Categorial Grammar: Logical Syntax, Semantics, and Processing

✍ Scribed by Glyn V. Morrill

• Publisher: Oxford University Press
• Year: 2011
• Tongue: English
• Leaves: 253
• Category: Library

✦ Synopsis

This book provides a state-of-the-art introduction to categorial grammar, a type of formal grammar which analyzes expressions as functions or according to a function-argument relationship. The book's focus is on linguistic, computational, and psycholinguistic aspects of logical categorial grammar, i.e. enriched Lambek Calculus. Glyn Morrill opens with the history and notation of Lambek Calculus and its application to syntax, semantics, and processing. Successive chapters extend the grammar to a number of significant syntactic and semantic properties of natural language. The final part applies Morrill's account to several current issues in processing and parsing, considered from both a psychological and a computational perspective. The book offers a rigorous and thoughtful study of one of the main lines of research in the formal and mathematical theory of grammar, and will be suitable for students of linguistics and cognitive science from advanced undergraduate level upwards.

✦ Table of Contents

Cover......Page 1
Contents......Page 6
Preface......Page 9
Acknowledgements......Page 10
List of figures......Page 11
List of tables......Page 15
Abbreviations and symbols......Page 16
Part I. Lambek Categorial Grammar......Page 18
1.1. Formal grammar......Page 20
1.2. Categorial syntax......Page 21
1.3. Categorial semantics......Page 24
1.5. Outline of the book......Page 25
2. Syntax......Page 27
2.1. Categorial logic......Page 28
2.2. Proof theory of categorial connectives......Page 29
2.3. Model theory of categorial connectives......Page 31
2.4. Lambek categorial grammar......Page 33
2.5. Cut-elimination......Page 35
3. Semantics......Page 38
3.1. Intuitionistic implication and conjunction......Page 40
3.2. Typed lambda calculus and the Curry–Howard correspondence......Page 42
3.3. Semantic readings of the Lambek calculus (derivational semantics)......Page 46
3.4. Classical propositional logic......Page 48
3.5. Classical first-order logic......Page 52
3.6. Classical higher-order logic......Page 53
3.7. Lexical semantics......Page 54
3.8. Natural deduction for the Lambek calculus......Page 56
3.9. Natural deduction for the Lambek calculus with semantic annotation......Page 59
3.10. Coordination of standard and non-standard constituents......Page 61
4. Processing......Page 68
4.1. Introduction......Page 69
4.2. Proof nets for the Lambek calculus......Page 70
4.3. The semantic trip and the semantic reading of a proof net......Page 75
4.4. Incremental parsing algorithm and complexity metric......Page 77
4.5. Predicting performance......Page 83
Part II. Logical Categorial Grammar......Page 98
5. Bracket operators for extraction......Page 100
5.1. Theory......Page 101
5.2. Application......Page 103
5.3. Medial extraction......Page 104
5.4. Semigrammaticality......Page 106
5.5. Parasitic extraction......Page 108
6.1. Introduction......Page 112
6.2. Theory of discontinuous Lambek calculus......Page 113
6.3. Applications of discontinuous Lambek calculus......Page 122
7. Additive operators for polymorphism......Page 145
7.1. Curry–Howard semantic interpretation......Page 147
7.2. Polymorphism......Page 149
7.3. Coordination of unlike types......Page 151
8. Modality for intensionality......Page 156
8.2. Intensional lambda calculus......Page 157
8.3. Curry–Howard semantic interpretation......Page 159
8.4. Example intensional fragment......Page 160
Part III. Further Processing Issues......Page 166
9. Aphasic comprehension......Page 168
9.2. Sentences......Page 169
9.3. Results......Page 180
10. Lexico-syntactic interaction......Page 184
10.1. Nets......Page 185
10.2. Words......Page 193
10.3. Sentences......Page 201
11. Memoizing Lambek theorem-proving......Page 206
11.1. Background......Page 207
11.2. Chart theorem-proving......Page 208
12.1. Grammar......Page 214
12.2. Processing......Page 216
12.3. Open problems......Page 218
A.1. Naturals......Page 220
A.2. Sets......Page 221
A.3. Mappings......Page 222
A.5. Data structures and formal languages......Page 223
A.7. Operations......Page 224
A.8. Algebras......Page 225
A.9. Structures......Page 226
A.11. Decidability......Page 227
A.12. Computational time complexity......Page 229
B.1. Program listing......Page 230
B.2. Session log......Page 234
References......Page 235
B......Page 244
C......Page 245
D......Page 246
H......Page 247
L......Page 248
N......Page 249
P......Page 250
S......Page 251
Z......Page 253