, before Sadler and Arnold’s.) Under his analysis, modifiers of APs are not required to have Pr/Pr and (N/N)/(N/N) and (N\N)/(N/N) as categories. Instead, a single categorization of Pr/Pr for adjectival modifiers will suffice, since the lexical rule will allow the modifier to have the category (N/N)/Pr as well. The derivation of apparently as (N/N)/Pr in (301) demonstrates this fact. To complete the picture, a derivation of apparently available solution is given in (302).

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Page 206 (301) Application of predicative-to-attributive lexical rule: apparently

(302)

Derivation of attributive apparently available solution

Interestingly, Carpenter’s approach does not make the assumption that the head of an attributive AP has to be attributive itself. This will be the case only if the head adjective is not modified, as in available solution. When a modifier is present, as in apparently available solution, the adjective available has its predicative Pr categorization, and it is the adverb apparently that turns the whole AP into an N/N. In this respect, Carpenter’s analysis has much in common with Kasper’s HPSG-based one, which similarly has the choice of predicative or attributive made at the highest projection of the AP. Now that the issue of recursive modification has been examined, the advantage of the predicative-toattributive direction, and disadvantage of the attributive-to-predicative direction, can be seen. Going from predicative to attributive, it is correctly predicted that exclusively attributive adjectives cannot be modified, since the modifying adverbs take only Pr as their argument category. This prediction is borne out in the ungrammaticality of phrases such as *apparently former, *definitely utter . In contrast, a lexical rule converting attributives to predicatives predicts that these phrases will be grammatical. In such an analysis, adjective-modifying adverbs would have as their basic category either (N/N)/(N/N) or (N/N)/Pr. In the (N/N)/(N/N) case, phrases like *apparently former would be licensed as attributive APs; furthermore, the lexical rule would also assign the adverbs the category Pr/(N/N), since both (N/N)/(N/N) and (N/N)/Pr are instances of (N/N)$. Consequently, *apparently former would also be generated as a predicative AP. These are more damaging overgenerations than those discussed before, since they arise in the syntax. That is, the lexical rule must apply to apparently in order for it to have category Pr/(N/N) and license phrases like is apparently available; but if apparently has this category, then *apparently former will inevitably be generated via the

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Page 207 syntactic rules of inference. In the (N/N)/Pr case, ruling out *apparently former is not a problem, but note that apparently will also need to have the category (N\N)/Pr, in order to license attributive APs such as apparently eager to go; and if it has both these categories, then apparently eager to go will also be generated as an N/N, as in *the apparently eager to go puppy (and similarly, apparently good will be generated as an N\N, as in *the book apparently good). Again, these are serious syntactic overgenerations, not forgivable lexical ones. For this reason, the predicative-to-attributive direction will be chosen for a lexical rule relating predicative and attributive APs and PPs. As written, however, the lexical rule in (298) is only a rough approximation. For example, it will convert any predicative AP or PP (by converting the head adjective or preposition) to an undesired prenominal (i.e. N/N) attributive. This can be seen in the application of the rule to in shown in (303); here, the sequence of abstracts λx1…λ xn is realized as λP1. (303) Application of predicative-to-attributive lexical rule: in A finer-grained approach is needed in order to ensure that PPs and phrasal APs are assigned to N\N, or that other special cases (such as tough adjectives) are assigned the proper category. This is not a big problem, though, since the $ convention is only a means of referring to many lexical rules at once in a minimum of space. All that needs to be done here is to abandon the $, and specify the predicative-toattributive lexical rules as appropriate individually. This set of lexical rules would include at least those in (304): (304) Finer-grained set of predicative-to-attributive lexical rules a. (e.g. red) b. (e.g. tough) c. (e.g. with) d. (e.g. very, as in very good) e. (e.g. very, as in very eager to go) The lexical rules above specify that there will be two lexical entries for attributive and predicative adjectives (and heads of attributive or predicative PPs). Recall that in Chapter 2 (section 2.5.1), it was pointed out that if a word w has categories A and B in the lexicon, then the frame semantics guarantees that

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Page 208 it will have category in the language. This fact means that under the current theoretical assumptions, there can be no formal distinction between ambiguity and category neutrality. If this theoretical situation accurately reflects how natural language works, then it is predicted that predicativeattributive category neutrality for APs and PPs should exist. In this case, the ungrammaticality of the various test coordinations in sections 5.3.1 and 5.3.2 will have to be explained without appealing to ambiguity. On the other hand, if there is a real difference between ambiguity and neutrality, then the lexical rules here will need to specify that they are encoding ambiguity, and not neutrality. How to do this in a type-logical framework remains to be discovered. 5.3.3.2 Lexical Rules for Predicative and A dverbial PPs Turning to neutrality for PPs, the lexical rule in (305) states that any preposition that can head a predicative PP (e.g., in, with; but not into, onto) can also head an adverbial PP. The semantic term adv(α) is an abbreviation for whatever the adverbial translation of a predicative PP with meaning α would be. With this rule in place, a preposition such as in will have two categories, Pr/NP and (S\S)/NP, in the lexicon. (305) Pr-to-S\S lexical rule for prepositions If, as brought up in Chapter 2, there is no formal distinction between ambiguity and category neutrality, then the above lexical rule is enough to allow neutrality for PPs. If not, however, then there will need to be some means of distinguishing lexical rules that encode neutrality from those that encode ambiguity, as stated earlier. 5.3.3.3 Lexical Rules for Attributive and Adverbial PPs Achieving neutrality for PPs could be quite simple or very tricky, depending on one’s assumptions about lexical ambiguity and neutrality. Note that there are already two lexical rules concerning attributive and adverbial PPs: (304c) states that if a word has category Pr/NP, then it also has category (N\N)/NP, and (305) states that if a word has category Pr/NP, then it also has category (S\S)/NP. If there truly is no difference between ambiguity and neutrality, then these rules alone guarantee that a PP can have category If not, then there will need to be a lexical rule deriving (S\S)/NP

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Page 209 from (N\N)/NP,43 and specifically a lexical rule that encodes neutrality rather than ambiguity. 5.4 Category Neutrality and Noun Phrases It was seen in section 5.2 that having the category Pr for noun phrases allows coordinations of predicative noun phrases with predicative APs or PPs without the need for a neutral category for the copula. Now, however, there are three categorial possibilities for noun phrases: In addition to category NP (type Ind) for referential usages, and category (type (Ind→Prop)→Prop) for quantificational usages, noun phrases are now assumed to have category Pr (type Ind→Prop) for predicative usages. Therefore, there are three binary possibilities for neutrality: and These possibilities are explored in sections 5.4.1–5.4.3. Evidence is not found for neutrality, but and neutrality do exist. 5.4.1 Examination: Referential and Quantificational Noun Phrases In fact, little needs to be said about neutrality. First, the category will be available to any NP, since is derivable from NP. A proof is shown in (306); since it involves the rule of proof for the proof is in Gentzen sequent style. (306) Proof that

Second, even though this neutrality is automatically available to any NP, there does not seem to be a linguistic need for it. As has been seen in earlier chapters, the most common way for a category of form to be used is for it to be the argument to a coordination of functors, one with category C/A, and the other with category C/B. In this case, therefore, it might seem that neutrality would be 43. Deriving (N\N)/NP from (S\S)/NP is not a good choice, since not every adverbial PP can be used as an attributive one, as seen in *the book onto the table .

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Page 210 required if an extensional verb such as find, of category VP/NP, is coordinated with an intensional verb such as seek, of category However, since is derivable from VP/NP, neutrality is not necessary even here. A syntactic derivation of sought and found Kim is given in (307). In this derivation, the NP Kim is converted to an but not (307) Derivation of sought and found Kim; a. Syntactic only

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Page 211 b. Syntactic and semantic

In sections 5.4.2 and 5.4.3, then, the other two possibilities for neutrality, examined.

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Page 212 5.4.2 Examination: Predicative and Referential Noun Phrases At this point the possibility of neutrality will be considered. In fact, such cases exist, as shown in (308), including an attestation in (308c): (308) a. He wishes he could be or meet {Tiger Woods/that man}. VP/Pr VP/NP b. That woman neither is nor is impersonating Eva Peron. VP/Pr VP/NP (slightly modified from a sentence from Robert Levine, p.c.) c. Be and do your best. VP/Pr VP/NP (from a list of rules posted in preschool classroom, Reynoldsburg, Ohio, 2003) The VP in (308a) can be derived if Tiger Woods has the category and term as in (309). (How Tiger Woods will get this category assignment will be addressed in section 5.4.4.) The derivation appears in (310). (309) Tiger Woods: (310) Derivation of be or meet Tiger Woods; a. Syntactic only

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Page 213 b. Syntactic and semantic;

In addition to the predicatives seen above, special note needs to be taken of what I will call the “Malkovich predicative.” In discussing predicative sentences where the idea of being someone else is involved, many people immediately think of the 1999 movie Being John Malkovich as a good context for uttering these kinds of sentences. In this movie, it is possible for characters to live for a period of time in the body of real-life actor John Malkovich. They see the world through his eyes, and feel what he physically feels. So if someone did this, and then met John Malkovich, (311) would be a truthful summation of events. (311) He was and then met John Malkovich. VP/Pr VP/NP There are two positions that one could take here. One would be to say that be in this case is not really a copula, but just a VP/NP meaning “inhabit the body of.” After all, John Malkovich and the person visiting his body maintain separate consciousnesses: Malkovich (for the most part) is in control and unaware of the visitor, and the visitor realizes that s/he is not really Malkovich, but maintains his/her true self inside Malkovich’s body. In essence, be here is much like the be in this sentence from Partee (1987): (312) (Partee 1987, (23)) Olivier is Richard III.

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Page 214 Here, Partee notes, be could be taken as just a VP/NP meaning “play the role of” (analogous to the VP/NP meaning of “inhabit the body of’ above). However, Partee promotes a different analysis of (312): that be is still (in type-logical terms) VP/Pr, and that (p. 136) “Richard III as a role is a non-rigid individual concept” with type Ind→Prop. That explanation certainly would seem apply in the case of (311), where John Malkovich no longer means the unique individual John Malkovich, but rather a position (much like the role of Richard III, or the president of the United States, or Miss Universe) that can be filled by different individuals at different times. If this analysis is correct, then (311) is indeed an instance of neutrality, except that the semantic term for John Malkovich (as used in this sentence) will not be simply (analogous to the term for Tiger Woods above), but This special version of John Malkovich would have to be entered into the lexicon individually. In short, though, sentence (311) could be an idiosyncratic example of a neutrality, if one accepts Partee’s analysis of sentences like (312). Before finishing with neutrality, some suggestive evidence involving wh words will be noted, along the same lines as that presented for neutrality for PPs in section 5.3.2. If the phrases be or meet and created and wished he could be have category then interrogative and relative who will need to be recategorized in the lexicon to license the item in (313a). Similarly, other relative clauses will need to be formalized so as to allow for the gaps in (313b, c): (313) a. Who does Kim want to be or meet VP/Pr VP/NP b. a character Stan Lee created and often wished he could be VP/NP VP/Pr c. You have so much to be and to do VP/Pr VP/NP (The Lord of the Rings: The Return of the King, 2003) In these phrases, the categories VP/Pr and VP/NP will have to be strengthened via ASt to to be coordinated; consequently, the phrase Kim want(ed) to be or meet will have category In order for who to be able to combine with this phrase, it will have to have categories as given in (314). As with the case of where in section 5.3.2, although (313) does not prove that neutrality exists for noun phrases, it does show that it exists in argument categories for who, and thus increases the plausibility of such neutrality for noun phrases.

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Page 215 (314) Categories for interrogative and relative who a. (nonembedded) interrogative: b. relative: Also, just as free relative clauses suggested neutrality for PPs, they also suggest neutrality for noun phrases. Consider the sentences in (315). (315) a. I’ll imitate whoever you want me to become. VP/NP VP/Pr b. I’ll become whoever you want me to imitate. VP/Pr VP/NP c. I’ll imitate whoever you want me to imitate. VP/NP VP/NP d. I’ll become whoever you want me to become. VP/Pr VP/Pr In (315a), whoever needs to be have category NP/(S/Pr); in (315b), Pr/(S/NP); in (315c), NP/(S/NP); and in (315d), Pr/(S/Pr). As with free relative where, having four entries for whoever misses a generalization, and disregards the free-relative matching effect, whereby free relative pronouns have categories of form X/(S/X). It is overall more plausible to assign whoever the category which increases the plausibility of neutrality in noun phrases. Similar evidence is found in an attestation of a construction discussed in Williams (1983). The construction is the special use of everything seen in phrases like everything I hoped he would be. Williams’s analysis is summarized in section 5.5.1, but briefly, the claim is that everything quantifies over oneplace predicates; in type-logical terms, it has a categorization of with meaning λVs/prλWs/pr.every(V)(W). A similar category could be envisioned for the everything in everything she did: (These categories could also be assigned to other lexicalized quantifiers, such as someone, nothing, etc., whose ability to be modified by non-wh relative clauses is, to my knowledge, still unexplained.) Sentences like the attestation in (316), though, demand that the argument category be not just S/Pr or S/NP. (316) The only way she could avoid prison was to prove that everything she was and did was her parents’ fault. (Kurt Vonnegut, Jr., “The Big Space Fuck” 1972) Furthermore, the semantics of every demands neutrality in the result category, since the restriction argument and the scope argument of every must have the

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Page 216 same semantic type.44 This necessity will be easier to see if the result category is temporarily replaced with the type-equivalent S/(Pr\S), so that the category for everything is The restriction argument is the while the scope argument is the S/Pr, resulting in a type mismatch. To avoid this mismatch, the category will be needed; written with the constructor, this would be Overall, then, neutrality has been found not only in actual noun phrases (possibly including the Malkovich predication made salient by Being John Malkovich ), but also in the gap categories for wh words and the special usage of everything. 5.4.3 Examination: Predicative and Quantificational Noun Phrases In investigating neutrality, it will be convenient to discuss noun phrases whose basic category is NP (such as Kim or that man) separately from those whose basic category is (such as every cat\ since the semantic terms for the two kinds will be different. The former will be covered in section 5.4.3.1; the latter in section 5.4.3.2. 5.4.3.1 Predicative-Quantificational Neutrality, Noun Phrases of Category NP To test for neutrality, an intensional verb (taking an complement) will be coordinated with one taking a Pr complement. Such a sentence is constructed in (317): (317) Kim sought and then became Robin. VP/Pr Unfortunately, this sentence is pragmatically odd: How could Kim be seeking someone who is presumably distinct from Kim, and then become that person? This oddness invites interpretations under which become could be argued not to be VP/Pr. For example, one could imagine that Kim seeks Robin, kills Robin, and then assumes Robin’s identity. If this reading is a predicative one, it is a case similar to “Malkovich” predication, as discussed in section 5.4.2, but the reading of interest here is the one with the ordinary predicative meaning, λy. (y=robin′). 44. This is true because the interpretation of every(P)(Q) requires that P and Q be comparable sets.

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Page 217 In fact, there is a context that renders (317) sensible, wherein Robin is someone who does not exist until Kim becomes Robin, and furthermore, there is no possibility of arguing that Kim is just pretending to be someone named Robin. This context comes from a novel whose relevant plot details will be summarized at the end of this section. However, for readers who prefer to accept the example in (317) and avoid the plot spoiler to come, a derivation of sought and became Robin is given below. The derivation will hinge on Robin having the category If Robin starts as a as Tiger Woods did in the earlier example, the fact that is derivable from NP allows Robin to be derived as a as shown in (318). Since this derivation involves the introduction rule for it will be presented in Gentzen sequent style, with the semantic terms shown only on the bottom line. (318) Deriving Robin as

With Robin as a with the above meaning, the rest of the derivation can proceed along the same lines as others we have seen: The categories for sought and became will be strengthened to and conjoined, and then combined with Robin . The steps are shown in (319). (319) Derivation of sought and became Robin; a. Syntactic only

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Page 218 b. Syntactic and semantic;

The only remaining item to discuss is the novel (alluded to above) that could provide an appropriate context for a sentence like (317). Spoilers follow. Readers who do not want the plot revealed should skip to section 5.4.3.2. The novel is The Anubis Gates, by Tim Powers. In this novel, protagonist Brendan Doyle travels back in time to 19th century London in order to interview an obscure Romantic poet named William Ashbless. Doyle is an expert on Ashbless, and knows all about his few works and his later life, but Ashbless’s early life is a complete mystery. When Doyle appears in London, he goes by all the places that Ashbless is known to have visited, in an attempt to meet him, and even out of boredom writes from memory a poem that Ashbless is known to have written at this time. Meanwhile, there is a supernatural being which has the ability to take over and inhabit people’s bodies. It can possess a given body only for a few weeks, however, because as soon as it takes possession, the body begins to grow hair all over it, and eventually is too conspicuous to be useful. At this point, the creature has to find a new body to inhabit. When it finds one, it “swaps souls” with the new body’s owner, projecting its own consciousness into the new body, and sending that of the body’s original owner into the creature’s cast-off, hair-covered body—which it has taken care to poison just before the swap, in order to eliminate the witness. Doyle falls victim to the body-snatching creature, and wakes up to find himself in an unfamiliar body. Realizing he has

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Page 219 been poisoned, he manages to find an antidote in time; then, after shearing off most of the hair that covers the face and body, he looks in a mirror and recognizes the face of William Ashbless. He realizes that he himself is Ashbless, and the reason for the mystery of Ashbless’s early life is now clear: Ashbless did not exist until the combination of Doyle’s consciousness and this particular body existed. Summing up Doyle’s adventure, one could say (320): (320) Brendan Doyle sought and then became William Ashbless. Here, became cannot be dismissed as a synonym for “inhabit the body of,” as with the Malkovich example. The body that Doyle now inhabits was not Ashbless prior to Doyle’s inhabiting it; it was just the unlucky previous victim of the supernatural creature, with some other identity. Only this particular body with Doyle’s consciousness inside it constitutes William Ashbless. 5.4.3.2 Predicative-Quantificational Neutrality, Noun Phrases of Category In example (321), a verb taking an argument (seek) is coordinated with a verb taking a Pr argument (become), and a noun phrase with category (a celebrity) serves as the argument for the coordination. (321) Kim sought and became a celebrity. VP/Pr This sentence is derivable if a celebrity has the category and term (via means to be discussed in section 5.4.5) in (322); the derivation is shown in (323). (322) a celebrity:

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Page 220 (323) Derivation of Kim sought and became a celebrity

45 Interestingly, neutrality can also occur when a VP/Pr is coordinated with a VP/NP. In (324), a VP/Pr (be) is coordinated with a VP/NP (meet) just as in (308a), and the coordinated phrase will have category However, instead of the Tiger Woods, the argument is the a celebrity . (324) John wishes he could be or meet a celebrity. VP/Pr VP/NP Furthermore, since is not derivable from a celebrity will have to remain a while be and meet are strengthened to For be, this is straightforward via ASt. For found, however, getting to is more complex, since the starting category is VP/NP, not The strengthening can be thought of as two steps: strengthening VP/NP to as was done in (307); and strengthening to via ASt. Another possible derivation is shown in (325). The main derivation of be or meet a celebrity is shown in (326)–(327). 45. This is the de dicto reading of sought a celebrity; I have not determined whether a de re reading is derivable.

