Foundations of Intensional Semantics (eBook)

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).

Preface.

1. 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 PTCT.

3.6 Conclusions.

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 PTCT: A Curry-Typed Theory.

5.2 PTCT: Syntax of the basic theory.

5.3 A Proof Theory for PTCT.

5.4 Example Proof.

5.5 Intensional Identity v. Extensional Equivalence.

5.6 Extending the Type System.

5.7 A Model Theory for PTCT.

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 Cardinaltiy.

6.1 Proportional Cardinality Quantifiers.

6.2 Peano Arithmetic.

6.3 Number Theory in FIL.

6.4 Proportional Generalized Quantifiers in FIL.

6.5 Number Theory in PTCT.

6.6 Proportional Generalized Quantifiers in PTCT.

6.7 Presburger Arithmetic.

6.8 Presburger Arithmetic in PTCT.

6.9 Conclusions.

7. Anaphora and Ellipsis.

7.1 A Type-Theoretical Approach to Anaphora.

7.2 Ellipsis in PTCT.

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 PTCT to Computational Semantics.

9.7 Conclusions.

10. Conclusions.

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 _-Terms of the
Representation Language.

10.8 PTCT and Computational Semantics: Directions for Future
Work.

Bibliography.

Author Index.

Subject Index.

"The book is a must reading for any semanticist who has ever asked
herself what intensions actually are." The Linguist
List

"Fox and Lappin present a new solution to one of the
long-standing issues in formal semantics: how to distinguish
logically equivalent from semantically equivalent propositions.
This is a valuable contribution to the foundations of formal
semantics of natural language." Stephen G. Pulman, Oxford
University

"This is an excellent addition to the literature on the
foundations of natural language semantics. The logical issues are
carefully and insightfully addressed and much advanced material is
brought together for the first time. Semanticists cannot afford not
to read it." Raymond Turner, University of Essex