Taking Scope: The Natural Semantics of Quantifiers

Contents

Contents Preface xiii Acknowledgments xvii Chapter 1 Prologue 1 1.1 Why Quantifiers Matter 2 1.2 Quantifiers and Question Answering 7 Chapter 2 Introduction 11 2.1 Representing Scope Alternation 12 2.2 Grammar and Explanation 13 2.3 Natural Grammar 14 2.4 Composition, Constructions, and Strong Lexicalization 17 2.5 Against (Most) Generalized Quantifiers 21 2.6 Processing Scope 23 2.7 The Argument 24 vi Contents Part I Natural Semantics Chapter 3 The Natural History of Scope 29 3.1 Asymmetries in Scope Taking 30 3.2 The Canadian Flag Exception 33 3.3 Plural Quantifier Nominals 34 3.4 Negation and Scope 35 3.5 Pronouns and Scope 36 3.6 A Narrow Definition of Bound-Variable Anaphora 38 3.7 Early Approaches to Scope Alternation 41 Chapter 4 Semantics without Existential Quantifiers 45 4.1 Donkey Sentences 45 4.2 Intensionality 50 4.3 Definites 51 4.4 Pronouns 52 4.5 Indefinites 53 4.6 Distributivity 54 4.7 Maximal Participancy of Plurals 55 Contents vii 4.8 Negation, Polarity, and Monotone Entailment 56 Chapter 5 Model Theory (with Stephen Isard) 61 5.1 Nonstandard Features of the Model Theory 61 5.2 Syntax 63 5.3 Semantics 65 5.4 Examples 67 5.5 Remarks 71 Part II Natural Grammar Chapter 6 Combinatory Categorial Grammar 77 6.1 The Categorial Lexicon 77 6.2 Combinatory Rules 79 6.3 Binding and Control 84 6.4 Relativization 87 6.5 Embedded Subject Extraction 89 6.6 Pied-Piping and In Situ Wh-Items 89 6.7 Coordination 91 viii Contents 6.8 Apparent Exceptions to the Across-the-Board Condition 94 6.9 Argument/Adjunct Cluster Coordination 95 6.10 Coordination of “Unlike” Types 99 6.11 On the Symmetry of Left and Right Extraction 101 6.12 Expressive Power and Computational Complexity of CCG 103 6.13 A Comparison with Categorial Type Logic and Lambek Grammars 106 Chapter 7 Quantification and Pronominal Anaphora 109 7.1 Generalized Quantifiers 109 7.2 Skolem Terms 111 7.3 Definites 117 7.4 Pronouns 117 7.5 Bound-Variable Anaphora 122 Contents ix Part III Scope, Coordination, and Polarity Chapter 8 Inverse Scope 127 8.1 How True Universal Quantifiers Invert Scope 127 8.2 “Inverse Linking” 129 8.3 “Frozen” Scope 133 8.4 “Intermediate” Scope 134 8.5 Asymmetric Scope in English Embedded Universal Subjects 136 8.6 Asymmetric Scope in German and Dutch 137 8.7 Why Nonuniversals Do Not Invert 144 Chapter 9 Distributional Scope of Plurals 147 9.1 Distributivity 147 9.2 The Proportion Problem 151 9.3 Counting Quantifiers 153 9.4 Distributivity and Word Order in English and Japanese 154 Chapter 10 Coordination and Scope 159 10.1 Plural Coordination 160 x Contents 10.2 Quantifier Coordination 161 10.3 “Branching Quantifiers” 164 10.4 Across-the-Board Scope Alternation 165 10.5 Parallelism and ATB Scope Taking 170 Chapter 11 Negation and Polarity 175 11.1 Negation and Entailment 175 11.2 Polarized Determiners 180 11.3 “Split Scope” 196 11.4 Not Every and Not All 198 11.5 Pronouns and Polarity 201 11.6 Multiple Negation 203 11.7 A Note on Negative-Concord Dialects of English 206 11.8 Negative Scope and Coordination 207 Chapter 12 Related Approaches 209 12.1 Discourse Representation Theory 209 12.2 E-Type Pronouns 211 Contents xi 12.3 Underspecification 214 12.4 Storage 215 12.5 Call-by-Name 216 Part IV Applications and Conclusions Chapter 13 Efficient Processing with CCG 221 13.1 Parsing with CCG 223 13.2 Building Logical Forms with CCG 225 13.3 Processing Scope and Pronominal Reference in CCG 228 13.4 String Generation from Logical Forms Using CCG 235 13.5 The Use of Scope 235 13.6 Entailment 238 13.7 Human Sentence Processing 241 Chapter 14 Conclusion 249 References 255 Index 297 ...