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Page 221 (325) Strengthening the category of meet to

(326) Coordinating be and meet;

(327) Combining be or meet a celebrity

In actuality, there is a way to derive (324) with be or meet as to (somehow) begin with a celebrity as category instead of could be

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Page 222 derived, and taken as an argument to be or meet. The problem here, though, is that a celebrity will necessarily take wide scope over be or meet, meaning that the celebrity that John wants to be and the one that John wants to meet must be one and the same—i.e., that John wants to meet himself! Therefore, the conclusion here is that is the required category for derivation of (324). A simplified derivation is given in (328), with wishes omitted to show that the undesired semantics appears even before the intensionality of wish comes into play. The modal could is also omitted for ease of readability. The semantics for be or meet is taken from the derivation in (310). (328) Undesired derivation of he could be or meet a celebrity, with a celebrity as

In short, in this section and the previous one, predicative-quantificational neutrality has been found in noun phrases whose usual category is NP (e.g. Robin ) and in those whose usual category is (e.g. a celebrity). It is now time to address how to allow noun phrases to actually have category Pr. Section 5.4.4 will present how to allow NPs to have category Pr; section 5.4.5 will do the same for 5.4.4 Lexical Rules for Predicative and Referential Noun Phrases In sections 5.4.1 through 5.4.3, the need for various kinds of neutrality for noun phrases was assessed. In this section and the next one, the mechanics of achieving the neutrality will be shown. With respect to predicative-referential neutrality, since Pr is not derivable from NP, some other means will have to be

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Page 223 used to relate these two noun phrase categorizations. An adaptation of a referential-to-predicative lexical rule from Carpenter (1992) is shown in (329). This rule states that if a lexical NP has meaning a, it will also have category Pr and meaning λy.(y=α)—that is, the property of being identical to itself. This operation is given the name IDENT in Partee (1987:121); Carpenter (1997:100) notes that it is also known as QUINING. As with previously discussed lexical rules, the $ indicates that (329) actually a family of lexical rules, applying not only to lexical items such as Tiger Woods, but also to determiners with category NP/N (e.g., that ). Each kind of application is illustrated in (330). (329)Referential-to-predicative lexical rule (from Carpenter 1995, (178)) (330) Referential-to-predicative lexical rule applied to Tiger Woods and that a. Tiger Woods: b. that: As with the lexical rules in section 5.3.3, there is the question of how to distinguish ambiguity from category neutrality in a TLG. If there is no distinction, then this lexical rule will allow for neutrality for noun phrases of category NP. It will also allow for neutrality, since is derivable from On the other hand, if there is a difference between ambiguity and neutrality that needs to be captured, then some means of specifying the above rule as a “neutrality-encoding” rule will have to be found. In any case, a separate lexical rule will be needed to allow neutrality for noun phrases whose initial category is This rule will be presented in the following section. 5.4.5 Lexical Rules for Predicative and Quantificational Noun Phrases Before discussing how to achieve predicative-quantificational neutrality in quantificational noun phrases, there is the question of which quantified predicative noun phrases46 can have the category Pr at all, much less Partee (1987:121) takes the position that “all NPs in principle have an [Ind→Prop] interpretation, but some of them…yield unsatisfiable or otherwise degenerate predicates.” This is the position that will be taken here as well. To see how these unsatisfiable or otherwise degenerate predicates come about, the semantics of quantified predicative noun phrases will need to be 46. This seemingly oxymoronic term is intended to refer to noun phrases that are in predicative positions but would ordinarily have category

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Page 224 established. Partee defines the type-shifting operation be, with domain Term(Ind→Prop)→Prop and range TermInd→Prop as follows: (331) Partee’s (1987) type-shifting operation BE λV((Ind→Prop)→Prop)λx. V(λz.(x=z)) This operation is applied to the term for a Republican in (332). In the lambda-conversion step, the scope argument for some is filled by (λz.(x=z )). The resulting term, λx.some(repub′)(λz.(x=z)), is logically equivalent to repub′, a fact noted by Dowty et al. (1981:229). To verify this equivalence, note that for any properties P and Q, some(P)(Q)=1 iff therefore, λx.some(repub′)(λz.(x=z)) is the set Since λz.(x=z ) is the singleton set {x}, the set is equivalent to the set which is equivalent to or just repub′. (332) BE applied to term for a Republican λV((ind→Prop)→Prop)λx. V(λz.(x=z))(some(repub′)) ≡λ x.some(repub')(λz.(x=z))≡repub′ Partee notes (p. 126) that BE can also be written as To illustrate, if V is some(repub′), then λx.some(repub′)(λz.(x=z)) is the set of individuals x such that the set or in other words, such that When BE is written this way, it is clear that when V does not contain any singletons, will be the empty set. Partee argues that these are the cases when unsatisfiable or degenerate predicates arise. To use Partee’s example, consider most men. The interpretation of most (P)(Q) is that When will most(man′) contain singletons? In other words, when will it be possible for Q to be a singleton? If Q is the singleton {x}, then it must be the case that However, since card{x}=1, it follows that From this, it follows card(man′-{x})<1, and therefore that card(man′)<2. In other words, most(man′) contains singletons when there is at most one man, which violates most speakers’ presuppositions about most . To illustrate further, a similar argument can be made for every man. The interpretation of every(P)(Q) is that If P is man′, and Q is the singleton {x}, then which entails that man′ is either a singleton or the null set. In the former case, Partee (p. 127) observes, “ the or the only would be appropriate and more straightforward,” and in the latter, conversational maxims are certainly being violated.

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Page 225 It should be noted that predicative noun phrases introduced by determiners such as most, or cardinal numerals, are acceptable in sentences such as (333). (333) Kim and Robin are two people I know. However, this is a group reading, in which two groups (i.e., Kim and Robin and two people I know) are being equated, as opposed to a distributive reading, in which Kim is two people, and Robin is also two people. Citing Link (1983), Partee (p. 127) observes that group readings are “predicted if groups or plural individuals are treated as entities.” This is the position that will be taken here, although the details of the type-shifting between plurals as groups and plurals as individuals will not be explored in this dissertation. The case of no deserves special comment. The interpretation of no (P)(Q) is that illustrating again with man, if Q is the singleton {x}, then or in other words, x man′. Thus, {x} can be a member of no(man′) without any restrictions being placed on man′ (e.g., that it contain at most one member, as in the case of most or every above). Therefore, noun phrases with no as a determiner should be acceptable in predicative positions. Indeed, they are, as in (334): (334) I’m no angel. The complication is that (334) does not simply mean that the speaker is not an angel; it means that the speaker is not even close to being an angel. Therefore, it could be argued that the semantics of sentences like this one requires a different analysis, and that noun phrases introduced by no are not truly acceptable as ordinary predicatives. In that case, Partee’s rule for what determiners can introduce predicative noun phrases would need to be revised. However, Partee touches on this issue (p. 127), noting that “BE(no man′)=not(BE(a man′)); English seems to prefer the latter construction, Dutch the former….” Given that there are two logically equivalent ways of stating the same fact, it is not surprising that the marked construction (in the case of English, be no man) should acquire a degree of metalinguistic meaning not present in the unmarked one. At this point, Partee’s BE operation can be encoded in a lexical rule, as in (335). It is applied to the determiner a in (336). (335) Quantificational-to-predicative lexical rule

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Page 226 (336) Application of quantificational-to-predicative lexical rule: a(n) Once again, if there is no distinction between ambiguity and neutrality, then this rule is sufficient to allow for neutrality; if not, then this rule must somehow be modified to specify that it is a “neutralityproducing” lexical rule. 5.5 Proposed Reasons for Noun Phrases of Category Pr As discussed in section 5.1, there are two basic strategies for handling predicative noun phrases. One is for the copula to take arguments of different categories: or depending on one’s view of the categories for APs and PPs. The other strategy, which has been pursued in this chapter, is to specify the copula just as VP/Pr, and provide a means for noun phrases to have category Pr. This idea of letting noun phrases share a semantic type with other is developed in Partee (1987), who describes type-shifting operations to allow noun phrases to be used referentially (i.e., with type Ind), predicatively (with type Ind→Prop) and quantificationally (with type (Ind→Prop)→Prop). With these shifting operations in place (specifically, those that shift noun phrases to type Ind→Prop), be can just be specified as taking a complement of type Ind→Prop, and handle APs, PPs, and noun phrases alike. Though it is often Partee who is cited when such an analysis is discussed, she credits Williams (1983) with the idea. An earlier version also appears in the GPSG analysis of Sag et al. (1985), who create the feature PRD, appropriate for APs, PPs, and noun phrases. The copula’s complement is specified as PRD +, but APs, PPs, and noun phrases are unspecified for PRD; thus, their feature structures can unify with that specified for the copula’s complement. This tactic is maintained in HPSG in Pollard and Sag (1994). It is carried into the type-logical framework by Bayer (1996), who cites Partee in maintaining that predicative noun phrases and APs can have the same semantic type, and thus that a semantically active neutral category for the copula is not necessary.47 During this history of the VP/Pr analysis of the copula, various arguments in favor of it have been given, especially by Williams. However, many of these arguments are not entirely convincing. The reason that the VP/Pr analysis has 47. It should be noted that Bayer does not go so far as to say that predicative noun phrases should have the category Pr; indeed, he argues against this. For details, see section 5.5.2.2.

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Page 227 here been chosen over the one is that even after discounting the unconvincing reasons, the VP/Pr analysis still has at least one advantage over the alternative. In section 5.5.1 this convincing argument for the VP/Pr analysis is presented; in section 5.5.2, an argument against it is presented, with the reasons that it does not prevail. Finally, section 5.5.3 is a cautionary section, discussing the invalid arguments that have been presented in the literature in favor of the VP/Pr analysis. 5.5.1 One Reason to Allow Noun Phrases to Have Category Pr The most convincing reason to have predicative noun phrases as type Ind→Prop is presented by Williams (1983). He notes that in predicative positions, it is impossible to have quantificational noun phrases, citing the example in (337). Although there is a sensible reading with wide-scope every (specifically, for every professor, there was a student who grew up to become that professor), the sentence sounds quite bad, even when a student is replaced with some student or other and stressed appropriately. A speaker would be much more likely to say something like Every professor was once a student . This ungrammaticality is predicted if predicative noun phrases have the type Ind→Prop instead of the quantificational type (Ind→Prop)→Prop. (337) *A student became every professor. Williams’s point cannot be dismissed by appealing to the same reasoning as used for other predicative noun phrases introduced by every —i.e., that the set of professors must be a singleton or null set, which violates conversational maxims. Such an argument could serve to rule out *Kim was every professor, but not to rule out (337). For *Kim was every professor, disregarding the past tense semantics, the translation would be every(prof′)(λz.(kim′=z)). For this to be true, it must be true that prof’ and consequently that prof’ be a singleton or the null set. Similar reasoning also accounts for the impossibility of a narrow-scope every reading of (337). However, the wide-scope reading for every is every(prof′)(λz.some(student′)(λy.(λy=z))),which means that prof′ λz.some(student ′)(λy.(y=z)). The set λz.some(student′)(λy. (y=z)) is the set {z| student′ or equivalently, {z |z or just student′. In other words, prof′ which certainly does not require that prof′ be a singleton or the null set. Therefore, some other explanation for the ungrammaticality of (337) with wide-scope every is needed. Now if it is assumed that quantified predicative noun phrases have category Pr instead of the impossibility of wide scope for every in (337) is guaranteed, since the

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Page 228 scoping constructor is not being used. With category Pr, the every professor can scope only in situ, for the reading that is ruled out on the pragmatic grounds mentioned earlier. Williams elaborates: In certain cases, where the noun phrase actually does quantify over predicates instead of individuals, quantification IS possible. His example of such a case is the noun phrase headed by everything in (338), briefly discussed in section 5.4.2. In a type-logical framework, this special version of everything could be given the category and the sentence could be derived as in (339). (338) John is everything I hoped he would be. (339) Derivation of John is everything I hoped he would be

Therefore, this argument seems to be one good reason to have Pr as a category for predicative noun phrases. 5.5.2 One Reason Not to Allow Noun Phrases to Have Category Pr In the literature, there is only one argument that I know of that would favor the analysis of the copula, and ironically, it is made by Bayer (1996), who does not believe in category neutrality. Although Bayer believes (à la Partee 1987) that predicative noun phrases, APs and PPs share a common

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Page 229 semantic type, he rejects the extending the category Pr to cover noun phrases.48 The reason is overgenerations such as those in (340): (340) a. Kim wanted Robin (angry, at home, *a partner} b. *LaToya grew [i.e. became] a huge success. (Bayer 1996, (54c)) If distinct category names are maintained on the one hand for predicative APs and PPs, and on the other for predicative noun phrases, then the verb can be specified as to whether it can take noun phrases or not, and gain the advantage of finer-grained control in licensing or ruling out sentences involving other predicative-taking verbs, such as those in (340) above. Here, want can be assigned the category (VP/Pr)/NP, and grow, VP/Pr, and the noun phrases a partner and a huge success will not be able to combine with them, even though a such as be could. However, overgeneration due to the category Pr is not limited to coordinations involving noun phrases. It also occurs when a distinction between APs and PPs is required, as in (342): (341) a. Kim became {angry, *at home}. b. Kim made Robin {angry, *at home}. Indeed, this is a general problem in having the same category for APs and PPs, whether Pr or N\N, as illustrated in (342), where the adverb very selects for an AP, but not for a PP: (342) a. The book is very {interesting, *on the table}. b. A person very (eager to speak with you, *under the influence of drugs} called. Thus, the fact that Pr overgenerates is not a definitive reason to favor the analysis of the copula over the VP/Pr analysis. Either way, Pr will need to be decorated, perhaps by means of feature structures, with information as to whether it is an AP, a PP, or possibly a noun phrase. 48. In order to do this while still rejecting the analysis, Bayer (p. 608) suggests having typeshifting rules in the grammar, or “explicitly abandon[ing] the principle that each syntactic category is assigned a single semantic type,” neither of which options is available in the strict type-logical framework assumed here. Therefore, Bayer’s rejection of noun phrases as Pr is taken as an argument in favor of the analysis of the copula.

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Page 230 5.5.3 Invalid Reasons to Allow Noun Phrases to Have Category Pr In addition to the argument presented in section 5.5.1, other arguments have been made in favor of the VP/Pr analysis of the copula. These arguments are not as convincing as the foregoing one, as will be demonstrated in this section. 5.5.3.1 Assumption that Unlike Coordination Does Not Happen One reason for using the VP/Pr analysis that can immediately be discarded is the assumption that since noun phrases can coordinate with predicative APs and PPs, these constituents must all have the same type—the very assumption that is under question in this dissertation. This assumption is the reason given by Partee (1987:119): “I assume that true constituent conjunction requires identical types….” Essentially the same reason resurfaces as Bayer’s (1996) and Heylen’s (1996, 1999) rejection of semantically active type conjunction. In all fairness, for Bayer and Heylen, this reason is not an assumption, but a conclusion based on the possibility of massive overgeneration if any homophonous words are allowed to be collapsed into a single neutral lexical entry. To be sure, this possibility does need to be addressed, but given that category neutrality is needed whether or not the VP/Pr analysis is chosen, avoiding category neutrality for the copula cannot be an argument for the VP/Pr categorization. 5.5.3.2 Claim of More Accurate Semantics Another claim that has been made in favor of predicative noun phrases having category Pr is that this approach is more accurate semantically. For example, Williams (1983:424) quotes Geach (1962:35) as saying, “…it is clearly nonsense to ask which cat cat stands for in Jemima is a cat, or which dog dog stands for in Jemima isn’t a dog… .” However, it has already been noted that, for example, λx.some(cat ′)(λz.(x=z)), is logically equivalent to cat′, even though the former term makes it look as if a particular cat is being sought. Therefore, the claim of more accurate semantics does not hold up. 5.5.3.3 Non-Passivizability of Predicative Sentences A third argument favoring noun phrases as Pr is based on a syntactic difference between the copula and transitive verbs; specifically, the copula cannot be

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Page 231 passivized (noted in Williams 1983; Huddleston 1984). A common example of this non-passivizability is that in (343): (343) *A doctor was become by John. (Williams 1983, (4)) However, Huddleston (1984:440) notes a constraint on passives: “Where a verb has a sense in which it is logically ‘symmetrical’ passivization is unlikely or excluded altogether for some speakers.” Thus, the ungrammaticality of the above sentence can be predicted without invoking a new category for predicative noun phrases. 5.5.3.4 Facts about Pseudoclefts A fourth argument, presented in Williams (1983), builds on some facts involving pseudoclefts. Williams argues that if noun phrases are allowed to have category Pr, the contrast seen in (344) (and similar ones involving other syntactic tests) has a ready explanation. (344) a. What John is is important to himself. b. Important to himself is what John is. c. What John, is is important to him,. d. Important to {*him i/him j} is what Johni, is. Williams’s argument will be recast here in type-logical terms. Sentence (344a) presupposes that there is some salient property that John has, and asserts that this property is that of being important to himself. In other words, be seems to be equating two properties, and therefore has the category (Pr\S)/Pr. In this case, via an appropriate category assignment for what, the phrase What John is has category Pr. This Pr combines with the Pr\S is important to him, to yield an S. Moving to (344c), this sentence says that the issue or question of what John is is important to John. To get this semantics for this sentence, it will be assumed that, via another appropriate category and term for what, the phrase What John is has category NP, and the meaning “the issue or question of what John is.” In this sentence, then, the NP What John is and the VP is important to him combine as an ordinary subject and VP, with appropriate binding constraints assumed to be built in. The syntactic difference between (344a) and (344c) is that the subject and complement in (344a) can be inverted to yield (344b), but those in (344c) cannot be inverted to yield (344d)—at least, not with him and John co-referring. (If

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Page 232 they do not co-refer, then the sentence can be parsed in the same way as (344b)). This difference is predicted by the categorizations for be. With be as (Pr\S)/Pr in (344a, b), it is predicted that the subject and complement can invert, since both have the same category, Pr. On the other hand, with be as (NP\S)/Pr in (344c, d), it is predicted that the subject and complement cannot invert, since NP and Pr are different categories. Although Williams may be on the right track with this analysis of the contrast in (344), this account does not come for free once noun phrases are allowed to have category Pr. Another assumption needs to be brought in, namely the (Pr\S)/Pr category for be. Therefore, the facts about pseudoclefts discussed here are not a completely compelling reason for noun phrases to have category Pr—at least, not without independent motivation for this new category for be. 5.5.3.5 Facts about Equative Be A fifth argument made by Williams (1983) in favor of predicative noun phrases having type Ind→Prop is as follows. If one maintains that predicative and referential noun phrases have the same category, and have a separate “equative” be (with category VP/NP in our system), then there is no way of explaining the contrast in (345): (345) (Williams 1983, (24)) a. John is a man b. *A man is John. This argument is hinted at in two short paragraphs, and is unfortunately not further developed. As it is presented, the argument makes little sense. Having a VP/Pr entry for the copula instead of (or even in addition to) a VP/NP entry will not rule out (345b), as far as I can see. Whether the is in (345b) has category VP/Pr or VP/NP, it will still take an NP subject, and a man certainly qualifies as such. The only way I can see of making (345b) ungrammatical is to say that Pr is the only category that a man has, and this is certainly not a reasonable position to take. 5.5.3.6 Facts about Color Words The final arguments from Williams (1983) concerns the word color, and words naming various colors. He observes the contrast between (346a) and (346b); specifically, the same predicative noun phrase in each sentence, a certain color, makes a different semantic contribution. In (346a), it means that the subject has

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Page 233 a certain color, while in (346b) it works as an ordinary predicative noun phrase, completely parallel to examples like Pat is a Republican . (346) (Williams 1983, (25), (26)) a. My house is a certain color. b. Blue is a certain color. Williams attempts to equate this difference to the difference between referential and predicative noun phrases, so that a certain color has category NP in (346a), and Pr in (346b). However, this linkage is fallacious. If a certain color is an NP in (346a), then to get the desired semantics for the sentence, then an additional lexical entry for be like that shown in (347) will be required, with a restriction that the NP argument must either be headed by the word color or be a color name. (347) Additional lexical entry for “color” be under Williams’s proposal be: VP/NP: λx.POSSESS(x) As pointed out by Partee (1987), a more straightforward way to allow this special predicative use of color words is to encode the special behavior in the color words themselves, not to write a very general lexical entry for the copula and then try to unnaturally restrict it. This can be done with lexical entries like the following for blue and other color names: (348) blue: (VP/Pr)\VP: λV.V(POSSESS(blue′)) This lexical entry simply has blue taking the copula as an argument so that it can pass the specialized predicative meaning to the whole VP. The general word color can be treated in essentially the same way, except that color is categorized so that the special predication takes effect only at the projection. In fact, this categorization of color will be almost entirely parallel to that of the adverbial nouns to be discussed in Chapter 6, reflecting Partee’s (1987), observation that color and a handful of other nouns naming attributes, such as size, length, weight and price, are like these nouns with special adverbial properties. Williams’s other argument involving color words is that in (349), a widescope reading of every is possible, contrary to ordinary cases of predicative complements (discussed in section 5.5.1). (349) At one time or another my house has been every color. (Williams 1983, (28))

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Page 234 However, this wide scoping is also possible with the categorization described above; it can be seen demonstrated with an adverbial noun in (366) in section 6.3.3 of Chapter 6. 5.5.4 Summary Despite the various unconvincing reasons for allowing noun phrases to have category Pr, there is one convincing reason for doing so, and consequently choosing the VP/Pr categorization of the copula over the categorization. Specifically, that reason is the regular lack of quantificational readings for predicative noun phrases. The only reason for not allowing noun phrases to have this category that I have found in the literature is unconvincing, as the problem described (i.e. some kinds of overgeneration) exists whether or not one chooses the VP/Pr categorization. 5.6 Conclusions Be and similar verbs can take APs, PPs and noun phrases as complements; furthermore, combinations of these three kinds of complements are often grammatical, too. To reflect this fact in a grammar, one choice is to accept category neutrality immediately for be, by giving it multiple categorizations: Or, one can reduce somewhat the neutrality of the verb by creating a category, Pr, for predicative APs and PPs, and categorizing be as One can even eliminate the verb neutrality by providing a means for noun phrases to have category Pr as well; in this case, be can be categorized simply as VP/Pr. However, when the door is closed on verb neutrality for be, another door is opened for argument neutrality. It arises in sentences where be or other predicative-complement verbs are coordinated with other verbs. In fact, even without considering the category Pr, it turns out that in some of these cases PPs need to have the category And once Pr is introduced, PPs also need to have the category Regarding noun phrases, both and neutrality exist. Thus, choosing the VP/Pr categorization for be does not eliminate the specter of neutrality. Whichever choice one makes, neutrality exists. The question now is which categorization of be is better on other grounds than avoidance of neutrality. It has been argued here that the VP/Pr categorization is the preferable one, and therefore that it is in the APs, PPs and noun phrases that neutrality occurs.

