Foundations of Intensional Semantics

by Fox, Chris; Lappin, Shalom

• ISBN13: 9780631233756
• ISBN10: 063123375X
• eBook ISBN(s): 9780470775295
• Edition: 1st
• Format: Hardcover
• Copyright: 2005-08-05
• Publisher: Wiley-Blackwell
• More Book Details

Summary

This book provides a systematic study of three foundational issues in the semantics of natural language that have been relatively neglected in the past few decades. It focuses on the formal characterization of intensions, the nature of an adequate type system for natural language semantics, and the formal power of the semantic representation language. The theory proposed offers a promising framework for developing a computational semantic system that is sufficiently expressive to capture the properties of natural language meaning while remaining computationally tractable. Written by two leading researchers in the field, Foundations of Intensional Semantics will be of interest to students and researchers in formal semantics, computational linguistics, logic, artificial intelligence, and the philosophy of language.

Author Biography

Chris Fox is a Reader in the Department of Computer Science at the University of Essex. In addition to numerous papers, his previous publications in the area of computational semantics include The Ontology of Language: Properties, Individuals, and Discourse (2000).

Shalom Lappin is Professor of Computer Science at King’s College, London. He has published extensively on issues in computational linguistics and formal grammar, and his books include Local Constraints vs. Economy (with David Johnson, 1999), Fragments: Studies in Ellipsis and Gapping (edited with Elabbas Benmamoun, 1999), and The Handbook of Contemporary Semantic Theory (edited, Blackwell, 1996).

Table of Contents

PREFACE	XI
LIST OF ABBREVIATIONS	XV
1 INTRODUCTION	1	(12)
1.1 Montague's Intensional Logic	4	(3)
1.2 Architectural Features of IL	7	(2)
1.3 Structure of the Book	9	(4)
2 ALTERNATIVE APPROACHES TO FINE-GRAINED INTENSIONALITY	13	(25)
2.1 An Algebraic Representation of Possible Worlds Semantics	13	(6)
2.2 Two Strategies for Hyperintensionalism	19	(4)
2.3 Thomason's Intentional Logic	23	(2)
2.4 Bealer's Intensional Logic	25	(3)
2.5 Structured Meanings and Interpreted Logical Forms	28	(2)
2.6 Landman's Data Semantics	30	(1)
2.7 Situation Semantics and Infon Algebras	31	(2)
2.8 Situations as Partial Models	33	(1)
2.9 Topos Semantics	34	(3)
2.10 Conclusion	37	(1)
3 INTENSIONS AS PRIMITIVES	38	(18)
3.1 A Simple Intensional Theory	39	(5)
3.2 Types and Sorts	44	(1)
3.3 Abstraction and Application	45	(1)
3.4 PT: An Untyped Theory	46	(7)
3.5 Intensionality in FIL and PTCT	53	(1)
3.6 Conclusion	54	(2)
4 A HIGHER-ORDER, FINE-GRAINED INTENSIONAL LOGIC	56	(14)
4.1 Introduction	57	(1)
4.2 Fine-Grained Intensional Logic	57	(7)
4.3 A Semantics for FIL	64	(5)
4.4 Conclusion	69	(1)
5 PROPERTY THEORY WITH CURRY TYPING	70	(40)
5.1 PTCT: A Curry-Typed Theory	72	(2)
5.2 PTCT: Syntax of the Basic Theory	74	(1)
5.3 A Proof Theory for PTCT	75	(9)
5.4 Example Proof	84	(1)
5.5 Extending the Type System	85	(9)
5.6 Intensional Identity vs. Extensional Equivalence	94	(2)
5.7 A Model Theory for PTCT	96	(7)
5.8 Types and Properties	103	(1)
5.9 Separation Types and Internal Type Judgements	104	(4)
5.10 Truth as a Type	108	(1)
5.11 Conclusion	108	(2)
6 NUMBER THEORY AND CARDINALITY	110	(13)
6.1 Proportional Cardinality Quantifiers	111	(2)
6.2 Peano Arithmetic	113	(2)
6.3 Number Theory in FIL	115	(1)
6.4 Proportional Generalized Quantifiers in FIL	115	(1)
6.5 Number Theory in PTCT	116	(2)
6.6 Proportional Generalized Quantifiers in PTCT	118	(1)
6.7 Presburger Arithmetic	119	(1)
6.8 Presburger Arithmetic in PTCT	120	(1)
6.9 Conclusion	121	(2)
7 ANAPHORA AND ELLIPSIS	123	(11)
7.1 A Type-Theoretical Approach to Anaphora	124	(3)
7.2 Ellipsis in PTCT	127	(3)
7.3 Comparison with Other Type-Theoretical Approaches	130	(3)
7.4 Conclusion	133	(1)
8 UNDERSPECIFIED INTERPRETATIONS	134	(16)
8.1 Underspecified Representations	135	(9)
8.2 Comparison with Other Theories	144	(4)
8.3 Conclusion	148	(2)
9 EXPRESSIVE POWER AND FORMAL STRENGTH	150	(13)
9.1 Decidability and Completeness	150	(2)
9.2 Arguments for Higher-Order Theories	152	(1)
9.3 Arguments against Higher-Order Theories	153	(2)
9.4 Self-application, Stratification and Impredicativity	155	(1)
9.5 First-Order Status and Finite Cardinality	156	(5)
9.6 Relevance of PTCT to Computational Semantics	161	(1)
9.7 Conclusion	161	(2)
10 CONCLUSION	163	(9)
10.1 Montague Semantics and the Architecture of Semantic Theory	163	(1)
10.2 Algebraic Semantics and Fine-Grained Alternatives to MS	164	(1)
10.3 A Conservative Revision of MS	165	(1)
10.4 Enriching Property Theory with Curry Typing	166	(1)
10.5 An Intensional Number Theory	167	(1)
10.6 A Dynamic Type-Theoretic Account of Anaphora and Ellipsis	168	(1)
10.7 Underspecified Interpretations as A-Terms of the Representation Language	169	(1)
10.8 PTCT and Computational Semantics: Directions for Future Work	170	(2)
BIBLIOGRAPHY	172	(9)
AUTHOR INDEX	181	(2)
SUBJECT INDEX	183

Excerpts

"Foundations of Intensional Semantics will be of interest to students and researchers in formal semantics, computational linguistics, logic, artificial intelligence, and the philosophy of language."--BOOK JACKET.