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Language in Action: Categories, Lambdas and Dynamic Logic / Edition 2

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Overview

This monograph began life as a series of papers documenting five years of research into the logical foundations of Categorial Grammar, a grammatical paradigm which has close analogies with Lambda Calculus and Type Theory. The technical theory presented here stems from the interface between Logic and Linguistics and, in particular, the theory of generalized quantification. A categorical framework with lambda calculus-oriented semantics is a convenient vehicle for generalizing semantic insights (obtained in various corners of natural language) into one coherent theory.

The book aims to demonstrate to fellow logicians that the resulting applied lambda calculus has intrinsic logical interest. In the final analysis, the idea is not just to 'break the syntactic code' of natural languages but to understand the cognitive functioning of the human mind.

This monograph began life as a series of papers documenting five years of research into the logical foundations of Categorial Grammar, a grammatical paradigm which has close analogies with Lambda Calculus and Type Theory. The technical theory presented here stems from the interface between Logic and Linguistics and, in particular, the theory of generalized quantification. A categorical framework with lambda calculus-oriented semantics is a convenient vehicle for generalizing semantic insights (obtained in various corners of natural language) into one coherent theory.

The book aims to demonstrate to fellow logicians that the resulting applied lambda calculus has intrinsic logical interest. In the final analysis, the idea is not just to 'break the syntactic code' of natural languages but to understand the cognitive functioning of the human mind

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Editorial Reviews

From the Publisher
At present the research programme presented in van Benthem's monograph is intensively developed by logicians, mathematicians, and specialists in computer science and linguistics. Language in Action conveniently reports in detail and in a compact form the results hitherto obtained. Certainly it becomes the standard reference in the area.
From the Logical Point of View
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Product Details

Meet the Author

Johan van Benthem is Professor of Logic at the University of Amsterdam (Department of Mathematics and Computer Science) as well as at Stanford University (Bonsall visiting chair, Department of Philosophy). His research interests include modal and dynamic logic, type-theoretic semantics, and proof-theoretic grammars. Address: Department of Mathematics and Computer Science, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands.

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Table of Contents

Preface
I Introduction 1
1 Two Traditions 1
2 Lambda Calculus and Theory of Types 5
3 Categorial Grammar 21
II A Logical Perspective 35
4 The Hierarchy of Implicational Logics 35
5 Proofs, Terms and Meanings 51
III Proof Theory 71
6 Exploring Categorial Deduction 71
7 Cut Elimination and Decidability 83
8 Recognizing Power 93
IV Model Theory 111
9 Enumerating Readings 111
10 Computing Denotational Constraints 127
11 Boolean Structure 139
V Variations and Extensions 155
12 Intensionality 156
13 Variable Polymorphism and Higher Type Theories 169
VI Toward a Logic of Information 185
14 Language Families 188
15 Modal Logic of Information Patterns 203
16 Relational Algebra of Control 225
17 Dynamic Logic 251
VII A Tour of Basic Logic 271
Bibliography 327
Addenda to the American Paperback Edition, Summer 1994 345
Index 361
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