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Page 235 CHAPTER 6 Category Neutrality and Adverbial Nouns 6.1 Introduction In the past three chapters, category neutrality has been sought in bare-plural and mass nouns (Chapter 3), various verbal valence alternations (Chapters 3, 4), and predicative phrases (Chapter 5). In this chapter, the focus will be on a smaller set of words, specifically, certain nouns that have an adverbial component to their meaning. It will be seen that these nouns exhibit category neutrality with respect to their ordinary-noun category and special adverbial category. The nouns of interest are those that can project ADVERBIAL NPs,49 first discussed in Larson (1983, 1985). These are NPs that can act as locative, temporal, or manner adverbs without any kind of morphological marking, as in the following examples: (350) a. They visited Kim {last Thursday, one day, this week, that year}. b. I lived every place that I could afford . c. We worked the problem every possible way. In short, these phrases have the internal structure of a regular NP, but the external syntax of VP modifiers. The nouns that can project these adverbial NPs will be referred to as ADVERBIAL NOUNS, following McCawley (1988). Larson notes that adverbial nouns are a restricted set. For example, although most nouns denoting periods or instances of time can head a temporal adverbial NP, not all of them can, as seen in (351a). For adverbial NPs of location or 49. In fact, Larson uses the term BARE-NP ADVERBS, but the more intuitive terminology of McCawley (1988) is adopted here.

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Page 236 manner, only the specific words place and way are eligible, as can be seen by comparing (350b, c) with (351b, c). (351) a. *They visited Kim that {occasion, period}. b. *I lived every {location, city} that I could afford. c. *We worked the problem every possible method. Neutrality with respect to this property is seen in sentences such as those in (352). In (352a), every place on this list acts as an adverb with respect to lived, but as an NP with respect to visited: in (352b), the phrase what places in Ohio fills an NP gap after in, but an adverbial gap after lived. (352) a. I’ve lived or visited every place on this list. b. What places in Ohio have you spent time in or lived? Larson (1985:616) discusses a second property that adverbial nouns possess: They “can head non- wh adverbial relatives without preposition stranding.” Examples are shown in (353): (353) a. the {day, *occasion} (that) they visited Kim b. the {place, *town} (that) I lived as a child c. every way/*method (that) we worked the problem Neutrality with respect to this property is seen in sentences such as the attestations in (354). In (354a), place fills both an NP gap (after loved) and an adverbial gap (after felt comfortable) in the following relative clause. A similar situation occurs with the infinitival relative clause in (354b), with an NP gap after cross, and an adverbial gap after locate people. (354)a.He decided to remain because it was a place he loved and felt comfortable. (Rich Warren. “Ghost stories: an old friend drops in for a séance.” Columbus (Ohio) Alive, 4 Nov. 1999, p. 10.) b.It’s a difficult place to cross or locate people once they are in the area. (US Border Patrol agent Maurice Moore, National Public Radio interview, 24 May 2001) The two properties of adverbial nouns are summarized in (355):

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Page 237 (355) Properties of adverbial nouns a. PROPERTY 1: Ability to project an adverbial NP b. PROPERTY 2: Ability to head a non-wh adverbial relative clause In addition to the neutrality with respect to Property 2 observed above, Property 2 also seems to give rise to neutrality without coordination. To see how, it will be useful to survey the four possible combinations of these properties; they are illustrated in (356) with the sample adverbial noun day. (356) Combinations of Property 1 and Property 2 a. Property 1: no Property 2: no I remember the day when we first met. b.Property 1: yes Property 2: no We had a picnic every day. c. Property 1: no Property 2: yes I remember the day the music died. d.Property 1: yes Property 2: yes Something touched me deep inside the day the music died. (Don McLean, American Pie ) In (356a), day acts as an ordinary noun both as head of the NP complement of remember, and as head of the wh adverbial relative clause when we first met . (The adverbial functionality resides in the when, not in the noun.) In (356b), day exhibits Property 1 in projecting an adverbial NP modifying We had a picnic. In (356c), day exhibits Property 2 by heading the non-wh relative adverbial clause the music died, but acts as an ordinary noun as head of the NP complement of remember. In (356d), day exhibits both properties of adverbial nouns: It projects an adverbial NP modifying something touched me deep inside (Property 1); and it heads the non- wh relative adverbial clause the music died (Property 2). Of the four cases, the “mixed” case in (356c) is particularly interesting, as it is reminiscent of the kind of “upstairs-downstairs” category neutrality seen in Chapter 5 with free relatives. For comparison, consider (357), in which the entire free relative clause whoever you want me to be functions as an NP object of imitate, but contains a predicative gap after be. (357) I’ll imitate whoever you want me to be. Similarly, in (356c), the day the music died acts as an NP object of remember, but contains an adverbial gap after died . Before category neutrality with respect to either of these properties can be properly considered, an analysis of the basic facts of Property 1 and Property 2

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Page 238 needs to be developed. In section 6.2, previous analyses will be reviewed, and in sections 6.3–6.5, a type-logical analysis of adverbial nouns will be presented, with Property 1 addressed in section 6.3, Property 2 in section 6.4, and the interaction of Properties 1 and 2 in section 6.5, which also discusses the possible upstairs-downstairs neutrality of (356c). Section 6.6 focuses on the possibility of category neutrality with respect to Properties 1 and 2 individually. Conclusions are presented in section 6.7. 6.2 Previous Analyses 6.2.1 Larson (1985) Larson’s (1985) analysis has two parts. He first proposes an Adverbial θ-Role Assignment (AA) rule, which optionally assigns a θ-role (specifically TEMP(oral), LOC(ation), DIR(ection)or MAN(ner), as appropriate) to any phrase. Most of these phrases will be ruled out by the Case filter, since they will not appear adjacent to a Case assigner (a verb or preposition). The second part of Larson’s analysis allows adverbial NPs to pass through the Case filter by giving adverbial nouns the ability to assign Case to themselves. Specifically, adverbial nouns are marked with a feature [+F], which allows them to optionally selfassign a general “Oblique” case. In this way, an adverbial NP is allowed to take its place in a sentence (Property 1). Furthermore, with Case assigned, adverbial nouns can participate in adverbial relative clauses in the same way that ordinary words can participate in relative clauses with NP gaps (Property 2). The optionality of this case-marking allows for the mixed usage seen in (356c). Although this theory rules in what it needs to rule in, and rules out what it needs to rule out, there are two reasons for wanting a different one. First of all, of the two parts in Larson’s analysis, only the optional self-assignment of Case is specific to adverbial nouns; in contrast, the AA rule can assign an adverbial θ-role to any phrase whatsoever. Instead of vastly overgenerating adverb phrases via AA, and then relying on the Case filter to discard most of them, a simpler solution would be one in which the adverbial capability was completely built into the adverbial nouns’ lexical entries. Second, it is not certain that adverb phrases should occupy θ-roles as arguments to a verb. If θ-roles are removed from the analysis, not only is there nothing to license adverbial NPs syntactically; there is nothing to give them their adverbial semantics. That is, if an adverb phrase cannot get its meaning by virtue of occupying some thematic role in a verb’s meaning, then it must supply the meaning itself, a requirement that is not fulfilled simply by having a feature like [+F] percolate up.

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Page 239 6.2.2 Larson (1983) An earlier proposal in Larson (1983) has adverbial NPs subordinate to prepositionless PP nodes, a strategy that deserves further comment. There is an intuitive appeal to positing something like an “understood” preposition in front of an adverbial NP, or at the end of a non- wh relative adverbial clause. Furthermore, as noted by McCawley (1988), adverbial NPs have more in common with PPs in particular than with adverb phrases in general. First of all, their distribution is similar, right down to adverbial NPs’ having the ability to modify nouns (e.g., McCawley’s example your brother’s arrival last week), which PPs can do, but other adverbs cannot. Also, McCawley points out, adverbial NPs have the same semantics as similar phrases with prepositions; thus, I saw her Tuesday and I saw her on Tuesday have the same meaning. However, taking such an approach would not really save any work. To mention the lesser problem first, there is the issue of what meaning should be posited for this null preposition. Even if some kind of general spatiotemporal preposition is hypothesized for adverbial NPs of location and time, the issue gets murkier when manner adverbials are considered. Manner adverbials seem quite different semantically from spatiotemporal ones: Whereas adverbs of location and time can be seen as referring to actual portions of the space-time continuum, manner adverbs cannot. For the moment, though, let us assume that there is such a null, spatiotemporal/manner preposition, or perhaps more than one null preposition. The larger problem is to ensure that a null preposition is used only with adverbial nouns, in order to rule out ungrammatical phrases such as *we stayed every location and *every hotel that we stayed. So even with a null preposition, some of the work will have to be done by the individual lexical items, and therefore it makes sense to see if they can be made to do all of the work. 6.2.3 Kasper (Forthcoming) Kasper (forthcoming) also addresses adverbial NPs, in the larger context of how, in general, to modify words and phrases that have uniform “internal semantics” but “combinatory semantics” that varies according to their syntactic placement. His prime example of such words, discussed in Chapter 5, is attributive vs. predicative adjectives. The problem is not just that predicative and attributive adjectives have different meanings (that is, if a predicative adjective has meaning α, the attributive version of the same adjective will have meaning the problem is that modifiers of these adjectives (for instance, very) will also have to have different meanings, one suitable for modifying predicatives and one for modifying attributives—a seemingly

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Page 240 needless proliferation of meanings. Kasper’s HPSG-based solution allows there to be a single lexical entry for an adjective that can be either predicative or attributive, and eliminates the need for creating new categories for modifiers of adjectives. Having finished with adjectives, Kasper shows how his approach could be applied to other modifiers, including adverb phrases and (the relevant part for this chapter) adverbial nouns. Like attributive and predicative adjectives, adverbial nouns have basically the same core meaning wherever they appear, but have different combinatorial semantics depending on how they are used. For instance, place always has the same basic meaning of “place,” even though it functions as a direct object in Search the place and adverbially in live someplace. Furthermore, any modifier of an adverbial noun will have to be able to preserve both its ordinary and its adverbial meaning, which could lead to the same needless proliferation of lexical entries as discussed above for modifiers of adjectives. For details of this analysis, the reader is referred to Kasper (forthcoming). Kasper’s characterization of adverbial nouns works in showing how the compositional semantics of an adverbial NP is built up. Unfortunately, it deals only with Property 1 of adverbial nouns, i.e. their ability to project an adverbial NP. His analysis has nothing to say about their ability to head non- wh relative adverbial clauses without preposition stranding. 6.2.4 Summary In short, Larson’s analysis covers both properties of adverbial nouns, but is weak semantically; Kasper’s analysis deals well with the semantics, but only for one of the two properties of adverbial nouns. An analysis is needed that covers both properties of adverbial nouns, while doing justice to their semantics. 6.3 Property 1: Projection of Adverbial NPs 6.3.1 Insufficiency of Simple Feature Passing At issue is how to endow adverbial nouns with their special adverbial property at the lexical level and allow it to percolate up to the NP level. One way that comes to mind is to mark adverbial nouns with a feature, and have a feature-passing mechanism propagate it, in the same way as features such as case or number are propagated. That is, one might have a feature called adv on all nouns, and then declare that adverbial nouns as adv +. However, such a strategy

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Page 241 falls short with respect to the semantics, as it is essentially a categorial version of Larson’s (1985) proposal. Although it would be possible derive an NP(adv +) from an adverbial noun, the problem would be to specify how an NP’s having a (+) value for its adv feature actually translates into its behaving as an adverb semantically. In order for a feature-passing analysis to work, a rule like the following would be needed, to convert an NP( adv +) to an adverb (category S\S): (358) Rule converting NP( adv+) to S\S

There are two reasons that such a rule would not be desirable. From a theoretical standpoint, such a rule would not be used in a type-logical grammar, simply because it is nonlogical; i.e., it cannot be derived by any of the rules of inference in a type-logical grammar. Therefore, it would have to be stipulated, which would defeat the purpose of attempting to describe linguistic phenomena in a strictly logic-based system, and it would result in the loss of Cut Elimination. To illustrate, consider the derivation in (359). At the bottom, there is simply no rule that can be applied except for Cut, since there are no constructors to eliminate. (359) Non-Cut-free derivation involving NP( adv +)

Furthermore, there is a linguistic reason for not wanting a rule like (358). Note that as written above, the adverbial semantic term contains the term prep, mnemonic for preposition. This term is not intended as a claim that an adverbial noun is preceded by an understood preposition (a proposal rejected in section 6.2.2); rather, it is an abbreviation for whatever set of lexical entailments is appropriate for a given adverbial noun. For example, place would have a number of entailments about x, and these entailments would more or less coincide for the entailments in the lexical entry for on, in, or at . The trouble is that different adverbial nouns can have slightly (or very) different sets of entailments, but the prep in (358) can abbreviate only one set. In other words,

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Page 242 (358) is not sensitive to the adverbial information contributed by the different adverbial nouns. The strategy taken in this dissertation will be to put all relevant information about an adverbial noun’s semantics into its lexical entry, and give it all the tools it needs to project its adverbial semantics to the NP level. To do this, a category constructor will be needed that was not introduced in Chapter 2. A definition and explanation of this constructor, known as q, is given in section 6.3.2. In section 6.3.3, this constructor will be used to create a category for adverbial nouns that accurately reflects Property 1. 6.3.2 Moortgat’s Generalized Scoping Constructor The generalized scoping constructor q (defined in Moortgat 1996) is a generalized version of the scoping constructor discussed in section 2.6.2. The type for categories constructed with and the Elimination rule for are repeated below: (360) (361) Elimination rule for (from Carpenter 1997:225)

This schema says that with meaning a should be treated as a B, with a variable for a semantic term, until a phrase of category A (with meaning β) has been derived, at which point the semantics of the phrase is turned into α(λx.β). In (86) in Chapter 2, a derivation of Every cat meows was given, in which the Every cat acted as an NP assigned to the variable x until an S with meaning meow′(x) was derived. The next step in the derivation resulted in a different meaning—every′(cat′)(meow′) — but the same category, S. The idea behind the generalized scoping constructor is to allow the final step to change not only the meaning, but also the category of the phrase projected by the

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Page 243 expression with the scoping category. That is, instead of creating a category of type (Typ(B)→Typ(A))→Typ(A) as does, it creates a category of type (Typ(C)→Typ(B))→Typ(A). The definition is given in (362): (362) Typ( q (A,B,C))=(Typ(C) → Typ(B)) → Typ(A) At this point, the scoping constructor can be seen as just a special case of q —specifically, the case in which A=B. For example, the for every cat could be written as q (S, S, NP). The q constructor has been used for analyses of pied-piping (Morrill 1994; see also Carpenter 1997:364–366) and reciprocal pronouns (Carpenter 1997:355–363). The Elimination rule for q is given in (363). It is parallel to the rule in (85), except that the final step involves a change in category (from B to A). (363) Elimination rule for q (from Carpenter 1997)

This rule states that something of category q (A,B,C) acts as a C until a B is derived, at which point the derived phrase acts as an A. This rule will be illustrated in the next section, when a generalized scoping category is assigned to adverbial nouns. No Introduction rule is given for q . The reason for this is that such a rule can be formulated only for the case in which A=B. To see why, first note that the type for q (A, B, C) is (Typ(C)→Typ(B))→Typ(A), which is the same type as for A/(C\B). Therefore, a proof deriving a q (A, B, C) from a C is semantically isomorphic to a proof deriving an A/(C\B) from a C. Now whereas A/(C\A) is derivable from C, A/(C\B) is not; it would involve proving that A is derivable from B, as can be seen in (364):

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Failed attempt to derive A/(C\B) from C

In fact, there is a solution for this lack of an Introduction rule, which involves reformulating q by way of a wrapping modality (Morrill 1994:234–8). However, since a q type will never need to be introduced in a derivation (all of them being lexically assigned), in this dissertation the q notation will be used instead of Morrill’s formulation. 6.3.3 A Category for Adverbial Nouns In (365), a first pass at a category and term for day in its adverbial capacity is given. (For now, adverbial nouns in their ordinary N capacity will be ignored.) This category uses the generalized scoping constructor q, defined above. Words with this category can act as an N in order for an to be derived, at which point the projected phrase acts as an This is the desired behavior of adverbial nouns, since a phrase such as every day, which is an needs to shift to category S\S in order to modify a sentence. Furthermore, it needs to be able to scope over the whole sentence, to allow widescope readings in sentences such as Someone died every day; hence, the scoping category (365) Category and term for sample adverbial noun day: By the definition in (362), the type for day will be Therefore, the first argument taken by day is something of type i.e. a generalized determiner, which takes an N complement and yields an This determiner corresponds to the abstracted variable D in (365). After this argument is taken, the resulting type will be which by the definition in (360) is equivalent to In other words, day will need to take a sentence with an adverbial gap (that is, something of type Typ(S\S)→Typ(S)) as its second argument, in order to end up as an S. This second argument corresponds to the abstracted variable V in (365). The meaning for the ultimate S will be

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Page 245 obtained by providing the generalized determiner D with arguments for its restriction and scope. Its first argument, of type Typ(N), is the restriction, for which day′ is supplied. The phrase every day will then have type or (Typ(NP)→Typ(S))→Typ(S). The argument here, of type Typ(NP)→Typ(S), is the scope argument for D, for which λz. V(on′(z))) is supplied. A derivation of Someone died every day, with every day taking wide scope, is given in (366) to illustrate how this categorization works. (366) Derivation of Someone died every day (wide scope every ) a. Syntactic only

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Page 246 b. Syntactic and semantic

This is the basic analysis of Property 1 of adverbial nouns. Sections 6.3.4 and 6.3.5 briefly discuss some further details of the analysis before Property 2 is taken up in section 6.4. 6.3.4 Eliminating Overgeneration Though the preceding analysis gets the semantics right for adverbial NPs with regard to the adverbial meaning at the NP projection, there is an overgeneration problem. The deduction schema for q(A, B, C) in (363) allows an A to be derived after successful derivation of a B; however, this B might not be the first one that is derived after the q E step. This indeterminacy is deliberate, as it is what allows for different scopings in cases of multiple quantifiers. For adverbial nouns,

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Page 247 though, the conversion to must occur at the first opportunity. Otherwise, it would be predicted that an such as a claim that Kim cherishes each day could act as an adverb. Similar difficulties are encountered in preventing quantifiers from scoping outside relative clauses, and to overcome them, Carpenter (1997:240) mentions using a unary modal operator. This is the solution that will be pursued here. A sorted typing along the lines of Moortgat and Oehrle (1994) will be used, wherein any category A will be decorated with the tag ordinary or adverbial. Next, the inclusion postulate in (367) is introduced. This postulate states that any Aadverbial counts as an Aordinary, with no change in semantics. (367) Inclusion postulate Aadverbial→Aordinary The final component of the analysis is to assign new categories to nominal modifiers and determiners, and a revision of the q category for adverbial nouns: (368)Revised categories for nominal modifiers, determiners, and adverbial nouns, where i is either ordinary or adverbial a. Nominal modifiers: N i/Ni, N i\Ni b. Determiners: c. Adverbial nouns: With these categories in place, a claim that Kim cherishes each day would be ruled out as an adverb as follows. First, all other categories with N or NP as an argument category are now understood to seek N ordinary or NP ordinary, respectively. The phrase each day would have (after the step) category NP adverbial, but in order to be parsed as part of Kim cherishes each day, this category would first have to become NP ordinary, via the inclusion postulate in (367). Once this happens, the conversion to can never take place, given the revised category for adverbial nouns in (368c).50 With this solution introduced, though, henceforth the ordinary and adverbial subscripts will be suppressed for better readability. At this point, it may seem that the proposed analysis is just that adverbial nouns are marked as special, and that this mark is propagated through category assignments to modifiers and determiners—much like the feature-passing analyses rejected earlier. The difference here is in the q category for adverbial 50. In fact, such a derivation would ultimately fail, as it would be incomplete until an was derived, at which point the q E schema could be completed. But the would never appear. How to allow adverbial nouns to be used as ordinary nouns in sentences like Kim cherishes every day is taken up in section 6.5.

