ANAPHORA AND TYPE LOGICAL GRAMMAR

Transcription

1 ANAPHORA AND TYPE LOGICAL GRAMMAR

2 TRENDS IN LOGIC Studia Logica Library VOLUME 24 Managing Editor Ryszard Wójcicki, Institute of Philosophy and Sociology, Polish Academy of Sciences, Warsaw, Poland Editors Vincent F. Hendricks, Department of Philosophy and Science Studies, Roskilde University, Denmark Daniele Mundici, Department of Mathematics Ulisse Dini, University of Florence, Italy Ewa Or owska, National Institute of Telecommunications, Warsaw, Poland Krister Segerberg, Department of Philosophy, Uppsala University, Sweden Heinrich Wansing, Institute of Philosophy, Dresden University of Technology, Germany SCOPE OF THE SERIES Trends in Logic is a bookseries covering essentially the same area as the journal Studia Logica that is, contemporary formal logic and its applications and relations to other disciplines. These include artificial intelligence, informatics, cognitive science, philosophy of science, and the philosophy of language. However, this list is not exhaustive, moreover, the range of applications, comparisons and sources of inspiration is open and evolves over time. Volume Editor Heinrich Wansing The titles published in this series are listed at the end of this volume.

3 ANAPHORA AND TYPE LOGICAL GRAMMAR by GERHARD JÄGER University of Bielefeld, Germany

4 A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN (HB) ISBN (HB) ISBN (e-book) ISBN (e-book) Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. Printed on acid-free paper All Rights Reserved 2005 Springer No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed in the Netherlands.

5 Contents List of Tables vii Preface ix Acknowledgments xiii 1. TYPE LOGICAL GRAMMAR: THE FRAMEWORK 1 1 Basic Categorial Grammar 1 2 Combinators and Type Logical Grammar 17 3 Historical and Bibliographical Remarks THE PROBLEM OF ANAPHORA 69 1 Anaphora and Semantic Resource Sensitivity 69 2 Variables in TLG 72 3 Previous Categorial Approaches to Anaphora 76 4 Summary LAMBEK CALCULUS WITH LIMITED CONTRACTION The Agenda Contraction? The Logic LLC Relation to Jacobson s System PRONOUNS AND QUANTIFICATION Basic Cases Binding by wh-operators Binding by Quantifiers Weak Crossover Precedence Versus c-command 169 v

6 vi ANAPHORA AND TYPE LOGICAL GRAMMAR 6 Backward Binding and Reconstruction VERB PHRASE ELLIPSIS Introduction VPE: The Basic Idea Interaction with Pronominal Anaphora Interaction of VPE and Quantification VPE and Polymorphism Parallelism Versus Source Ambiguity INDEFINITES Introduction Dekker s Predicate Logic with Anaphora Bringing PLA into TLG Donkey sentences Indefinites and Scope Sluicing Summary and Desiderata 269 References 273 Index 283

7 List of Tables 1.1 The structural hierarchy Substructural Curry-Howard correspondences Categorial approaches to anaphora 118 vii

8 Preface This book discusses how Type Logical Grammar can be modified in such a way that a systematic treatment of anaphora phenomena becomes possible without giving up the general architecture of this framework. By Type Logical Grammar, I mean the version of Categorial Grammar that arose out of the work of Lambek, 1958 and Lambek, There Categorial types are analyzed as formulae of a logical calculus. In particular, the Categorial slashes are interpreted as forms of constructive implication in the sense of Intuitionistic Logic. Such a theory of grammar is per se attractive for a formal linguist who is interested in the interplay between formal logic and the structure of language. What makes Lambek style Categorial Grammar even more exciting is the fact that (as van Benthem, 1983 points out) the Curry-Howard correspondence a central part of mathematical proof theory which establishes a deep connection between constructive logics and the λ-calculus supplies the type logical syntax with an extremely elegant and independently motivated interface to model-theoretic semantics. Prima facie, anaphora does not fit very well into the Categorial picture of the syntax-semantics interface. The Curry-Howard based composition of meaning operates in a local way, and meaning assembly is linear, i.e., every piece of lexical meaning is used exactly once. Anaphora, on the other hand, is in principle unbounded, and it involves by definition the multiple use of certain semantic resources. The latter problem has been tackled by several Categorial grammarians by assuming sufficiently complex lexical meanings for anaphoric expressions, but the locality problem is not easy to solve in a purely lexical way. The main purpose of this book is to develop an extension of Lambek style Type Logical Grammar that overcomes these difficulties and handles anaphora in a systematic fashion. The linguistic applications of the theoretical framework that is developed here focus on three classes of ix

