Type-Logical Semantics

by Bob Carpenter

Overview

Based on an introductory course on natural-language semantics, this book provides an introduction to type-logical grammar and the range of linguistic phenomena that can be handled in categorial grammar. It also contains a great deal of original work on categorial grammar and its application to natural-language semantics. The author chose the type-logical categorial grammar as his grammatical basis because of its broad syntactic coverage and its strong linkage of syntax and semantics. Although its basic orientation is linguistic, the book should also be of interest to logicians and computer scientists seeking connections between logical systems and natural language.

The book, which stepwise develops successively more powerful logical and grammatical systems, covers an unusually broad range of material. Topics covered include higher-order logic, applicative categorial grammar, the Lambek calculus, coordination and unbounded dependencies, quantifiers and scope, plurals, pronouns and dependency, modal logic, intensionality, and tense and aspect. The book contains more mathematical development than is usually found in texts on natural language; an appendix includes the basic mathematical concepts used throughout the book.

Product Details

ISBN-13:	9780262531498
Publisher:	MIT Press
Publication date:	07/24/1998
Series:	Language, Speech, and Communication
Pages:	598
Product dimensions:	7.00(w) x 8.80(h) x 1.40(d)

Table of Contents

Preface
Acknowledgments
Chapter 1
Introduction
1.1 Truth and Reference
1.2 Topics in Semantics
1.3 Topics in Pragmatics
1.4 Methodology
EXercises
Chapter 2
Simply Typed Calculus
2.1 Simple Types
2.2 Terms
2.3 Functional Models
2.4 Proof Theory for Simply Typed Calculus
2.5 Combinators and VariableFree Logic
2.6 Products
2.7 Sums
EXercises
Chapter 3
HighOrder Logic
3.1 HigherOrder SyntaX
3.2 HigherOrder Models
3.3 Quantifiers in Natural Language
3.4 Negative Polarity Items
3.5 Definite Descriptions
3.6 Proof Theory for HigherOrder Logic
EXercises
Chapter 4
Applicative Categorial Grammar
4.1 The Category System
4.2 Semantic Domains
4.3 Categorial LeXicon
4.4 Phrase Structure
4.5 A Categorial LeXicon
4.6 Tree Admissibility
4.7 Ambiguity, Vagueness, and Meaning Postulates
EXercises
Chapter 5
The Lambek Calculus
5.1 Lambek's Sequent Calculus
5.2 The NaturalDeduction Lambek Calculus
5.3 Products
5.4 Categorial Grammar as Logic
EXercises
Chapter 6
Coordination and Unbounded Dependencies
6.1 Coordination
6.2 Conjunctive and Disjunctive Categories
6.3 Unbounded Dependency Constructions
EXercises
Chapter 7
Quantifiers and Scope
7.1 Quantifying In
7.2 Cooper Storage
7.3 Scoping Constructor
7.4 Type Raising and Quantifier Coordination
7.5 Embedded Quantifiers
7.6 Quantifiers and Coordinate Structures
7.7 Quantification and Negation
7.8 Quantification and Definite Descriptions
7.9 Possessives
7.10 Indefinites
7.11 Generics
7.12 Comparatives
7.13 EXpletives and the Unit Type
EXercises
Chapter8
Plurals
8.1 An Ontology of Groups
8.2 A Plural Grammar
8.3 Distributors and Collectors
8.4 Coordination, Negation, and Argument Lowering
8.5 Adverbial Distribution
8.6 Plural Quantification
8.7 Partitives and Pseudopartitives
8.8 Nonboolean Coordination
8.9 Comitative Complements
8.10 Mass Terms
EXercises
Chapter 9
Pronouns and Dependency
9.1 Pronouns and RefleXives
9.2 Pronouns and Agreement
9.3 Pronouns as Variables
9.4 A Quantificational Approach to RefleXives
9.5 Plural Pronouns
9.6 Reciprocals and Generalized Quantification
9.7 Pied Piping
9.8 Ellipsis and Sloppy Anaphora
9.9 Interrogatives
EXercises
Chapter 10
Modal Logic
10.1 Modes of Truth
10.2 S5: A Modal Logic of Necessity
10.3 IndeXicality
10.4 General Modal Logics
10.5 Strict Implication and Counterfactuals
10.6 FirstOrder Tense Logics
10.7 Tense Logic and Natural Language
10.8 TemporalPeriod Structures
10.9 HigherOrder Modal Logic
EXercises
Chapter 11
Intensionality
11.1 An Intensional Grammar
11.2 Individual Concepts and Quantificational Definites
11.3 Alternatives to Possible Worlds
11.4 LeXical Relations
EXercises
Chapter 12
Tense and Aspect
12.1 Reichenbach's Approach to Simple and Perfect Tenses
12.2 Tense adn Discourse
12.3 Vendler's Verb Classes
12.4 A Semantics Approach to Aspect
12.5 A Grammar of Tense and Aspect
EXercises
AppendiX A
Mathematical Preliminaries
A.1 Set Theory
A.2 Functions and Relations
A.3 Orderings, Well Orderings, and Lattices
A.4 Proof by Induction
A.5 Formal Languages
A.6 Trees
A.7 FirstOrder Logic
A.8 Algebras and Equality
References
IndeX