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Page 248 nouns, which makes explicit how an adverbial noun will contribute its adverbial semantics to a sentence. 6.3.5 Adverbial Nouns in Wh -NPs Before concluding this section, one more fact needs to be addressed. Up until now, the behavior of adverbial nouns in wh-NPs has been ignored, but in fact, adverbial nouns can project adverbial wh-NPs, too. Examples are provided in (369): (369) a. What day did they visit Kim? b. What places in Russia have you lived? c. What way did we work the problem? To cover these cases, the same approach can be used as above: The determiner (in this case, a wh determiner) will be taken as a complement, and the result will be a wh adverb phrase. That is, just as adverbial nouns as used in section 6.3.3 had the type or more perspicuously, adverbial nouns as used in this section will have type Typ(WhDet)→Typ(Wh-Adv), where Wh-Det stands for whatever category is assigned to the determiners what, which and whose, and Wh-Adv stands for whatever category is assigned to wh-adverbs such as where and when. For further details on this aspect of the analysis, see Whitman (2002). This concludes the analysis of Property 1 of adverbial nouns, allowing them to act as ordinary nouns up to their projection, and then access the adverbial semantics wired into their lexical entry. The next step is to allow adverbial nouns to head non- wh adverbial relative clauses.

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Page 249 6.4 Property 2: Heading Non-Wh Adverbial Relative Clauses 6.4.1 Non-Wh Adverbial Relative Clauses as Complements As mentioned in section 6.1, phrases like those in (370) (repeated from (353)) contain an adverbial noun that is modified by an adverbial relative clause (RC) introduced by that or 51 without a stranded preposition at the end. (370) a. the day/*occasion (that) they visited Kim b. the place/*town (that) I lived as a child c. every way/*method (that) we worked the problem In these RCs, that cannot simply be treated as a relative pronoun like who, with category and term along the lines of First of all, a different category would be required: (N\N)/(S/(S\S)). That is, that combines with a sentence containing not an NP gap, but an adverbial gap52 to form a postnominal modifier. However, if such an entry for that were used, prepositional information would need to be included in the semantic term: in’ for locative and temporal adverbials; something else for manner adverbials. In other words, there would actually have to be several more entries for that, thus duplicating the information supplied by individual adverbial nouns. Moreover, the same problem seen in the null preposition analysis of section 6.2.2 would be re-created: Nothing would prevent ordinary nouns from being modified by adverbial RCs headed by a that enriched with prepositional meaning. A different problem arises in non-wh RCs introduced by In these cases, there is no word at all upon which to pin any kind of combinatory semantic term. Of course, this is a general problem for all non-wh RCs introduced by Rather than try to include any prepositional meaning in that or in a phonologically null relativizer, nonwh adverbial RCs will be taken to be ordinary or complementized sentences (with adverbial gaps). Thus, non-wh adverbial RCs will be of category S c /(S\S) or S/(S\S), where S c is the category to be given to complementized sentences, and Typ(Sc )=Typ(S)=Prop. The question now is how these RCs will be connected with the nouns they modify. The answer is that they will be selected as complements. In this way, the 51. As a convenience, I refer to RCs with no relativizer as being “introduced by ” though I am not proposing that a phonologically null relativizer is there to introduce the RC. 52. For a discussion on the choice of this category instead of the simpler (N i\Ni)/S, see the beginning of section 3.2 in Chapter 3.

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Page 250 adverbial nouns have access to the semantics of these clauses, and can turn them into adverbial RCs. The category and term for the adverbial noun day taking this kind of complement is shown in (371): (371) Category and term for adverbial noun with non- wh adverbial RC complement

day: There are only two changes from the earlier category and term for day in (365): First, another variable U is abstracted, corresponding to the S/(S\S) argument.53 Second, the determiner’s restriction argument is no longer just day′, but For some speakers, similar categorizations will be needed for adverbial nouns in wh-NPs, to allow for interrogatives such as (372). As with Property 1, further details concerning adverbial nouns in wh-NPs can be found in Whitman (2002). (372) What day that it rained did we cancel the picnic? 6.4.2 Objections to Non-Wh Adverbial RCs as Complements One argument (brought up by an anonymous Journal of Linguistics reviewer) against having RCs of any kind as complements is the prediction that they will always be adjacent to their head noun. This, of course, is not borne out, as seen in the examples below and in many instances of extraposed RCs: (373) a. a place in Paris that we stayed during our vacation b. the day in March that the visitor arrived c. no way in hell to succeed Larson provides another example in (374): The RC that John spent sleeping (which is still assumed to be a modifier, with category N\N) intervenes between hours and the supposed complement that he was supposed to have been on watch . 53. For ease of presentation, the non-wh adverbial RC complement is arbitrarily assumed to be an S/(S\S) rather than an S c /(S\S) A truer categorization of the adverbial noun would be If one made use of the disjunction constructor, this category could also be written as

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Page 251 (374)The hours that John spent sleeping that he was supposed to have been on watch nearly cost him his stripes. (Larson 1985, (49)) However, there are other cases of complement extraposition; to give just one example, there are sentences like (375): (375) She said loudly that she had to go to the bathroom. To overcome this problem, a solution along the lines of the analysis for nonadjacent complements developed in Moortgat and Oehrle (1994) could be implemented. Therefore, this objection does not seem to be fatal for an analysis of non- wh adverbial RCs as complements. Another argument against having RCs as complements is their iterability (also brought up by an anonymous Journal of Linguistics reviewer). In this case, if these adverbial RCs are indeed complements, it is predicted that they will not be iterable. This prediction is not met, as (376) illustrates: (376) that place we stayed that we had so much fun Discussion of this issue is more tangential to the issue of category neutrality than is necessary here; for those interested, it is taken up in Whitman (2002). 6.4.3 Summary In the preceding sections, the necessary categories for Property 1 and Property 2 of adverbial nouns have been described. For Property 1, adverbial nouns need to have the category For Property 2, they need to have the category The task now is to capture the generalization that any noun with Property 1 also has Property 2. This will be the focus of the section 6.5. 6.5 Interaction of Property 1 and Property 2 6.5.1 Category Overview In the analysis as developed so far, any adverbial noun will have three categories. The first category, of course, is the plain N category. With this category, an adverbial noun can do all the things an ordinary noun can do. Thus, sentences such as those in (377a) are licensed. Second, there is the

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category, which allows an adverbial noun to project an that can convert to an adverb phrase of category (Property 1). This category licenses sentences such as those in (377b). Third, there is the category, which allows an adverbial noun (used in its adverbial capacity) to head a non- wh adverbial RC (Property 2). This category licenses sentences such as those in (377d). (377) Combinations of Property 1 and Property 2 (repeated from (356)) a. Property 1: no Property 2: no I remember the day when we first met. b. Property 1: yes Property 2: no We had a picnic every day. c. Property 1: no Property 2: yes I remember the day the music died. d.Property 1: yes Property 2: yes Something touched me deep inside the day the music died. (Don McLean, American Pie ) However, there is still have no way of generating (377c), the seeming upstairs-downstairs neutrality with respect to Property 2, where day heads a non- wh adverbial RC, but is used as an ordinary noun in the matrix clause. Therefore, one final category is needed for adverbial nouns to allow for this case. In fact, it turns out that there is no need for category neutrality here. The category can just be N/(S/(S\S)): The S/(S\S) argument is the adverbial relative clause, and the N result category allows the noun+(adverbial RC) phrase to be used as an ordinary noun. The noun day is given as an example in (378), summarizing the four categorizations and terms needed for it: (378) Four categories and terms needed for sample adverbial noun day a. Property 1: no N: day′ Property 2: no b. Property 1: yes Property 2: no c.

Property 1: no

Property 2: yes

d.

Property 1: yes

Property 2: yes

Even though category neutrality did not turn out to be necessary to describe the seeming case of neutrality without coordination, the issue returns when the

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Page 253 problem of how to relate these four categories to one another is considered. This will be seen in the next section, where lexical rules are introduced to capture the relationships between an adverbial noun’s various categorizations. 6.5.2 Lexical Rules and Category Neutrality of Adverbial Nouns At this point, the relationship between the categorizations of an adverbial noun summarized in section 6.5.1 needs to be formalized. The starting point will be the category The generalization to be captured is that any word with this category will also have the categories shown in (378c,d); that is, it will also be able to take a non- wh adverbial RC complement. Thus, as a first pass, two lexical rules might be written as in (379): (379) Adverbial RC addition lexical rules for adverbial nouns (preliminary) a. b. There is a problem, however, concerning the semantic portion of these rules. As can be seen by comparing the terms in (378b) for the category and in (378d) for the category, the main difference between them is the extra information in the restriction argument for D: day′ vs. λx(day′(x) U (on′(x))). The problem is that the lambda calculus does not provide a means to reach into the term λ, DλV.D(day′)(λz. V(on′(z))) and pull out the restriction argument day’ in order to assemble the semantic term in (378d). Of course, the desired term is easily accessible in the term for the N category in (378a), so as a second pass, lexical rules like those in (380) might be written: (380) Adverbial RC addition lexical rules for adverbial nouns (intermediate) a. b. The trouble with this formulation is that now any noun (not just adverbial nouns) can have the categories and N/(S/(S\S)). This is not a fatal flaw, since (as discussed in Chapter 2) lexical rules are known for being semiproductive, with many theoretically possible outputs which nevertheless are not in the lexicon. Nevertheless, a formulation of the rules is possible which avoids this overgeneration, if a conjunctive-type lexical entry is

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Page 254 allowed. Using the conjunction constructor, the category and term for the sample adverbial noun day would be as in (381), with both associated terms listed and accessible by the projection functions π1 and π2: (381) Conjunctive category and term for sample adverbial noun day With this category, everything that was derivable with the unconjoined N or categories is still derivable, since both N and are derivable from the conjoined category in (381). And now it is possible to express the desired semantics, in a single lexical rule. The lexical rule in (382) will add an S/(S\S) argument slot for a non- wh adverbial RC, and the output can be used either as an N or as a (382) Adverbial RC addition lexical rule for adverbial nouns (final)

One aspect of this lexical rule deserves comment: the term p0. This is a lexically determined constant ranging over preposition meanings. In light of this term, one might argue that this formulation suffers from the same problem seen in the rejected “null preposition” analyses discussed earlier. However, the problem here is less serious that the one in the null preposition analysis, as it is known that lexical rules do not always completely determine the meanings of their outputs (also as discussed in Chapter 2). Words generated by lexical rule often accrue elements of meaning that are not predictable from the rule; an often cited case is the word readable, which does not mean simply “capable of being read,” but something more like “easy to read.” In this case, it is reasonable to imagine that a lexical rule would generate an adverbial noun taking an adverbial RC complement with an as-yet-unspecified prepositional meaning, and that in entering such a word into his/her lexicon, a speaker would supply the most logical prepositional meaning—i.e., the one present in the input semantics. To illustrate how (382) works, α for day is the term in (381), i.e. and π1α would be day′. Thus, lexical rule (382) would generate the following category and term for day, suitable for heading a non- wh adverbial RC, and for projecting either an ordinary NP or an adverbial NP:

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Page 255 (383)Conjunctive category and term for sample adverbial noun day, with argument slot for non- wh adverbial RC

A derivation of place we stayed is shown in (384), using the category from (383). The phrase we stayed is derived as having an adverbial gap by making use of the hypothetical reasoning available in the Associative Lambek calculus, hypothesizing an S\S and withdrawing the assumption at the step labeled /I1. (384) Derivation of place we stayed a. Syntactic only

b. Syntactic and semantic

Thus, even without considering coordination tests, there is motivation for adverbial nouns to have category neutrality.

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Page 256 6.6 Category Neutrality At this point, the cases of category neutrality mentioned at the beginning of the chapter will finally receive an analysis. Neutrality with respect to Property 1 is covered in section 6.6.1; with respect to Property 2 in 6.6.2. 6.6.1 Category Neutrality and Property 1 With regard to Property 1 (the ability to project an adverbial NP), since adverbial nouns have category then sentences in which an adverbial noun must be taken simultaneously as both an N and a should be possible. Two such sentences were given earlier, and are repeated here: (385) (repeated from (352)) a. I’ve lived or visited every place on this list. b. What places in Ohio have you spent time in or lived? To demonstrate how conjoined categories for adverbial nouns would license these sentences, a syntactic derivation of the NP\S live or visit every place is presented in (386)–(394). The first step is to strengthen the categories of live and visit to as done in (386) and (387) below. Once this is done, the two verbs can be coordinated, since they will have like categories.

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Strengthening live to a. Syntactic only

b.

Syntactic and semantic

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Strengthening visit to a. Syntactic only

b.

Syntactic and semantic

The next step is to coordinate live and visit, as shown in the next portion of the derivation:

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Page 259 (388) Coordinating live and visit:

The next step is to derive every place as an in order to be a suitable complement to live and visit. This will require the use of the Introduction rule for therefore, following the practice used in earlier chapters, the derivation will be presented in Gentzen sequent style. To this end, the Left rule for q in the Gentzen sequent calculus is shown in (389), followed by the derivation of every place as in (390)–(393). (389) Left rule for q

The derivation of every place as an needs to be broken into several pieces in order to fit on the page. The bottom line of the derivation is written in (390), with only the categories shown for spacing considerations. The corresponding phonological strings and semantic terms for these categories are listed separately in (391). (390) Bottom line of proof deriving every place as

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Page 260 (391) Phonological and semantic components for categories in (390) a. every: b. place: c.

everyplace:

Immediately above the step in (390), the derivation will split into two halves, one proving that every place can be derived as an and the other proving that it can be derived as an These two halves are shown in (392) and (393). (392) Deriving every place as

(393)

Deriving every place as

Now that it has been proven that every place can have the category with the semantic term given in (391c), the final step is to combine it with live or visit, as done in (394):

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Page 261 (394) Combining live or visit with everyplace

In section 6.5, it was seen that having a conjunctive category for adverbial nouns facilitated specifying lexical rules involving them. That coordinations such as live or visit every place are empirically possible provides independent motivation for choosing a conjunctive category for adverbial nouns. 6.6.2 Category neutrality and Property 2 The preceding category neutrality involved only Property 1 of adverbial nouns; that is, the adverbial noun was used as a normal noun and as an adverbial noun in a main clause. It is reasonable to ask whether category neutrality involving Property 2 is possible: whether an adverbial noun can simultaneously fill both an NP and adverbial gap in a non-wh RC. In my dialect, the answer is no, but consider the attestations in (395), repeated from (354). In these sentences VPs with an NP gap (loved, cross) are coordinated with VPs with an adverbial gap (felt comfortable, locate people once they are in the area) . (395)a.He decided to remain because it was a place he loved and felt comfortable. (Rich Warren. “Ghost stories: an old friend drops in for a seance.” Columbus (Ohio) Alive, 4 Nov. 1999. 10.) b.It’s a difficult place to cross or locate people once they are in the area. (US Border Patrol agent Maurice Moore, National Public Radio interview, 24 May 2001)

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Page 262 The analysis presented in the earlier sections will not license these sentences.54 For example, for (395a) to be grammatical under the assumptions made about adverbial RCs earlier, he loved and felt comfortable would be a complement to place. However, the lexical rule for adding adverbial RC complements adds an argument of category S/(S\S), and therefore, place would have category here. But he loved and felt comfortable will have category since it contains a gap that is simultaneously an NP and an adverb. Therefore, in order for place to combine with he loved and felt comfortable, it needs to have category To see the problem more clearly, think of category as A; S as B; NP as C; and S\S as D. It must be proven that is derivable from A/(B/D). The failed sequent-style proof in (396), while not a complete proof search, indicates the basic problem: At some point must be derived from D, which is not allowed since ν(D) is not a subset of (396) Attempted proof that

The fact that the current analysis fails to license the sentences in (395) is not necessarily a drawback, since there are speakers with different grammaticality judgments for the sentences in (385) and in (395). To describe the grammar of people who allow category neutrality with respect to Property 2, probably the simplest amendment to the analysis as presented would be to change the adverbial RC addition lexical rule to add an argument of category instead of S/(S\S): 54. Thanks to an anonymous Journal of Linguistics reviewer for noticing this.

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Page 263 (397) Non- wh adverbial RC addition lexical rule for adverbial nouns, for dialects that allow (395) Depending on one’s analysis of parasitic gaps, this lexical rule might also be in the grammar of speakers who accept phrases such as the following (suggested by an anonymous Journal of Linguistics reviewer): (398) ?the place that the spies met without bothering to properly secure Here, the RC containing a parasitic gap would presumably have category The rule in (397) would still work for individual adverbial RCs. For example, to license place that he felt comfortable, the phrase that he felt comfortable would have category Sc/(S\S), but could easily be strengthened to in order to combine with place: Although cannot be derived from A/(B/D), on the other hand CAN be derived from B/D. In fact, this lexical rule would work for nonadverbial RCs, too. If one were just deriving place that he loved, the S c /NP for that he loved could be strengthened to So for adverbial nouns in the JL reviewer’s grammar, the RCs-ascomplements approach extends to nonadverbial RCs. 6.7 Conclusions In this chapter, Property 1 of adverbial nouns (i.e. their ability to project adverbial NPs) was initially described by assigning adverbial nouns the category In order to describe Property 2 (their ability to head non- wh adverbial relative clauses), lexical rules were introduced that allowed an adverbial noun to take a non- wh adverbial relative clause as a complement, and it was found that having the category for adverbial nouns facilitated the stating of the lexical rules’ semantics. This conjoined category led to a prediction about adverbial nouns regarding Property 1: that they should be able to be used simultaneously as an ordinary NP and an adverbial NP. This prediction proved to be true. Furthermore, regarding Property 2, for some speakers it is possible for an adverbial noun to head a non- wh relative clause that contains both an NP gap and an adverbial gap. This possibility is also analyzable by way of category neutrality. Overall, then, the existence of category neutrality is confirmed in one more part of English grammar, further eroding the claim that it does not exist.