9 x ANAPHORA AND TYPE LOGICAL GRAMMAR anaphora that are well-studied and well-understood as far as the empirical generalizations go. First and foremost, I will discuss the grammar of anaphoric third person singular pronouns, as illustrated by the following example. (1) a. John i invented a problem that he i could not solve. b. [Every student] i invented a problem that he i could not solve. The second empirical domain that we are going to look at is verb phrase ellipsis, i.e., constructions like (2). (2) a. John revised his paper, and Bill did too. b. John is happy with his job, but Bill isn t. As is well-known, VP ellipsis interacts with pronominal anaphora and quantification in complex ways. The logic of anaphora resolution that I will propose lends itself readily to a simple theory of this kind of ellipsis which covers the basic facts in an empirically adequate way. Finally, I will discuss a third class of anaphora, a version of ellipsis that has been called sluicing in the literature. Thereby I mean constructions in which a bare wh-phrase is interpreted as a (direct or indirect) question, as illustrated in (3). (3) a. She s reading something, but I can t imagine what. b. A: She s reading something. B: What? The main goal of this work is not so much to develop a novel descriptive theory of anaphora but rather to demonstrate that anaphora can be integrated into Type Logical Grammar without giving up the attractive design of this theory of grammar. Nonetheless, the empirical predictions that we end up with do not always coincide with those of competing analyses, and I (naturally) try to argue that my analysis also gets the facts right in these cases. So the discussion might be interesting for non-categorial grammarians who are interested in the analysis of anaphora as well. Also, the type logical analysis of donkey anaphora led to a partially novel account of the grammar of indefinites that diverges from established theories in several respects, both theoretically and empirically. The book does not expect prior knowledge of Categorial Grammar or any acquaintance with proof theory that goes beyond the level of some introductory logics course. I do assume though a working knowledge of set theory, first order logic and the typed λ-calculus. The technical level of the book should be easily accessible to anybody who has mastered

10 Preface xi some standard textbook on formal linguistics like Dowty et al., 1981 or Gamut, The structure of the book is as follows. Chapter 1 gives a selfcontained introduction to the framework of Type Logical Grammar. It does not make any reference to the issue of anaphora whatsoever. It can be used as an introductory text on its own. Readers that are already familiar with TLG, on the other hand, can safely skip this chapter. Chapter 2 discusses previous Categorial approaches to (pronominal) anaphora. This chapter too can be read on its own (or in combination with Chapter 1). The remainder of the book does not build on it in any significant way, so this chaper is not essential for understanding of the subsequent material. Chapter 3 is the core of the book. There I develop the novel type logical machinery that enables us to analyze anaphora resolution. In this chapter I focus on the proof theoretic properties of the resulting type logical calculus, i.e., I present the calculus in different proof theoretic formats, establish their equivalence, and prove essential meta-logical properties like Cut elimination, decidability, finite reading property, strong normalization, and completeness. The remaining chapters apply these theoretical tools to the mentioned empirical areas. Chapter 4 focuses on anaphoric pronouns and their interaction with quantification. Chapter 5 discusses two options for a type logical treatment of verb phrase ellipsis. In Chapter 6 I propose another extension of the underlying formalism to accommodate certain peculiarities of indefinite NPs. This has an impact on the issue of anaphora for two reasons. First, I believe that the problem of donkey anaphora is mainly a problem of indefiniteness, less a problem of anaphora. So an adequate treatment of donkey pronouns requires a theory of indefiniteness. Furthermore, sluicing is a form of ellipsis that interacts closely with the grammar of indefinites. I discuss these anaphora related aspects of indefiniteness, and I also consider some empirical issues pertaining to the grammar of indefinites as such, namely their peculiar scope taking behavior. Now that I have explained what the book is intended to be, a few words about what it is not. The intended audience are mainly formally inclined linguists and computational linguists with an interest in logic. I try to illustrate how a logical grammar can contribute to a both formally precise and empirically comprehensive linguistic theory. It is not my goal to give an introduction into the Lambek calculus and related substructural calculi for logicians. Therefore, issues that are important to logicians but of lesser relevance to the linguistic applications are not covered in great depth. This concerns especially model theory and the

