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.

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, Iogic, artificial intelligence, and the philosophy of language.

PREFACE

1 LIST OF ABBREVIATIONS INTRODUCTION

 1.1 Montague's Intensional Logic

 1.2 Architectural Features of IL

 1.3 Structure of the Book

2 ALTERNATIVE APPROACHES TO FINE-GRAINED INTENSIONALITY

 2.1 An Algebraic Representation of Possible Worlds Semantics

 2.2 Two Strategies for Hyperintensionalism

 2.3 Thomason's Intentional Logic

 2.4 Bealer's Intensional Logic

 2.5 Structured Meanings and Interpreted Logical Forms

 2.6 Landman's Data Semantics

 2.7 Situation Semantics and Infon Algebras

 2.8 Situations as Partial Models

 2.9 Topos Semantics

 2.10 Conclusion

3 INTENSIONS AS PRIMITIVES

 3.1 A Simple Intensional Theory

 3.2 Types and Sorts

 3.3 Abstraction and Application

 3.4 PT: An Untyped Theory

 3.5 Intensionality in FIL and PTGT

 3.6 Conclusion

4 A HIGHER-ORDER, FINE-GRAINED INTENSIONAL LOGIC

 4.1 Introduction 

 4.2 Fine-Grained Intensional Logic

 4.3 A Semantics for FIL

 4.4 Conclusion

5 PROPERTY THEORY WITH CURRY TYPING

 5.1 PTGT: A Curry-Typed Theory

 5.2 PTGT: Syntax of the Basic Theory

 5.3 A Proof Theory for PTGT

 5.4 Example Proof

 5.5 Extending the Type System

 5.6 Intensional Identity vs. Extensional Equivalence

 5.7 A Model Theory for PTGT

 5.8 Types and Properties

 5.9 Separation Types and Internal Type Judgements

 5.10 Truth as a Type

 5.11 Conclusion

6 NUMBER THEORY AND CARDINALITY

 6.1 Proportional Cardinality Quantifiers

 6.2 Reano Arithmetic

 6.3 Number Theoryin FIL

 6.4 Proportional Generalized Quantifiers in FIL

 6.5 Number Theory in PTGT

 6.6 Proportional Generalized Quantifiers in PTGT

 6.7 Presburger Arithmetic

 6.8 Presburger Arithmetic in PTGT

 6.9 Conclusion

7 ANAPHO1G AND ELLIPSIS

 7.1 A Type-Theoretical Approach to Anaphora

 7.2 Ellipsis in PTGT

 7.3 Comparison with Other Type-Theoretical Approaches

 7.4 Conclusion

8 UNDERSPECIFIED INTERPRETATIONS

 8.1 Underspecified Representations

 8.2 Comparison with Other Theories

 8.3 Conclusion

9 EXPRESSIVE POWER AND FORMAL STRENGTH

 9.1 Decidability and Completeness

 9.2 Arguments for Higher-Order Theories

 9.3 Arguments against Higher-Order Theories

 9.4 Self-application, Stratification and Impredicativity

 9.5 First-Order Status and Finite Cardinality

 9.6 Relevance of PTGT to Computational Semantics

 9.7 Conclusion

10 CONCLUSION

 10.1 Montague Semantics and the Architecture of Semantic Theory

 10.2 Algebraic Semantics and Fine-Grained Alternatives to MS

 10.3 A Conservative Revision of MS

 10.4 Enriching Property Theory with Curry Typing

 10.5 An Intensional Number Theory

 10.6 A Dynamic Type-Theoretic Account of Anaphora and Ellipsis

 10.7 Underspecified Interpretations as A-Terms of the Representation Language

 10.8 PTGT and Computational Semantics: Directions for Future Work

BIBLIOGRAPHY

AUTHOR INDEX

SUBJECT INDEX