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Page 265 CHAPTER 7 Conclusion 7.1 Summary Category neutrality has been an overlooked phenomenon in natural language. Few cases have been reported (to my knowledge, all in Sag et al. 1985), and have for the most part been analyzed in a way that did not require any word to have more than one category simultaneously. As expressed by linguists such as Bayer (1996) and Heylen (1997, 1999), the reason for disallowing category neutrality in a grammar was the problem that once multiple categories could be assigned to a given phonological form, then any two or more homophones could be neutralized, resulting in tremendous overgeneration. However, in Chapters 3–6, several cases were described in which the most reasonable explanation involved category neutrality. In Chapters 3 and 4, verbs participating in a number of argument alternations were shown to be able to have two categories simultaneously in coordination tests. Furthermore, even when the coordinations were ungrammatical, the ungrammaticality had less to do with any category neutrality for the verbs than with conversational implicature. Evidence came from the fact that some ungrammatical coordinations involved no category neutrality at all, while many of those that did could be improved with the right context. In Chapter 5, postcopular predicative phrases were addressed. These were some of the cases of category neutrality reported by Sag et al. (1985). In this chapter, it was seen that even if one chooses an analysis in which the copula does not exhibit category neutrality, category neutrality turns up in NPs and PPs when the copula is coordinated with other verbs. In Chapter 6, category neutrality was in evidence for at least some speakers for English adverbial nouns. Furthermore, even for speakers who never use these nouns with more than one category at a time, it was seen that there might

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Page 266 still be reason for these words to have category neutrality: to constrain the input to a lexical rule that applies only to adverbial nouns. In addition, in Chapters 3 and 5 it was shown that category neutrality is not limited to lexical items, but can arise in entire phrases that do not contain any lexical item assigned to multiple categories in the lexicon. These were the coordinated-wh adverb interrogatives with differing scope for the different wh adverbs in Chapter 3, and the simultaneous NP and usage of noun phrases in Chapter 5. 7.2 Directions for Further Research Several areas for further research are suggested by the findings in the earlier chapters. This dissertation has focused on only a small sample of the various regular phonological identities in English. Others that could be investigated are the various uses of present participles and gerunds, as illustrated in (399): (399)a.*The dog’s loudly and incessant barking drove me crazy. (due to Carl Pollard; “verb-like” gerund vs. “noun-like” gerund) b.*his driving the car and of the motorcycle (Pullum and Zwicky 1986, (42b); “verb-like” and “noun-like” gerund) c. ?At first he avoided, but later was continually, bursting into tears. (adapted from Pullum and Zwicky 1986, (42c); gerund vs. participle) Also, there are the different senses of various modal auxiliaries, such as epistemic vs. deontic must, or similar alternations for other modals. On the subject of systematic meaning differences, one might branch out to examine possible cases of category neutrality when the categories happen to be the same—that is, words that have categories of form This was already seen in Chapter 3, when the coordination why and how was derived to have category in order for how and why to have different scopes. At the lexical level, it is worth asking if a category such as would be useful for encoding the kind of meaning alternations analyzed in Generative Lexicon (GL) theory by Pustejovsky and others. For example, would it be useful for a noun such as book to be given category with meaning How different verbs such as read or burn would select for the different meanings would need to be worked out, but the possibility is interesting. (For one perspective on how to integrate the GL and TLG frameworks, see Mineur and Buitelaar 1995.)

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Page 267 7.3 Implications The main reason for linguists wanting to deny the existence of category neutrality is a theoretical one: As currently defined, type-logical grammars cannot formally distinguish between ambiguity and category neutrality. That is, even if one had foolproof diagnostics for identifying ambiguity and neutrality, the frame semantics for the constructor used to encode neutrality levels the distinction between the two. Therefore, it is easier to avoid having category neutrality in a grammar than to allow it and open the floodgates of unrestricted neutrality for homophones. However, the effect of the various cases examined here is to show that category neutrality is real, notwithstanding the dire theoretical implications. Two possibilities exist. One is that type-logical grammars as currently defined simply do not accurately represent natural language with respect to ambiguity and category neutrality. In this case, some wellmotivated means of formally encoding the distinction needs to be found. Concomitantly, all lexical rules that do not involve any overt morphology will have to be marked as relating two separate lexical entries, or specifying category neutrality in a single one. Even if a well-motivated formalism for keeping ambiguity and neutrality separate can be created, this marking of lexical rules seems distinctly ad hoc. The other possibility is that type-logical grammars as currently defined DO accurately model natural language with respect to ambiguity and category neutrality—in other words, there is no real difference between the two. In this case, the conventional assumption that ambiguous words occupy multiple lexical entries and neutral words occupy single lexical entries will have to be abandoned. Though one can still speak of ambiguity and neutrality, these terms will refer to endpoints on a continuum measuring relative difficulty in using a word with more than one sense at a time. This end of ambiguity as we know it is a daunting prospect, since it would mean that ANY zeugma that would have been ascribed to a word’s ambiguity will now have to be accounted for by way of pragmatics, processing difficulty, or some other explanation. The good news, though, is that such analyses will probably have better explanatory value than appeals to ambiguity do. This was seen in Chapter 4 in particular, where a greater range of coordination facts was able to be described once ambiguity was taken out of the picture. The phenomenon of neutrality, which has received so much attention in the literature on coordination of unlikes at the feature level, has been shown to extend to the level of syntactic category. The limits of category neutrality remain to be probed, and the messy task of figuring out how (or whether) to distinguish it from ambiguity must now be faced, but its existence can no longer be denied.

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Page 269 Appendix A Attestations of Mixed-Wh Interrogatives A.1 Optional NP-Gap Mixed-Wh Interrogatives (53) A.1.1 Those Involving Where (6) A.1.1.1 Where First (3) WHERE & WHAT TO BUY http://db.inman.coni/inman/qa/cbnorcal/buy.htm I own a 95 Geo Tracker and i want to customize it and make it very unique…have a few thousand dollars that i am looking to use and now just need help in find where and what to buy. http://forums.vmag.com/suvtrack0199/messages/454.html I need to know where and what Emerson taught after graduating from Harvard. http://www.hatterasHght.com/navy/RalphWaldoEmersonhall/cas/25.html A.1.1.2 Where Last (3) WHAT AND WHERE OUR CHILDREN EAT http://www.wisc.edu/uwcc/links/kidseat.html Who or where to send Songs? http://www.enteract.com/~digialex/wwwboard/messages/2414.html

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Page 270 We always travel all inclusive as I don’t want to think about what or where to eat on vacation. http://search.caribbeanmag.com/discuss/cozumel/messages/899.html A.1.2 Those Involving When (11) A.1.2.1 When First (4) What Immunizations, When and Whom to Immunize http://www.hetcat.uthscsa.edu/shots024.html When and what to negotiate with the project team http://www.soft.eom/QualWeek/OW2K/Papers/Al.html When and what do you report to the credit bureaus? http://www.afsa.com/ffe1/99faqs/qna/qna/delinq.htm In its simplest form, you just date the letter, say when and what you’re resigning, sign it, hand it over, and that’s about it. http://www.usjobs.com/ A.1.2.2 When Last (7) If you would like to input personal information on your soldier, I am looking for when and where born, when and where died, when and where buried, parents, brothers and sisters, who and when they married, and their children. http://vax1.vigo.lib.in.us/~jmounts/soldiers/index.htm Who and when are we playing this season? http://www.cf.ac.uk/psych/savagejc/football/index.html WHAT AND WHEN CAN I EAT BEFORE WALKING? http://www.racewalk.eom/WWBook/NS00009.htm\ You will learn to become a food detective and control what and when you eat. http://www.zonehome.com/whyzone.htm

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Page 271 You never know who or when we may call. http://www.histar.com/say_it_and_win/sayit_andwin.shtml At the same time, even if we are not at all sure what or when we are celebrating, we think it is a good principle that more celebration is better than less, and it is ultimately quite exhilarating to reflect that, as with all major jubilees, one may expect there will be all manner of literal and figurative jubilations, spontaneous and calculated acts of celebration, dancing in the streets, forgiveness of debts, fireworks, emptying of prisons, remission of sins, etc. http://www.mohawk.net/~barbaria/millennium.html The most important thing about a meal is not what or when you eat but with whom. http://www.perivar.org/mr/991002m.htm A.1.3 Those Involving How (15) A.1.3.1 How First (10) Week #29. How and What to Read http://www.missabigail.com/selection/selection29.html Computers: How and What to Buy http://www.christianlibrary.org/legal/how-what-to-buy.htm What questions do we need to ask to better understand how and what our students are learning? http://www.whittier.cps.k12.il.us/LEAP/LeapPhases.html I’ve always been a staunch defender of how and what we’ve paid Dr. Smith. (Mark Hatch, president of Columbus (Ohio) School Board, on departing superintendent Rosa Smith; heard on radio on 27 Feb. 2001) I believe in tolerance and love for all people, no matter what color or creed or how or who they choose to love. http://boards.parentsplace.eom/messages/get/ppreligiondebate2/6.html

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Page 272 How many such questions aren’t being asked by our students because, at those hours and under those deadlines, they simple don’t know how or whom to ask? http://www.english.upenn.edu/Writing/front.html There is no national organization or annual convention that dictates how or what we teach. http://we.got.net/~hughes/miller/home.htm The Standards don’t tell teachers how or what to teach. http://www.firn.edu/doe/curric/prek12/over.htm St Matthew Chapter 10, Verse 19: But when they deliver you up, take no thought how or what ye shall speak: for it shall be given you in that same hour what ye shall speak. http://users.50megs.com/scriptures/pages/stmatthew10v19.html#top About my writing… I didn’t go through a period of copying other people’s charts, and I’ve not done enough commercial where people have told me how or what to write. http://users.50megs.com/scriptures/pages/stmatthew10v19.html#top A.1.3.2 How Last (5) WHAT AND HOW TO PACK http://www.uwsp.edu/studyabroad/ What and How to Pay on Metro Transit http://transit.metrokc.gov/bus/whatpay.html Solid Waste/Recycling Bureau: What/How to Recycle http://www.marlboro-twp.com/orgs/recycling/whatandhow.asp Who and how to ask questions http://www/business.auc.dk/comp/info/questions.html Teaching Clientele What or How To Think http://www.joe.org/joe/1992spring/a2.html

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Page 273 A.1.4 Those Involving Why (1) A.1.4.1 Why First (0) A.1.4.2 Why Last (1) What and Why FoolProof. 162.127.88.3/foolproof/index.htm A.1.5 Those Involving Whether or If (14) A.1.5.1 Whether/If First (9) Prenatal Testing Board is for whether and what to test. http://boards2.parentsplace.com/messages/get/ppdecisions3.html We’ll visit with the telescope vendors and figure out whether and what to buy. http://www.discovery.com/stories/science/starparty/starparty.html The job market is competitive and employers decide if and who they will hire. http://www.ucalgary.ca/pubs/calendar/1997/How/coop.htm Determine the perfect price for your product. USE IT NOW. Decide if and what you will pay [for] it later! http://www.peterman.co.za/ They had a sister named Ida Thomson (don’t know if or who she married). http://www.greenpointusa.com/VWRMAIL.HTM At present we do not know if or who she married, nor do we have a death date. http://genforum.genealogy.com/carlisle/messages/163.html I don’t know if or who she married, but she had at least one child—NOAH H.STRICKLAND. http://archive.msstate.edu/listarchives/afrigeneas/199805/msg00201.html

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Page 274 Until last month I did not know if or who she had married. http://www.genforum.genealogy.com/whitford/messages/278.html There is a new RC5 project competing with Bovine in Finland. I haven’t decided IF or WHICH I’ll join yet. http://www.interhack.net/proiects/deschall/archive/199707/0006.html A.1.5.2 Whether/If Last (5) The question is taken up of what and whether editors should be paid. http://www.arl.org/scomm/subversive/toc.html Part of the problem in exposing OPT for what it is (or, is not), rests in the getting people to understand that there are many different variables that affect what and whether a child learns in school. http://cc.ysu.edu/~rlhoover/ClassConnections/OPT/index.html I admitted then that I wasn’t sure what or whether I believed, or whether that even mattered. http://www.seshat.org/journal/retro.htm Don’t know who or if she married. http://genforum.genealogv.com/scudder/messages/68.html It doesn’t matter what or if you ride or whether you are male, female or a doctor or a lawyer…you will be referred to as a “biker” while perusing this website. http://bikeweekreport.com/davtona.shtml

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Page 275 A.1.6 Those Involving a Combination (4) A.1.6.1 Adverbials First (2) I’ve reported when, how and what I’ve wanted. My only limitations have been those I’ve created. (Matt Drudge, quoted in “Manifesto provides inside scoop on ‘Drudge Report,”’ Mark R.Weaver, Columbus (Ohio) Dispatch, 7 Nov. 2000, E8) When, Where, and What To File http://www.irs.gov/forms_pubs/pubs/p154403.htm A.1.6.2 Nominal Wh Sandwiches (2) It seems that the ladies have all sorts of formulas about when and who and why to call back— usually the answer is, “ummm, he should.” http://www.metrosocialscene.eom/postboard/messages/31.html Their professor, Frank Hassebrock, wants to know: How, what and why do people remember? (Kirsten Chapman, “For key to memory, we seek to unlock corners of our minds,” Columbus (Ohio) Dispatch, 1 Feb. 2001, p. E1) A.1.6.3 Adverbials Last (0) A.1.7 Supplementary: Instances Found with Nominal Wh Phrase (2) A.1.7.1 Those Involving Where (1) I consider myself to be a fair and honest judge regardless of where or whose cats I judge. http://www.hotkey.net.au/~nswcfa/marjlavelle.html A.1.7.2 Those Involving When (0) A.1.7.3 Those Involving How (0)

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Page 276 A.1.7.4 Those Involving Why (0) A.1.7.5 Those Involving Whether/If (1) We will notify you if and which award you have won as well as include you on our Winners Circle. http://woodcraftdesign.com/fullindex/awards.htm A.2 Obligatory NP-Gap Mixed-Wh Interrogatives (63) A.2.1 Those Involving Where (6) A.2.1.1 Where First (6) Subject Gap:3 Object Gap:3 Where and what to charter. http://www.olyc.com/ Where and What to Download? http://www.delorie.com/djgpp/v2faq/faq4.html I’ll also be down in the Kenai tips there on where and what to use would help me too. http://www.denali.national-park.com/wwwboard/messages/279.html Need info about how the action is the next week. Where and what was working? http://www.greatlakesfishing.com/wwwboard/messages/153.html Does anyone have any idea where or who would be able to locate parts? http://www.siriusweb.eom/Fremlin/forum/messages/181.html If you do not know anything could you guide to where or who might know something about these. http://www.artindex.com/board/messages/347.htm A.2.1.2 where last (0)

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Page 277 A.2.2 Those Involving When (6) A.2.2.1 When First (6) Subject Gap:4 Object Gap:2 Identify when and who should contact the university’s attorneys. http://sports.mediachallenge.com/crisis/index.html At any time [this software] lets you know who was using your standalone/network computers, and when and what they were doing. http://www.download32.com/proghtml/54/5446.htm You can get a lot of yahoos on this track who aren’t worried about when or whom they hit into…and it happens a lot. http://www.ocnow.com/recreation/golf/gr_orange.html Included inside the magazine are editorials about traditional ceremonies, checklists for the bride and groom, schedules and pieces letting the bride know when or who should take care of certain responsibilities. http://www.public.usit.net/fcjacob/ Quite when or who dug up the first crashed aircraft in the name of Archaeology is lost in the mists of time. http://www.btinternet.com/~airresearch/aahome.htm I WOULD LIKE TO KNOW ABOUT THE T CELL LEVEL AND WHEN OR WHAT IS CONCIDERD TO LOW? http://www.thebody.com/cgi/fatigue_ans/24430BLO.html A.2.2.2 When Last (0) A.2.3 Those Involving How (8) A.2.3.1 How Lirst (7) Subject Gap: 2 Object Gap: 5 How and Who to Contact http://www.teamster.com/401k/contact.htm

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Page 278 By the end of that year, art directors from different ad agencies were calling to find out how or who could design and build sites for their clients. http://www.sprout.net/framedface/roots.html While there are absolutely no constraints on how or who designs and builds the contraption (or why), it must be entirely human powered and can be no wider than 8ft nor higher than 9ft (except while in the water). http://www.riverotter.com/ruies.html We are trying to find out how or who we can get to air it here as well. http://www.officialjanis.com/html/news.html I know they are out there but didn’t know how or who to contact. http://www.cadvision.com/Home_Pages/accounts/mclieshf/ She was very concerned that she didn’t know how or what to say. http://www.sonlife.com/wwwboard/messages/43.html How or what would i ask him? http://feedback.interplav.com/fallout2/msg2/13540.html A.2.3.2 How Last (1) Subject Gap: 0 Object Gap:1 You obviously very much need a lawyer since you do not know what or how to do. http://www.intelproplaw.com/Trademark/Forum/msg/144.shtml A.2.4 Those Involving Why (7) A.2.4.1 Why First (6) Subject Gap: 5 Object Gap: 1 Healthy Drinking Water: What’s Good, Bad, Why and What to Do. http://www.healthywater.com/index.html Why and what is surviving. I mean when it comes to the soul—what truely should be motivation for survival. http://www.sangraal.com/_disc3/00000008.htm

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Page 279 It is not known exactly why or who burned the village. http://www.madison.k12.wi.us/whitehorse/ss/walls.htm Don’t know how or why or who took on this indignity to the nation and the 1st Ammendment, but whoever and however, we thank you for prompt defense of our “rights”! http://pages.hotbot.com/arts/swseso/j_f_k_jr.html But, why or who is stopping all the news media, TV WEB, radio, from starting out with, HOW to safely work around it, NOT how many companies are not able to get to their e-mail? http://slampros.ulink.net/Safesurflng.htm Nor does she know why or who sent the portrait to Hugh. http://www.dragons-inn.org/staff.html A.2.4.2 Why Last (1) Subject Gap: 1 Object Gap: 0 No one will regret obtaining this book on mammal behavior which will give the observer the advantage of knowing what or why the animal is doing. http://www.nature-wildlife.com/booksto.html A.2.5 Those Involving Whether/If (12) A.2.5.1 Whether/If first (10) Subject Gap: 6 Object Gap: 4 This is not a question of selfishness, but whether and who will decide how to spend their money. http://www.reagan.com/HotTopics.main/HotMike/document11.11.1997.5.html While NSI is likely to remain the registrar for the three conventional domain names, say observers, the non-profit corporation will have to make some tough decisions about whether and who will have the right to be the registrar for new domain names. http://eb-mag.com/eb-mag/issues/1998/9809/0998bt.asp

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Page 280 An independent contractor usually must have the right to choose whether and who to hire as assistants. http://sago.tamu.edu/soba/ver1_96.htm Decisions about whether and who to send are tricky since they have to be made quickly and there are few guidelines or precedents. http://www.nando.net/newsroom/nt/1106tmlcolor.html You find out everything about someone: who their friends are, what their opinion is on a wide range of matters, whether and who they are having sex with, the full range of som[e]one’s activities and emotions. http://member.newsguy.com/~mayday/crvpto/crypto6d.html Read well; then decide whether and who to vote for. http://www.users.globainet.co.uk/~jclack/frames/europropaganda.html If I’m the power company and there is a dispute from the consumer, I need to know if and who screwed it up in the distribution. http://inelext1.inel.gov/science/prestige.nsf/ineel/opticsensor Would also like to know if and who makes different carriers for the front and rear that would update the old 19 spline axles to something stronger and maybe even a mild traction improvement for the rear end. http://forums.vmag.com/pm-0799/messages/820.html One sits on the edge of justice waiting to hear if and who of those Anna Mae knew may be indicted for her murder. http://www.dickshovel.com/clay8.html PCI 6 shares with the integrated sound—doesn’t share at all if sound is disabled in the BIOS (since I haven’t found a CNR card I don’t know if or what it shares with but would suspect PCI 6). http://www.specialtvtech.com/7isa.htm A.2.5.2 Whether/If Last (2) Subject Gap: 0 Object Gap: 2 Not sure what or IF we’re doing http://boards.parentsplace.eom/messages/get/ppphoenixaz2/51.html