11 xii ANAPHORA AND TYPE LOGICAL GRAMMAR relation of type logics to modal logic and Linear Logic. Likewise, extensions of the Lambek calculus that are interesting from a logical point of view but without obvious linguistic applications like negation or additive connectives are not discussed. Neither could I deal with all facets of Type Logical Grammar that emerged within the last decade. The focus of the book is on the treatment of anaphora. The introductory Chapter 1 gives an overview over the classical version of Type Logical Grammar, but various new developments that have no immediate connection to anaphora are left out. This concerns especially non-associative Categorial calculi, multimodal extions of TLG, and the calculus of proof nets.

12 Acknowledgments Most ideas that I present in this book were developed while I was a postdoc at the Institute for Research in Cognitive Science of UPenn in Philadelphia 1997 and It is no exaggeration to say that at that time, the IRCS was one of the best institutes in the world to conduct research on formal grammar. Thanks to Aravind Joshi for making the place what it is! I profited immensely from the discussions with my colleagues there. Many people gave me inspiration and feedback, but I feel the contacts to Robin Clark, Seth Kulick, Jeff Lidz, Mark Steedman and Yael Sharvit were especially important. Last but not least, Dick Oehrle s occasional visits to Philadelphia were very rewarding. Natasha Kurtonina deserves a special mention. Due to a lucky coincidence, we came to the IRCS at the same time and wound up being office mates. She has an extraordinary gift for explaining things, and most of what I know about the Logic in Type Logical Grammar, I learned from her. She never tired of pointing out the flaws in my proofs and digging out literature that might be relevant for my research. Last but not least, I thank her for always being a good friend. When I left Philadelphia, my work on anaphora in TLG consisted of a couple of half finished papers and a lot of loose ideas. My time as a visitor at the Utrecht Institute of Linguistics in 2000 and 2001 gave me the opportunity to finally write everything down in a coherent way. It is hard to find a place with a higher concentration of excellent categorial grammarians than the OTS, and this created the right atmosphere to finish this work. Thanks to my Utrecht colleagues, especially to Michael Moortgat, for making the time in Utrecht a pleasant and productive one. While I was finally writing down the manuscript, Cornelia Endriss got me interested into the issue of indefiniteness again. We had a vivid intellectual exchange on this over several months. The last chapter of the book would have taken a different shape without this, and perhaps it xiii

13 xiv ANAPHORA AND TYPE LOGICAL GRAMMAR would not exist at all. Even though we finally drew different conclusions on what a correct approach to specificity should look like, many of the ideas and observations from this chapter are due to Neli. I had the opportunity to present material from this book at various talks at Berlin, UPenn, the MIT, Utrecht, Düsseldorf, Amsterdam and Leiden, and I am grateful for the comments I received at these occasions. I am also indebted to the students of my Categorial Grammar classes in Potsdam and in Utrecht for the feedback they gave me. I owe a lot to Raffaella Bernardi, Christian Ebert, Bryan Jurish, Manfred Krifka, Glyn Morrill, and Willemijn Vermaat for reading previous versions of the manuscript or parts of it, and making numerous helpful suggestions for improvement. All remaining errors are of course mine. Special thanks go to Bryan for spending a lot of effort correcting my English. This book is a revised version of my habilitation thesis that I defended at the Humboldt-University at Berlin in I would like to thank the committe members Marcus Kracht, Manfred Krifka and Michael Moortgat for their encouragement and support. It was also Marcus who suggested that I submit the manuscript to the Trends in Logic. Last but not least I thank the series editor Heinrich Wansing for the very good cooperation during the final preparations for publication, and the two anonymous reviewers for their suggestions and comments.