Foundations of Intensional Semantics

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. 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 proposes a theory that offers a promising framework for developing a computational semantic system sufficiently expressive to capture the properties of natural language meaning while remaining computationally tractable written by two leading researchers and of interest to students and researchers in formal semantics, computational linguistics, logic, artificial intelligence, and the philosophy of language

This book provides a systematic study of three foundational issuesin the semantics of natural language that have been relativelyneglected in the past few decades.* focuses on the formal characterization of intensions, thenature of an adequate type system for natural language semanticsand the formal power of the semantic representation language* proposes a theory that offers a promising framework fordeveloping a computational semantic system sufficiently expressiveto capture the properties of natural language meaning whileremaining computationally tractable* written by two leading researchers and of interest to studentsand researchers in formal semantics, computational linguisticslogic, artificial intelligence, and the philosophy of language

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 WorldsSemantics.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 SemanticTheory.10.2 Algebraic Semantics and Fine-Grained Alternatives toMS.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 andEllipsis.10.7 Underspecified Interpretations as _-Terms of theRepresentation Language.10.8 PTCT and Computational Semantics: Directions for FutureWork.Bibliography.Author Index.Subject Index.