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Page 281 I don’t know what or if she is feeling but I know there is a sensation of “warmth”; we are together. http://www.beoutrageous.com/guestbook.htm A.2.6 Those Involving a Combination (4) A.2.6.1 Adverbials First (4) Subject Gap: 2 Object Gap: 2 If your product is mishandled the Clip will tell you exactly where, when and who mistreated your products. http://www.shockwatch.com/se/oshaif.html The rest of these documents hopefully will give the reader some idea of why, when and what to look for as regards satellites in the night sky. http://www2.satellite.eu.org/sat/vsohp/satintro.html Not to tell anyone how or if or who to vote for, but bear this in mind: http://www.earthsystems.org/list/stamp/0145.html Ryan knows he’s been marked for revenge, but doesn’t know how, when, or what will happen next. http://www.dvd-spin.com/revs/patriot.htm A.2.6.2 Nominal Wh Sandwiches (0) A.2.6.3 Adverbials Last (0) A.2.7 Supplementary: Instances Found with Nominal Wh Phrase(20) A.2.7.1 Those involving where (1) Subject gap: 0 Object gap: 1 Our Privacy policy describes where and what information we collect and where we disclose it. http://www.icollector.com/IG/index2.html

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Page 282 A.2.7.2 Those involving when (10) Subject gap:4 Object gap:6 (e) Secs. 416.1060 through 416.1061 describe when and what kind of assistance the Commissioner will provide State agencies to help them improve performance. http://www.lrp.com/ed/freelib/free_regs/c20416_1001.htm Custom-designed scans let users determine when and what files to scan, eliminating unnecessary rescanning of safe files. http://expresscomputerindia.com/ec/20000103/parade.html The choice of when and which faxes to use is left to the game manager although some suggestions are available in the teaching note which also accompanies the simulation. http://www.mit.edu/people/anajam/cl-game.html The important point is to know WHEN and WHICH cows to float, not to know that you CAN float a cow. http://www.downcow.com/homepage.html As a result, there are still a lot of athletes who need to be informed about the reasons why they must eat before exercise and, most importantly, when and which amounts and types of carbohydrate they should consume. http://www.xtri.com/1999/9909-ss.asp They have no way to know when and which person is busy, out of office or in the meeting http://www.telesvnergv.com/tele_faq.html Know when and which RS-232 signal is stuck or stops http://www.cpscom.com/wish.htm There are quite a few PC programs that track satellites in real time and these identify when and which satellite is in your stations range, the satellites that interest you are Russia’s MET 3–5 and America’s NOAA 12 or NOAA 14. http://www.elec.uow.edu.au/people/stafPron/div.html With Aquajeux random sequence, the user does not know when and which component will come into play. http://aquaieux.com/principale.html

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Page 283 The unit commitment problem is to decide when and which generating units to start-up and shutdown, in order to minimise the total fuel cost or to maximise the total profit, over a study period of typically a day, subject to a large number of difficult constraints that must be satisfied. http://www.dash.co.uk/app_gen.html A.2.7.3 Those involving how (0) A.2.7.4 Those involving why (1) Subject gap: 0 Object gap: 1 Why and which one do I choose? http://mann.library.cornell.edu/reference/FAQ.html A.2.7.5 Those involving whether/if (8) Subject gap:3 Object gap:5 If you don’t own a computer, you might want to look at our recommendations on whether and what hardware to buy and on educational discounts. http://www.auburn.edu/helpdesk/startup/stu.html We are still investigating whether and which of these shaped dielectric substrate[s] is suitable to our purposes. http://www.tuc.nrao.edu/~demerson/project_book/chap3/chap3.2/chap3.2.html You may ask the applicant to describe, or demonstrate, how s/he might carry out the job duties, with or without reasonable accommodation, but you may not inquire whether, or what type of accommodation, the applicant might need to perform the job duties. http://janweb.icdi.wvu.edu/kinder/pages/pre_employment_screening.html Also, decide if and what type of thermometer/hygrometer device you may want to use to monitor the humidity. http://www.cigarsavor.com/choosing.html Undecided if and whose side to join, they were persuaded by Britain and France to join the war on the Allied side. http://members.aon.at/philm/attvers.html

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Page 284 I do not know if or what kind of law I will practice again, though I am still interested in intellectual property and the internet; in the short term, it will be part time. http://laura.chinet.com/ At this early stage of planning, there has been no decision made as to if or which technical student organization will be available to students. http://www.csi.edu/ip/TI/draf/intech/brochure.htm As of now, they are still not sure if or what connection exists. http://neurowww.mgh.harvard.edu/forum_2/LandauKleffnerSvnF/9.14.996.09PMExperiencesw.html A.3 Missing NP-Gap Mixed-Wh Interrogatives (31) A.3.1 Those Involving Where (4); Where Always Last Who or where in Montreal can I learn Mantis or Eagle Kung Fu? http://www.wutang-canada.eom/wwwboard/messages/111.html Does anyone have a thought as to the origin of the term “NERF BARS”? Have had them on my CJ-5 since 1972, but have always wondered who or where they got their name. http://forums.vmag.com/suvx900199/messages/107.html I don’t know who or where to look first. http://www.onlinether.com/wwwboard/shipwreck/messages/523.htm What or where can I get information on the places I may take my companion dog/service dog. http://www.access-by-design.com/wwwboard/messages/604.html A.3.2 Those Involving When (4); When Always Last Do you want to know who and when anyone looks at or changes any information on your credit report? http://www.consumercreditreports.com/

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Page 285 We track orders by date and by email address, so letting us know who or when your item was ordered will speed your satisfaction. http://www.gamepreserve.com/Policies/NoHassleReturnPolicy.htm However, due to the nature of dating historical facts, there are opinions and disagreements as to who or when the actual event took place. http://www.rocheclan.com/html/antiquetimeline.html We never know what or when we are getting our newest shipments bet we keep you posted regularly with our Beanie Baby Town Hotline (415–898– TOWN/8696). http://www.goldengategifts.com/ A.3.3 Those Involving How (4); How Always Last If someone knows what or how to do this I’d much appreciate the help. http://www.homeimages.com/wwwboard/messages/1887.html What or how can I find where these bonds are and who they are for. http://www.wmbakerassociates.com/wwwboard/messagesliqa/1507.html The company found that, nationwide, most of the CDL Examination failures were due to people not knowing what or how to prepare themselves for the CDL Examination. http://www.cdltest.com/ Wouldn’t you rather have the vendor store this information down on your hard drive where you can see it and delete it instead of on the vendor’s server where you have no idea what or how long they are storing this info? http://www.librarv.wisc.edu/help/remote/remote_restrict.html A.3.4 Those Involving Why (8); Why Always Last Not sure what or why this happened. http://www.horsebrass.eom/wwwboard/messages/218.html I knew not what or why I was doing these things, but once I came to my crossroads, I knew which path I should take which has led me right here. http://www.partvtown.com/menus/bos.htm

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Page 286 Use this area to explain what or why you are needing this and give any other info that might encourage a seller to contact you. http://db1.mac4sale.com/sale/w2b/new.htm We apologize for these people even though we have no idea who or why they chose to do this. http://www.netwares.com/wwwboard/messages/169.html So who or why would you even need this thing. http://www.biznetonline.com/07–00/designtech.htm I don’t know who or why our memories were erased, who killed Wild Bill, what colors really go with lime green, but somehow I fear for our lives, and I think I should go to London and see if I can find my past there. http://www.actual-reality.co.uk/abroad/ju196/doree193.htm Nothing is more frustrating than being presented with a long list of hyperlinks at a web site without knowledge of who or why the links are provided. http://www.club-mgmt.com/manager/9910/eclubs.html I don’t remember ever hearing the official results of them and Who or why I even had them done. http://dem0nmac.mgh.harvard.edu/forum_2/FibromyalgiaF/Finelinehere.html A.3.5 Those Involving Whether/If (9); Whether/If Always Last I cannot remember who or if anyone person recommended her, but the process is to inform… http://www.defenselink.mil/news/Jan1998/t01271998_t0127asd.html Ray Shedrick and Ralph are drafted too but cant tell who or if any will have to go. http://www.geocities.com/Heartland/Prairie/7912/chloe.htm Any suggestions to what or if I need to strip the chairs first, or just sand and clean down before painting? http://www.furniturewizard.com/wwwboard/messages/7793.html

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Page 287 Initially it was questionable as to what or if I would recover. http://dem0nmac.mgh.harvard.edu/forum/ChronicPainF/2.18.9911.41PMFredallplea.html Any suggestions to what or if I need to strip the chairs first, or just sand and clean down before painting? http://www.fiirniturewizard.com/wwwboard/messages/7793.html I would like to know what or if King Duncan made good decisions. http://library.thinkquest.org/2888/wwwboard/msg/5863.html By now stating that defective filing “should be waivable” (maj opn at 8), the majority fosters serious uncertainty as to which or whether any of the various elements of filing specified in CPLR 304—the payment of fees, the delivery of documents to the clerk of the court or the proper form of initiatory documents--must be present for proper commencement of an action or special proceeding. http://www.law.cornell.edu/nv/ctap/089_0714.htm There are two slightly different size colored disks, shown in picture, to represent runners. I am not sure which or if either are original. http://www.fortycaroline.com/dusty.htm I am not aware which or if any of the backup vendors provide Linux support. http://teaparty.mathworks.com:1999/toasters/2374.html A.3.6 Those Involving a Combination (2); All Nominal Wh Sandwiches Managing Performance: Why, What and How to Proceed http://www.avcc.edu.au/avcc/staffdev/mpreport.htm The Basics of how, what and where to ftp the files http://support.netdoor.com/web/ftphome.html

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Page 288 A.4 Plural-Noun Mixed-Wh Interrogatives (40) A.4.1 Those Involving Where (3) A.4.1.1 Where First (2) But certainly it will mean shift of available resources for health care to areas and people where and whose needs are greater; it will mean less to the already privileged and more to the under-privileged, the vulnerable, the weak and the poor. http://dailvstarnews.com/199808/18/n8081809.htm If marble is available in the US is it good for sculpting? I have no idea where or what kind of stone is available to me and would greatly appreciate any information. http://www.natural-stone.com/messages/1528.htm A.4.1.2 where last (1) The public’s perspective in whose and where individual names are commemorated should be taken into account. http://rivertowns.net/news1999/pchrival/week51/frontpage/np/OPINA01.HTM A.4.2 Those Involving When (8) A.4.2.1 When First (8) In the coming weeks, the project will define a set of guidelines to determine when and what mailing lists are created. http://www.gjt.org/mail/ Use linker option -v to see when and which objects, archives and dsos are loaded. http://www.cs.tu-bs.de/softech/ddd/ddd-bugs/2195.html

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Page 289 Senators Patty Murray (D-Wash) and Robert Toricelli (D-NJ) recently introduced the “School Environment Protection Act,” which among other things would require schools to notify parents when and which pesticides are being used at school. http://www.acsh.org/press/editorials/pesticides010500.html In order to keep track of when and which students use the TLC, the sign in computers keep a log. http://sbhs.sburl.k12.vt.us/tlc/policies.htm How does CM control when and whose transmissions occur? http://wind.lcs.mit.edu/talks/sigcomm99-cm/tsld008.htm Labeling theory sensitizes us to when and whose viewpoint is relevant. http://www.indiana.edu/~socpages/causal_theories.html All pulls are random, Clyde, and the number of coins played has absolutely no effect on determining when or what type of winning symbols will appear on the machine. http://www.detnews.com/CASINO/columns/pilarski/0310/0310.htm Since no one can predict when or what features will be changed, the best any WWW publisher can do is make sure their pages are 100% compliant with today’s standards. http://www.hlis.com/Web/techinfo.html A.4.2.2 When Last (0) A.4.3 Those Involving How (2) A.4.3.1 How First (2) Filming the “Discovery” of America: How and Whose History Is Being Told http://www.swcp.com/~cmora/historia/historia-5–1.shtml They are not particularly exciting reading—that is, until they impact how or what things can be done. http://www.pforum.org/Ga211/Primer/index.htm

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Page 290 A.4.3.2 How Last (0) A.4.4 Those Involving Why (0) A.4.4.1 Why First (0) A.4.4.2 Why Last (0) A.4.5 Those Involving Whether/If (25) A.4.5.1 Whether/If first (24) It is for Congress in the first instance to determin[e] whether and what legislation is needed to secure the guarantees of the Fourteenth Amendment; and its conclusions are entitled to much deference. http://supct.law.cornell.edu/supct/html/95–2074.ZO.html Likewise, managed care organizations often make choices about whether and what equipment or prescription drugs will be included in its plan benefits. http://www.state.ma.us/dhcfp/pages/dhcfp_87.htm Whether and what type of preprocessing applies should be indicated by an Expansion/Interpretation attribute. http://lcweb.loc.gov/z3950/agency/attrarch/arch.html The forum in which state and local governments ITFA imposed a temporary, three-year moratorium on the imposition of new state and local taxes on Internet sales and Internet businesses to allow ACEC time to conduct a thorough study of the remote sales taxation issue and prepare recommendations to Congress on whether and what type of federal legislation might be warranted to resolve it. http://www.cbpp.org/12–13–99tax.htm (6) Whether and what types of technological measures can or should be employed to safeguard against unauthorized access to, and use or retention of, copyrighted materials as a condition of eligibility for any distance education exemption, including, in light of developing technological

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Page 291 capabilities, the exemption set out in section 110(2) of title 17, United States Code; http://www.tao.ca/wind/rre/0573.html The descriptions of each of the collections/categories that can be searched in the catalog includes information regarding whether and what kind of images will display inside and outside the Library of Congress. http://lcweb2.loc.gov/pp/pphelp.html Discussions during this phase may include whether and which species may occur in the proposed action area, and what effect the action may have on listed species or critical habitats. http://endangered.fws.gov/esasum.html It is always the prerogative of the receiving institution to determine whether and which credit will transfer. http://www.theology.edu/onlinecourses.html (4.1) whether and which access mechanisms to computerised data are an effective, efficient and adequate way to fight (organised) crime and mount effective prosecution of criminals, and http://catless.ncl.ac.uk/Risks/18.67.html You agree to access our list information only for the purpose of determining whether and which lists you may be interested in renting through us. http://www.greatlists.com/terms.htm Know whether or not the vote you are asking for will go against the legislator’s party line, and whether or what groups are against us. http://www.nvfc.org/hn_guidegrassroots.html When all the cards in a tableau pile have been played elsewhere, there is usually a rule about whether or what kind of cards can be moved to the empty space http://www.goodsol.com/pgshelp/tableau.htm Libraries in each state, however, should check with their state statutes to see whether or what kind of obscenity or harmful to minors laws exist, and they should ask their attorneys whether such laws apply to the library. http://www.ftrf.org/ennis.html

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Page 292 DOD refers to the Tomahawk as ‘nuclear-capable’—we do not confirm whether or what kinds of munitions were matched to the missiles at any particular location. http://www.channel4000.com/sh/technologv/siteoftheweek/nationaltechnology-siteoftheweek20000721–094416.html Now to my query, I am trying to determine whether or which Benjamin Collier is the father of Harrison Howard Collier. http://genforum.genealogy.com/collier/messages/523.html When a theft occurred at one telecentre, it was not clear whether or which equipment was ensured. http://www2.worldbank.org/hm/afrcomm/0022.html Eternal damnation remains a real possibility, but we are not granted, without special divine revelation, the knowledge of whether or which human beings are effectively involved in it. http://www.ewtn.com/librarv/PAPALDOC/JP2HEAVN.HTM Many companies have no means of determining whether or which parts of their inventories are: too high, too low, just right. http://www.automotiveadvisors.com/Inventory_Check/inventorycheck.html Parents and music teachers should consider whether or which courses would be cut and how any cuts will affect the music program. http://www.sciences.drexel.edu/block/profpaper/benham.html Find out if and which other library systems use the same database engine. http://www.home.aone.net.au/libauto/Tips.html Going beyond hydrodynamics it is not possible to predict, if and which non-hydrodynamic variables can become slow, although the generalized theory, which includes such variables, is still a powerful theory albeit less fundamental than a purely hydrodynamic theory. http://www-theory.mpip-mainz.mpg.de/~pleiner/proiect.html

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Page 293 Notwithstanding the possibility that Microsoft has been unfairly singled out for being too successful in the eyes of the government’s antitrust enforcers, there is a strong likelihood that Microsoft will lose the next stage of rulings that will decide if and which laws were broken. http://www.dismal.com/thoughts/th_sc_112299.stm With German troops deployed in the Balkans again today i was wondering if or which awards from WWII (and earlier) of the de-nazified 1957 variety are still valid. http://www.uwm.edu/~jpipes/wwwboard/messagesnew3/13489.html For example, we don’t know if by-products of fungus metabolism are or should be removed during treatment; we don’t know if or which treatment chemicals activate conidia. http://www.crest.org/efficiencv/strawbale-list-archive.old/1629.html A.4.5.2 Whether/If Last (1) It provides an encrypted filesystem that stores more than one piece of information in the same partition in such a way that it is computationally infeasible to prove what and if data exists. http://securitvportal.com/topnews/weeklv/tools20000922.html A.4.6 Those Involving a Combination (2) A.4.6.1 Adverbials First (2) The final draft must be approved by the teacher who will also decide when, where and whose work will be displayed. http://142.176.41.220/qees/handbook.html You may want to establish how, when and whose alerts are forwarded to avoid confusion and burnout. http://www.wfhesl.org/wwwboard/messages/427.html A.4.6.2 Determiner Sandwiches (0)

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Page 294 A.5 Copular Mixed-Wh Interrogatives (18) A.5.1 Those Involving Where (11) A.5.1.1 Where First (6) Where and what are these jobs and how do you get one? http://chat.careerpath.com/ Where and what is Newham Healthcare Trust http://www.newham-healthcare.org/links/wher.html So what IS the correct number (and what where and whose are the benchmarks from which it is derived)? http://www.beowulf.org/pipermail/beowulf/1999-October/007204.html The essence of career-self navigation is the ability to survive and succeed in your career by focusing on the work that needs to be done to get a new job, not on where or what you next job will be. http://www.acs.org/careers/ Re: Where or what is that gym? http://samson-power.com/samsonboard/messages/172.html But I don’t know where or who his parents were. http://genforum.genealogv.eom/ar/messages/7181.html A.5.1.2 Where Last (6) What and where is the Web? http://www.altorsvs.com/HTMLAltor/WebInfo.html Who and Where Are Our Children with Cochlear Implants? http://gri.gallaudet.edu/Cochlear/ASHA.1997/index.html Who, what, and where is Jeeves? http://www.taunton.com/knotsarch/messages/3527.htm

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Page 295 Today it stands ready—no matter what or where the emergency—to continue that tradition. http://www.accnorwalk.com/~coc612en/history.html One of the mistakes business owners can make is not understanding exactly who or where their customers are. http://www.dobusiness.com/web/services/market.htm Leo looked around; it was a bedroom but whose and where it was he didn’t know. http://www.paladar.com/fanware/room2/patel7.htm A.5.2 Those Involving When (0) A.5.2.1 When First (0) A.5.2.2 When Last (0) A.5.3 Those Involving How (1) A.5.3.1 How First (1) As long as I am distracted by how or what I should be, or how or what she should be, or how or what the marriage or relationship should be, I will not be able to see her, or myself, clearly, nor will I be able to see anything as it truly is. http://www.openmindopenheart.org/satsang/07092000.html A.5.3.2 how last (0) A.5.4 Those Involving Why (3) A.5.4.1 Why First (1) What, Why and Who are we? http://www.near.no/near/near.html

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Page 296 A.5.4.2 Why Last (2) What and Why is Computational Science? http://www.npac.syr.edu/users/gcf/cps615intro97/foilsepfocushtmldir/04… He also said he didn’t know who or why they are but they were good writers and funny. http://dispatches.azstarnet.com/zoe/girlfilm.htm A.5.5 Those Involving Whether/If (0) A.5.5.1 Whether/If first (0) A.5.5.2 Whether/If last (0) A.5.6 Those Involving a Combination (1) A.5.6.1 Adverbials First (1) I expect this will break some time in the next couple of years, but I have no idea when or how or what the new trend will be. http://www.writerswrite.com/journal/dec97/evans.htm A.5.6.2 Nominal Wh Sandwiches (0) A.5.6.3 Adverbials Last (0) A.5.7 Supplementary (2) In the case of Saul’s replacement, Samuel knows where and whose son the new king will be, but he does not know which one of the sons of Jesse. http://www.bible.org/docs/ot/books/1sa/deffin/1sam-13.htm Why and which one do I choose? http://mann.library.cornell.edu/reference/FAQ.html

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Page 297 Appendix B Questionnaire Items B.1 Items from Optional NP-Gap vs. Obligatory NP-Gap Questionnaires B.1.1 Experimental items B.1.1.1 Token Sets Token Set 1 How and what should we negotiate? How and what should we say? What and how should we negotiate? What and how should we say? Token Set 2 When and what can I eat? When and what can I do? What and when can I eat? What and when can I do? Token Set 3 How or what we think doesn’t matter. How or what we get doesn’t matter. What or how we think doesn’t matter. What or how we get doesn’t matter.

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Page 298 Token Set 4 We found out why and what she likes to cook. We found out why and what she likes to make. We found out what and why she likes to cook. We found out what and why she likes to make. Token Set 5 I always wonder when or what to tip someone. I always wonder when or what to ask for. I always wonder what or when to tip someone. I always wonder what or when to ask for. Token Set 6 I don’t know why or what he writes. I don’t know why or what he wants. I don’t know what or why he writes. I don’t know what or why he wants. Token Set 7 Do you know where or what she taught? Do you know where or what she found? Do you know what or where she taught? Do you know what or where she found? Token Set 8 They were asking where and what you want to build. They were asking where and what you want to take. They were asking what and where you want to build. They were asking what and where you want to take.

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Page 299 B.1.1.2 Preliminary Scripts Preliminary script 1 Token Set 1 How and what should we negotiate? Token Set 2 When and what can I eat? Token Set 3 What or how we get doesn’t matter. Token Set 4 We found out what and why she likes to make. Token Set 5 I always wonder what or when to tip someone. Token Set 6 I don’t know what or why he writes. Token Set 7 Do you know where or what she found? Token Set 8 They were asking where and what you want to take. Preliminary script 2 Token Set 1 How and what should we say? Token Set 2 When and what can I do? Token Set 3 How or what we think doesn’t matter. Token Set 4 We found out why and what she likes to cook. Token Set 5 I always wonder what or when to ask for. Token Set 6 I don’t know what or why he wants. Token Set 7 Do you know what or where she taught? Token Set 8 They were asking what and where you want to build. Preliminary script 3 Token Set 1 What and how should we negotiate? Token Set 2 What and when can I eat? Token Set 3 How or what we get doesn’t matter. Token Set 4 We found out why and what she likes to make. Token Set 5 I always wonder when or what to tip someone. Token Set 6 I don’t know why or what he writes. Token Set 7 Do you know what or where she found? Token Set 8 They were asking what and where you want to take.

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Preliminary script 4 Token Set 1 What and how should we say? Token Set 2 What and when can I do? Token Set 3 What or how we think doesn’t matter. Token Set 4 We found out what and why she likes to cook. Token Set 5 I always wonder when or what to ask for. Token Set 6 I don’t know why or what he wants. Token Set 7 Do you know where or what she taught? Token Set 8 They were asking where and what you want to build. B.1.2 Filler Items Items in boldface are intended to be completely grammatical. F1 It’s no big deal on my way to work to drop it off. F2 One the cats the carpet. F3 He is on trial for allegedly abusing a child. F4 The doctor will can’t see you now. F5 The structure wasn’t damaged, even though it directly was hit. F6 They don’t know or why safety device fail. F7 It happened on the third November, when Dorothy was turning 5. F8 What did you he? F9 You could me be prosecute belong this. F10 The movie was sold in time we it at the box office. F11 Was 2 years, and he’s still living sleeping here. F12 Nevermind what I’m wearing—what happened to your face? F13 When happen? F14 This is one my favorite movie of every time. F15 Who died made boss? F16 She start the job, and the be finish it. F17 Ceremony begin onto 7:00 sharp. F18 The garden never be the same. F19 Everyone knows that you can’t mix oil and water. F20 Please stop by if you’re in town. F21 It’s great that you’re finally graduating. F22 When and where the incident occur? F23 Marsha never answering to the phone during dinner. F24 I’m going this where you’ll never. F25 Will CDs go the way 8-track tape?

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Page 301 F26 You’ve so far, throw away, is not. F27 If and when she shows up, I will tell her happy birthday. F28 Why don’t we all just calm down and talk about this like adults? F29 If you done so already, you they immediately. F30 Nothing can stop them now. F31 All Sarah answered all the questions, she test. F32 Whatever you want is fine with me. B.2 Items from Plural-Noun vs. Obligatory NP-Gap Questionnaires B.2.1 Experimental Items B.2.1.1 Token sets Token Set 1 Do you know when or what reports need to be filed? Do you know when or what report needs to be filed? Do you know what or when reports need to be filed? Do you know what or when report needs to be filed? Token Set 2 Please explain how and what features will be altered. Please explain how and what feature will be altered. Please explain what and how features will be altered. Please explain what and how feature will be altered. Token Set 3 The public has no idea how or what products are created here. The public has no idea how or what product is created here. The public has no idea what or how products are created here. The public has no idea what or how product is created here. Token Set 4 I don’t care where or what fossils are discovered. I don’t care where or what fossil is discovered. I don’t care what or where fossils are discovered. I don’t care what or where fossil is discovered.

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Page 302 Token Set 5 Let’s find out where and what items have been disturbed. Let’s find out where and what item has been disturbed. Let’s find out what and where items have been disturbed. Let’s find out what and where item has been disturbed. Token Set 6 Do they know why and what signals are being sent? Do they know why and what signal is being sent? Do they know what and why signals are being sent? Do they know what and why signal is being sent? Token Set 7 Our agent will report on when and what activities were being conducted. Our agent will report on when and what activity was being conducted. Our agent will report on what and when activities were being conducted. Our agent will report on what and when activity was being conducted. Token Set 8 She can’t tell me why or what jobs are done by any employee. She can’t tell me why or what job is done by any employee. She can’t tell me what or why jobs are done by any employee. She can’t tell me what or why job is done by any employee. B.2.1.2 Preliminary Scripts Preliminary script 1 Token Set 1 Do you know when or what reports need to be filed? Token Set 2 Please explain how and what features will be altered. Token Set 3 The public has no idea what or how product is created here. Token Set 4 I don’t care what or where fossil is discovered. Token Set 5 Let’s find out what and where items have been disturbed. Token Set 6 Do they know what and why signals are being sent? Token Set 7 Our agent will report on when and what activity was being conducted. Token Set 8 She can’t tell me why or what job is done by any employee.

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Set Set Set Set Set Set Set Set

1 2 3 4 5 6 7 8

Token Token Token Token Token Token Token Token

Set Set Set Set Set Set Set Set

1 2 3 4 5 6 7 8

Token Token Token Token Token Token Token Token

Set Set Set Set Set Set Set Set

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Preliminary script 2 Do you know when or what report needs to be filed? Please explain how and what feature will be altered. The public has no idea how or what products are created here. I don’t care where or what fossils are discovered. Let’s find out what and where item has been disturbed. Do they know what and why signal is being sent? Our agent will report on what and when activities were being conducted. She can’t tell me what or why jobs are done by any employee. Preliminary script 3 Do you know what or when reports need to be filed? Please explain what and how features will be altered. The public has no idea how or what product is created here. I don’t care where or what fossil is discovered. Let’s find out where and what items have been disturbed. Do they know why and what signals are being sent? Our agent will report on what and when activity was being conducted. She can’t tell me what or why job is done by any employee. Preliminary script 4 Do you know what or when report needs to be filed? Please explain what and how feature will be altered. The public has no idea what or how products are created here. I don’t care what or where fossils are discovered. Let’s find out where and what item has been disturbed. Do they know why and what signal is being sent? Our agent will report on when and what activities were being conducted. She can’t tell me why or what jobs are done by any employee.

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Page 304 B.2.2 Filler Items Items in boldface are intended to be completely grammatical. F1 The structure wasn’t damaged, even though it directly was hit. F2 Cats and dogs are stereotyped as never got along with each other. F3 Bobby won’t stop kicking me! F4 If and when she shows up, I will tell her happy birthday. F5 That’s all hell broke loose. F6 Why you the siren hear, duck! F7 What’s the last thing you remember can? F8 Who died made boss? F9 Nevermind what I’m wearing—what happened to your face? F10 Sound crazy, but I’m believe that LaToya and Michael same person. F11 It’s great that you’re finally graduating. F12 I’m going this where you’ll never. F13 Who what to for Jenna? F14 It was that I discovered forgotten my wallet. F15 We encountered the creature at a depth of. F16 That’s already being care of. F17 I don’t care who it. F18 Sometimes I get the feeling that someone is watching me. F19 We’re ready for the check now. F20 A sudden, the host walked in. F21 Everyone knows that you can’t mix oil and water. F22 Who or is making that noise? F23 All I wanting do cheer up you. F24 When Tom woke up, the were gone. F25 It’s raining since we got here. F26 He is on trial for allegedly abusing a child. F27 Your friends have been arrested for drunk driving. F28 Tell her me where and you intend to this film. F29 I when remember somebody’s my name. F30 This medicine is not intended for internal use. F31 I don’t unicorns, and you either. F32 Penelope knows where find the best mushrooms.

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Page 305 Bibliography ADES, ANTHONY E., AND MARK STEEDMAN. 1982. On the order of words. Linguistics and Philosophy 4. 517–58. BACH, EMMON. 1981. In defense of passive. Linguistics and Philosophy 4.297–341. BARKER, CHRIS. 2000. WH2. Email to the author. 21 Dec. 2000. BAYER, JOSEF. 1988. Fortscritte der Syntaxtheorie. Linguistiche Berichte 117.410–26. BAYER, SAMUEL. 1996. The coordination of unlike categories. Language 72.579–616. BECHHOFER, ROBIN. 1976. Reduction in conjoined wh-questions. Harvard studies in syntax and semantics 2, ed. by Jorge Hankamer, and Judith Aissen, 68–120. Cambridge, MA: Harvard University. BOLINGER, DWIGHT. 1978. Asking more than one thing at a time. Questions, ed. by Henry Hiz, 87–106. Boston: Reidel. BRESNAN, JOAN, AND JANE GRIMSHAW. 1978. The syntax of free relatives in English. Linguistic Inquiry 9.331–91. CALCAGNO, MICHAEL. 1995. Interpreting lexical rules. Proceedings of the ACQUILEX II workshop on lexical rules. Cambridge. CALCAGNO, MICHAEL, AND CARL POLLARD. 1995. Lexical rules in HPSG: What are they? Columbus: The Ohio State University, ms. CARPENTER, BOB. 1992. Lexical and unary rules in categorial grammar. Formal grammar: Theory and implementation, ed. by Robert Levine, 168–24. New York: Oxford

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Page 306 University Press. http://www.colloquial.com/carp/PubIications7cglex.ps, draft of 27 Jul. 1995, downloaded 18 Feb. 2000. CARPENTER, BOB. 1997. Type-logical semantics. Cambridge, MA: The MIT Press. CHOMSKY, NOAM. 1957. Syntactic structures. The Hague: Mouton. COWART, WAYNE. 1997. Experimental syntax. London: SAGE Publications. DANIELS, MICHAEL W. 2002. On a type-based treatment of feature neutrality and the coordination of unlikes. In van Eynde, et al., 137–47. DOWTY, DAVID. 1979. Word meaning and Montague grammar. (Synthese Language Library 7.) Dordrecht: Reidel. ——. 1982. Grammatical relations and Montague grammar. The nature of syntactic representation (Synthese language library 15), ed. by Pauline Jacobson and Geoffrey K.Pullum, 79–130. Dordrecht: Reidel. ——. 1988. Type-raising, functional composition, and non-constituent coordination. Categorial grammars and natural language structures (Studies in linguistics and philosophy 32), ed. by Richard Oehrle, Emmon Bach, and Deirdre Wheeler, 153–97. Dordrecht: Reidel. ——. 1989. On the semantic content of the notion ‘thematic role.’ Properties, types, and meaning (Studies in linguistics and philosophy 38–39),ed. by Gennaro Chierchia, Barbara Partee, and Raymond Turner, 69–129. Boston: Reidel. ——. 1991. Thematic proto-roles and argument selection. Language 67.547–619. ——. 1997. Non-constituent coordination, wrapping, and multi-modal categorial grammars: syntactic form as logical form. Structures and norms in science, ed. by Maria Luisa Dalla Chiara et al., 347–68. ftp://ling.ohiostate.edu/pub/dowtv/nccwmmcg.ps.gz. downloaded 23 Oct. 2001. ——. 2000. The garden swarms with bees’ and the fallacy of ‘argument alternation.’ In Ravin and Leacock (2000b), 111–28. DOWTY, DAVID R., ROBERT E.WALL, AND STANLEY PETERS 1981. Introduction to Montague semantics. (Studies in Linguistics and Philosophy 11.) Dordrecht: Reidel.

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Page 307 DYLA, STEFAN. 1984. Across-the-board dependencies and case in Polish. Linguistic Inquiry 15.701–5. EISENBERG, PETER. 1973. A note on identity of constituents. Linguistic Inquiry 4.417–20. FELLBAUM, CHRISTIANE. 2000. Autotroponomy. In Ravin and Leacock (2000b), 52–67. FILLMORE, CHARLES J. 1986. Pragmatically controlled zero anaphora. Berkeley Linguistics Society 12, ed. by Vassiliki Nikiforidou, Mary Van Clay, Mary Niepokuj, and Deborah Feder, 95–107. FRANKS, STEVEN. 1993. On parallelism in across-the-board dependencies. Linguistic Inquiry 24.509–28. GEACH, PETER T. 1962. Reference and generality. Ithaca, NY: Cornell University Press. GENTZEN, GERHARD. 1934. Untersuchungen über das logische Schliessen. Mathematische zeitschrift 39. 176–210, 405–431. GIANNAKIDOU, ANASTASIA, AND JASON MERCHANT. 1998. Reverse sluicing in English and Greek. The Linguistic Review 15.233–56. GINZBURG, JONATHAN, AND IVAN A.SAG. 2000. Interrogative investigations: The form, meaning, and use of English interrogatives. (CSLI lecture notes 123.) Stanford, CA: CSLI. GROOS, ANNEKE, AND HENK VAN RIEMSDIJK. 1981. Matching effect in free relatives: A parameter of core grammar. Theory of markedness in generative grammar (Proceedings of the 1979 GLOW conference), ed. by Adriana Belletti, Luciana Brandi, and Luigi Rizzi, 171–216. Pisa: Scuola Normale Superiore. GROENENDIJK, JEROEN, AND MARTIN STOKHOF. 1997. Questions. In Van Benthem and Ter Meulen, 1055–124. HENDRIKS, PETRA. 1995. Comparatives and categorial grammar. Groningen: University of Groningen dissertation. HEYLEN, DIRK. 1996. On the proper use of booleans in categorial logic. Formal grammar 2, ed. by Geert-Jan Kruijff, Glyn Morrill, and Richard Oehrle, 71–84. Prague: Eighth European Summer School in Logic, Language, and Information.

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Page 308 http://wwwhome.cs.utwente.nl/~heylen/Publicaties/articles.html dowloaded 29 Aug. 2000. ——. 1997. Underspecification in type-logical grammars. http://wwwhome.cs.utwente.nl/~heylen/Publicaties/articles.html, dowloaded 29 Aug. 2000. ——. 1999. Types and sorts: resource logic for feature checking. Utrecht: Universityof Utrecht dissertation. http://wwwhome.cs.utwente.nl/~hevlen/Publicaties/articles.html, dowloaded 29 Aug. 2000. HINRICHS, ERHARD. 1985. A compositional theory of Aktionsarten and NP reference in English. Columbus: Ohio State University dissertation. HORN, LAURENCE R. 1984. Toward a new taxonomy for pragmatic inference: Q-based and R-based implicature. Meaning, form, and use in context: Linguistic applications (GURT ‘84), ed. by Deborah Schiffrin, 11–43. Washington: Georgetown University Press. HORN, LAURENCE R. 1989. A natural history of negation. Chicago: The University of Chicago Press. HUDDLESTON, RODNEY. 1984. Introduction to the grammar of English. Cambridge: Cambridge University Press. HUKARI, THOMAS.E., AND ROBERT D.LEVINE. 1995. Adjunct extraction. Journal of Linguistics 31.195– 226. INGRIA, ROBERT J.P. 1990. The limits of underspecification. Association for Computational Linguistics 29,194–204. JACKENDOFF, RAY. 1975. Morphological and semantic regularities in the lexicon. Language 51.639–71. JOHNSON,MARK, AND SAM BAYER. 1995. Features and agreement in Lambek categorial grammar. Formal grammar 1, ed. by Glyn Morrill and Richard Oehrle, 123–37. Barcelona: Seventh European summer school in logic, language and information. KANAZAWA, MAKOTO. 1992. The Lambek calculus enriched with additional connectives. Journal of Logic, Language and Information 1.141–71.

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Page 309 KASPER, ROBERT T. (forthcoming). The semantics of recursive modification. To appear in Journal of Linguistics. KAYNE, RICHARD S. 1975. French syntax: The transformational cycle. Cambridge, MA: MIT Press. KEHLER, ANDREW. 2002. Coherence, reference, and the theory of grammar. Stanford, CA: CSLI. KEMPSON, RUTH M. 1977. Semantic theory. Cambridge: Cambridge University Press. LAKOFF, GEORGE. 1986. Frame semantic control of the coordinate structure constraint. Chicago Linguistic Society 22 Part 2, ed. by Anne M.Farley, Peter Farley, and Karl-ErikMcCullough, 152–67. LAMBEK, JOACHIM. 1958. The mathematics of sentence structure. American Mathematical Monthly 65.154–70. ——. 1961. On the calculus of syntactic types. Structure of language and its mathematical aspects (Proceedings of symposia in applied mathematics), ed. by Roman Jakobson, 166–178. Providence, RI: American Mathematical Society. LARSON, RICHARD K. 1983. Restrictive modification: relative clauses and adverbs. Madison: University of Wisconsin dissertation. ——. 1985. Bare-NP adverbs. Linguistic Inquiry 16.595–621. LASCARIDES, ALEX, ANN COPESTAKE, AND TED BRISCOE. 1996. Ambiguity and coherence. Journal of Semantics 13.41–65. http://www.cogsci.ed.ac.uk/~alex/papers/zcugma.ps, draft of 12 Dec. 1999, downloaded 29 Oct. 2000. LEVIN, BETH. 1993. English verb classes and alternations. Chicago: University of Chicago Press. LEVINE, ROBERT D., THOMAS E.HUKARI, AND MICHAEL CALCAGNO. 2001. Parasitic gaps in English: some overlooked cases and their theoretical implications. Parasitic gaps, ed. by Peter W.Culicover, and Paul M.Postal, 181–222. Cambridge, MA: MIT Press. LEVY, ROGER, AND CARL POLLARD. 2002. Coordination and neutralization in HPSG. In van Eynde, et al., 221–34.

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Page 310 LINK, GODEHARD. 1983. The logical analysis of plurals and mass terms: A lattice-theoretical approach. Meaning, use, and interpretation of language, ed. by Rainer Bäuerle, Christoph Schwarze, and Arnim von Stechow, 302–23. Berlin: de Gruyter. McCAWLEY, JAMES D. 1988. Adverbial NPs: bare or clad in see-through clothes? Language 64.583–9. McCONELL-GINET, SALLY 1982. Adverbs and logical form: A linguistically realistic theory. Language 58. 144–84. MEURERS, DETMAR. 1995. Towards a semantics for lexical rules as used in HPSG. Proceedings of the ACQUILEX II workshop on lexical rules. Cambridge. ——. 1999. Lexical generalizations in the syntax of German non-finite constructions. Tübingen: University of Tübingen disseertation. Appeared 2000 as Volume 145 in Arbeitspapiere des SFB 340. http://ling.osu.edu/~dm/papers/diss.html http://w210.ub.uni-tuebingen.de/dbt/volitexte/2000/l18. dowloaded May 2000. MINEUR, ANNE-MARIE, AND PAUL BUITELAAR. 1995. A compositional treatment of polysemous arguments in categorial grammar. Semantic ambiguity and underspecification (CSLI lecture notes 55), ed. by Kees van Deemter and Stanley Peters, 125–43. Stanford, CA: CSLI. MOORTGAT, MICHAEL. 1988. Categorial investigations: logical and linguistic aspects of the Lambek Calculus. (Groningen-Amsterdam Studies in Semantics 9.) Providence, RI: Foris Publications. ——. 1996. Generalized quantifiers and discontinuous type constructors. Discontinuous constituency (Natural language processing 6), ed. by Harry Bunt, and Arthur Van Horck, 181–208. New York: Mouton de Gruyter. ——. 1997. Categorial type logics. In Van Benthem and Ter Meulen, 93–177. MOORTGAT, MICHAEL, AND RICHARD OEHRLE. 1994. Adjacency, dependency and order. Ninth Amsterdam Colloquium, ed. by Paul Dekker and Martin Stokhof, 447–66. Amsterdam: Institute for Logic, Language and Information. MORRILL, GLYN. 1994. Type logical grammar: categorial logic of signs. Boston: Kluwer Academic Publishers. PARTEE, BARBARA H. 1987. Noun phrase interpretation and type-shifting principles. Studies in discourse representation theory and the theory of generalized quantifiers

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Page 312 VAN BENTHEM, JOHAN. 1988. The semantics of variety in categorial grammar. Categorial grammar, ed. by Wojciech Buszkowski, Witold Marciszewski, and Johan van Benthem, 37–55. Amsterdam: Benjamins. VAN BENTHEM, JOHAN, AND ALICE TER MEULEN, eds. 1997. Handbook of logic and language. Cambridge, MA: MIT Press. VAN EYNDE, FRANK, LARS HELLAN, AND DOROTHEE BERMAN, eds. 2002. 8th International Conference on Head-Driven Phrase Structure Grammar. Stanford: CSLI. VAN NOORD, GERTJAN, AND GOSSE BOUMA. 1994. The scope of adjuncts and the processing of lexical rules. 15th conference on computational linguistics (COLING). Kyoto, Japan. WHITMAN, NEAL. 2002. A categorial treatment of adverbial nouns. Journal of Linguistics 38.561–97. WILLIAMS, EDWIN. 1981. Transformationless grammar. Linguistic Inquiry 12.247–89. WILLIAMS, EDWIN. 1983. Semantic vs. syntactic categories. Linguistics and Philosophy 6.423–46. ZAENEN, ANNIE, AND LAURI KARTTUNEN. 1984. Morphological non-distinctiveness and coordination. Eastern States Conference on Linguistics 1, ed. by Gloria Alvarez, Belinda Brodie and Terry McCoy, 309– 20. ZWICKY, ARNOLD M., AND JERROLD M.SADOCK. 1975. Ambiguity tests and how to fail them. Syntax and Semantics 4, ed. by John P.Kimball, 1–36. New York: Academic Press.

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Page 313 Index Across-the-Board constraint, 143 Ades and Steedman 1982, 204 Adverbial nouns, 5, 235–63 ability to head non -wh adverbial relative clauses, 249–51 type-logical analysis, 249–50 ability to project adverbial NPs, 240–48 type-logical analysis, 242–46 sample derivation, 245–46 and category neutrality, 251, 252, 256–63 lexical rule, 263 sample derivation, 256–61 definition, 235 feature-passing analysis of, 240–42 in wh phrases, 248 interaction of properties of, 251–55 lexical rules, 253–55 necessary categories, 251–53 previous analyses of, 238–40 properties of, 235–37 Adverbial NPs, 128 definition, 235 Ambiguity, 3, 4, 5, 13, 14, 126, 140, 163, 168, 173, 183, 184, 198, 199, 200, 208 definition, 7 feature ambiguity, 14 lexical, 8, 19 phonological resolution of, 15 tests for, 8–12 appeals to semantic differentiae, 12 coordination tests, 8–12 crossed-understandings test, 9–10 shortcomings of, 11–12 zeugma test, 10–12 vs. category neutrality, 59–63, 71, 99, 208, 223, 226, 267 vs. vagueness, 8–12 Antecedent Strengthening, 49, 95 plus Type Raising, 57–59, 129, 190 Anti-Pun Ordinance, 22 Argument neutrality. See Feature neutrality: argument neutrality Associative Lambek Calculus. See Type-logical grammar: syntax Attestations, 73, 74, 77, 79, 97, 103, 104, 121, 150, 152, 153, 160, 164, 172, 182, 186, 202, 212, 214, 215, 236, 269–96 Bach 1981, 155 Bare-NP adverbs, 235, See Adverbial NPs Barker 2000, 77 Bayer 1988, 18 Bayer 1996, 15, 17, 18, 19, 22, 23, 49, 53, 61, 63, 125, 186, 194, 228, 230, 265 Bechhofer 1976, 126, 128, 138, 142

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Page 314 Being John Malkovich. See Predicative phrases: Malkovich predicative Believe, 150 Bolinger 1978, 128, 138 Break, 171–72 Bresnan and Grimshaw 1978, 202 Brew, Chris, 121 Bryson, Bill, 182 Calcagno 1995, 66 Calcagno and Pollard 1995, 66 Carpenter 1992, 204–6 Carpenter 1997, 22, 25, 38, 40, 48, 52, 59, 68, 70, 91, 132, 187, 192, 243, 247 Categorial grammar comparison of combinatory and type-logical, 25–28 definition, 26 Lambek, 26, See Type-logical grammar Category neutrality, 3–5, 13, 28, 48, 54, 59, 68, 71, 91, 102, 104, 107, 109, 123, 127, 186, 195, 228, 230, 234, 265 and adverbial nouns, 251, 252, 256–63 and be, 190–94 and intransitives with understood object, 73, 95, 125 and lexical rules, 65, 99 and NPs predicative and quantificational, 216–22 predicative and referential, 212–16 referential and quantificational, 209–11 and plural and mass nouns, 74, 104, 112, 116 and PPs, 199–203 and predicative and attributive APs, 196–99 and verbal argument alternations, 148–73, 181, 182 definition, 19 in coordinated- wh interrogatives, 120 in Generative Lexicon theory, 266 in the literature, 21–23 upstairs-downstairs and adverbial nouns, 237, 252 and free relatives, 202 vs. ambiguity, 59–63, 71, 99, 208, 223, 226, 267 vs. polysemy, 20 vs. vagueness, 19–20 Chomsky 1957, 128 Coherence relations, 143 Conditional Proof, 26 Conjunctive categories, 47–51, See Category neutrality and feature neutrality, 49–51 incompleteness of conjunctive and disjunctive constructors, 54–57 Conversational implicature. See Q and R implicature Coordinate Constituent Constraint, 129 Coordination as synonym for coordination of unlikes, 17 Boolean vs. non-Boolean, 68 of interrogatives. See Interrogatives: conjoined- wh of unlikes, 3, 4, 14, 49, 128, 267, See Category neutrality: and be, See Category neutrality: and verbal argument alternations and disjunctive categories, 53–54 as synonym for verb neutrality, 17 of verbal dependents, 125–84 adjunct with adjunct, 130–48 sample derivation, 133, 134, 135

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Page 315 adjunct with complement, 163–73 complement with complement, 148–63 of wh elements. See Interrogatives: mixed- wh, See Interrogatives: conjoined- wh semantics of, 68–69 Cowart 1997, 83 Curry, 36, 119 Cut elimination, 37 Daniels 2002, 16, 17, 51 Diathesis alternations. See Verbal argument alternations Disjunctive categories, 51–54 and coordination of unlikes, 53–54 elimination of disjunction constructor, 56–57 incompleteness of disjunction and conjunction constructors, 54–57 Dowty 1979, 65 Dowty 1982, 153, 158 Dowty 1988, 106 Dowty 1989, 154 Dowty 1991, 154 Dowty 1997, 155, 178 Dowty 2000, 178 Dowty et al. 1981, 224 Dyla 1984, 15

Eat, 164–66 Eisenberg 1973, 17 Feature indeterminacy, 16, See Feature neutrality: argument neutrality Feature neutrality, 14–19, 51 and conjunctive categories, 49–51 argument neutrality, 14, 15–16 definition, 14 neutrality without coordination, 14, 17–18 upstairs-downstairs, 18, See Feature neutrality: neutrality without coordination verb neutrality, 14, 16–17 Fellbaum 2000, 13 Fillmore 1986, 102, 166 Fisher, Wild Man, 202 Forget, 150 Frame semantics, 29–32 definition, 30 Franks 1993, 15 Free relatives, 17–18, 202, 215–16 Frighten, 150, 170–71 Function Composition, 27, 34, 39, 44, 45 Functional Application, 26 as analog of Modus Ponens, 26 Functor neutralization, 17, See Feature neutrality: verb neutrality Geach 1962, 230 Generality, 3, See Vagueness Generalized scoping constructor, 242–44 Gentzen 1934, 37 Get, 172 Giannakidou and Merchant 1998, 74, 81, 102, 103 Ginzburg and Sag 2000, 139 Give, 158–61 Groenendijk and Stokhof 1997, 92 Groos and van Riemsdijk 1981, 17

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Hendriks 1995, 21, 53, 54, 188 Heylen 1996, 21, 125, 230 Heylen 1997, 19, 265 Heylen 1999, 19, 21, 50, 125, 230, 265 Hinrichs 1985, 132 Homonymy, 8, See Ambiguity Homophony, 8, See Ambiguity Horn 1984, 140, 141 Horn 1989, 140 HPSG, 27, 51, 65, 67, 205, 206, 226, 240 Huddleston 1984, 231 Hukari and Levine 1995, 76

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Page 316 Indeterminacy, 8, See Vagueness across features, 16, See Feature neutrality: argument neutrality Ingria 1990, 14, 15, 17 Interrogatives conjoined- wh, 91–94, 129, 138–40, 156, 162 sample derivation, 93–94 semantics, 91–92 mixed- wh. See Mixed- wh interrogatives multiple- wh, 139 types for, 91 Jackendoff 1975, 63 Johnson and Bayer 1995, 19, 50 Kanazawa 1992, 49, 50, 53 Kasper (forthcoming), 205, 206, 239– 40 Kayne 1975, 15 Kehler 2002, 143 Kempson 1977, 8 Lakoff 1986, 143 Lambek 1958, 37, 46 Lambek 1961, 27 Larson 1983, 235, 239 Larson 1985, 235, 236, 238, 251 Lascarides et al. 1999, 10, 11 Law of Coordination of Likes, 128 Levin 1993, 99, 102, 103, 163, 164, 166 Levine et al. 2001, 16, 18 Levy and Pollard 2002, 16, 17, 51 Lexical redundancy rules, 64, See Lexical rules Lexical rules, 63–67 and category neutrality, 100 conversion, 64 for adverbial nouns, 253–55, 263 for attributive and adverbial PPs, 208 for predicative and adverbial PPs, 208 for predicative and attributive APs and PPs, 203–8 for predicative and quantificational NPs, 223–26 for predicative and referential NPs, 222–23 for understood object alternation, 100 in HPSG, 65 description-level, 66 meta-level, 66, 67 zero-derivation, 64 Lexicon, 59–67 ambiguity vs. category neutrality in. See Ambiguity: vs. category neutrality definition, 60 lexical rules, 63–67 Lifting, 27, See Type Raising Link 1983, 225 Load, 104, 161–63 Locative alternation, 161–63 McCawley 1988, 235, 239 McConnell-Ginet 1982, 13, 76 McLean, Don, 237 Meurers 1995, 65 Meurers 1999, 65, 67

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Mineur and Buitelaar 1995, 266 Mixed- wh interrogatives, 4, 73–124, 158, 160, 166, 167, 168, 170, 171, 172 copular, 186 attestations, 294–96 definition, 79 definition, 73 missing NP-gap attestations, 284–87 definition, 78 obligatory NP-gap attestations, 276–84 definition, 78 optional NP-gap, 74, 75–104 attestations, 269–76

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Page 317 corpus search for, 77–80 definition, 75–77 IQ vs. DQ readings, 100–102 lexical rule, 100 psycholinguistic data, 83–90 reverse sluicing analysis, 81–83 sample derivations, 94–99 type-logical analysis, 91–102 plural-noun, 74, 104–20 attestations, 288–93 corpus search for, 105–10 definition, 104 IQ s. DQ readings, 119–20 psycholinguistic data, 110–16 reverse sluicing analysis, 107–10 sample derivation, 116–19 type-logical analysis, 116–20 without lexical neutrality, 120–23 sample derivation, 121–23 Modus Ponens, 26 Moortgat 1988, 27 Moortgat 1996, 242 Moortgat 1997, 25, 37 Moortgat and Oehrle 1994, 247 Morrill 1994, 21, 48, 51, 52, 53, 55– 56, 61, 188, 243 Neutrality, 3, 4, 15, 18 and coordination of unlikes. See Coordination of unlikes argument neutrality. See Feature neutrality: argument neutrality as synonym for vagueness, 8 category neutrality. See Category neutrality feature neutrality. See Feature neutrality upstairs-downstairs, 18, See Feature neutrality: neutrality without coordination, See Category neutrality: upstairs-downstairs verb neutrality. See Feature neutrality: verb neutrality without coordination. See Feature neutrality: neutrality without coordination Neutralizable polyvalency, 17, See Feature neutrality: verb neutrality Neutralization. See Neutrality Neutralization under phonological identity, 15, See Feature neutrality Notice, 166–67 Overspecification, 19 Parasitic gaps, 18, 263 Partee 1987, 22, 186, 213, 223–25, 226, 228, 230, 233 Pollard and Sag 1994, 22, 66, 226 Polysemy, 4, 13 definition, 7 vs. category neutrality, 20 Powers, Tim, 218 Prawitz 1965, 37 Predicative phrases, 5 and category for be, 187–95 and free relatives, 202, 215–16 argument against category Pr for NPs, 229 arguments for NPs as properties, 226–34 absence of quantificational readings in predicative positions, 227–28 assumption that conjuncts must have like categories, 230 claim of more accurate semantics, 230 color-denoting words, 232–34 equative be, 232

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facts about pseudoclefts, 231–32 nonpassivizability of predicative sentences, 230–31 categories for, 187–95 involving APs or PPs, 196–209 attributive and adverbial, 203 lexical rules, 208

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Page 318 predicative and adverbial, 200–202 lexical rules, 208 predicative and attributive, 199–200 lexical rules, 203–8 involving NPs, 209–26 predicative and quantificational, 216–22, 216–22 lexical rules, 223–26 sample derivation, 217–18, 219, 220, 221 predicative and referential, 212–16 lexical rules, 222–23 sample derivation, 212–13 referential and quantificational, 209–11 sample derivation, 210–11 Malkovich predicative, 213–14 with category neutrality for be, 190–94 sample derivation, 190–92, 193–94 without category neutrality for be, 194–95 Proto-role entailments, 154, 160, 162, 169, 170, 171–72, 173 Pullum and Zwicky 1986, 8, 14, 15, 17, 18, 21, 22, 61, 80, 266 Pustejovsky 1995, 13 Q and R implicature and verbal dependent coordination adjunct with adjunct, 140–48 functionally different, 141–45 functionally similar, 145–48 adjunct with complement, 166 complement with complement, 156–57 Q and R Principles defined, 141 q category constructor. See Generalized scoping constructor Ravin and Leacock 2000b, 13 Recursive modification and adverbial nouns, 239–40 and predicative and attributive APs, 205–7 Remember, 150 Reverse sluicing, 81–83, 107–10 Rubin, Trudy, 121 Rules of proof, 27 Rules of use, 27 Rylant, Cynthia, 141, 182 Sadler and Arnold 1994, 205 Sag et al. 1985, 21, 22, 23, 126, 129, 149, 185, 226, 265 Say, 149 Schachter 1977, 104, 125, 126, 128, 129, 138, 142 Scoping constructor, 69–71 Seem, 181 Serve, 155–57 Severe, Sal, 182 Shave, 168–70 Steedman 1994, 27 Steedman 1999, 27 Subformula property, 37 Syncretism, 16, See Feature neutrality: argument neutrality Szamosi 1976, 18 Type Raising, 27, 34, 39, 44, 45 plus Antecedent Strengthening, 57–59, 129, 190 Type-logical grammar categories. See Type-logical grammar: syntax: categories lexicon. See Lexicon multimodal

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and adverbial nouns, 246–48 and wrapping, 155, 174–78 semantics, 39–46 Gentzen sequent presentation, 43–44 natural deduction presentation, 45–46 terms, 41–42 constants, 41

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Page 319 functional abstractions, 41 ordered pairs, 41 variable naming conventions, 42 variables, 41 types, 40–41 functional, 40 product, 40 syntax, 28–39 categories, 28–32 conjunctive. See Conjunctive categories disjunctive. See Disjunctive categories functor, 28 interpretation of. See Frame semantics product, 29 Gentzen sequent presentation, 32–37 Cut elimination, 37 implicit associativity, 32 natural deduction presentation, 37–39 UnCurry, 36, 119 Unlike coordination. See Coordination: of unlikes Upstairs-downstairs neutrality. See Category neutrality: upstairs-downstairs, See Feature neutrality: upstairs-downstairs Vagueness, 3, 4, 8, 13, 14 definition, 7 vs. ambiguity, 8–12 vs. category neutrality, 19–20 Valence alternations. See Verbal argument alternations van Benthem 1988, 43 van Noord and Bouma 1994, 66 Verb neutrality. See Feature neutrality: verb neutrality Verbal argument alternations, 148–73 causatives, 171–73 dative, 103, 155–57 middle, 170–71 understood definite object, 102, 166–67 understood indefinite object, 76, 99, 164–66 understood reflexive object, 103, 168–70 Verbal dependent coordination, 125– 84 adjunct with adjunct, 130–48 semantic effects on, 131–35 adjunct with complement, 163–73 contrasting lexical entailments, 168–73 break, 171–72 frighten, 170–71 get, 172 shave, 168–70 walk, 172–73 identical lexical entailments, 164–68 eat, 164–66 notice, 166–67 and Q and R implicature. See Q and R implicature: and verbal dependent coordination complement with complement, 148–63 contrasting lexical entailments, 153–63 role rearrangement, 158–63 give, 158–61 sample derivation, 174–78 load, 161–63 role replacement, 155–58 serve, 155–57 write, 157–58 identical lexical entailments, 149–53 believe, 150

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forget, 150 frighten, 150 remember, 150 say, 149 want, 151–53

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Page 320 sample derivation, 174–78 involving wh elements. See Interrogatives: mixed- wh, See Interrogatives: conjoined- wh Vonnegut, Kurt, Jr., 215

Walk, 172–73 Want, 104, 151–53 Wasow’s Generalization, 80 Whitman 2002, 251 Williams 1981, 128 Williams 1983, 186, 194, 226, 227, 230–34 Wrapping, 30, 159 and multimodal type-logical grammar, 155, 174–78 Write, 157–58 Zaenen and Karttunen 1984, 14, 15, 22 Zwicky and Sadock 1975, 8, 9, 12, 14

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