Language in Action: Categories, Lambdas, and Dynamic Logic / Edition 1

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Overview

Language in Action demonstrates the viability of mathematical research into the foundations of categorial grammar, a topic at the border between logic and linguistics. Since its initial publication it has become the classic work in the foundations of categorial grammar. A new introduction to this paperback edition updates the open research problems and records relevant results through pointers to the literature.Van Benthem presents the categorial processing of syntax and semantics as a central component in a more general dynamic logic of information flow, in tune with computational developments in artificial intelligence and cognitive science. Using the paradigm of categorial grammar, he describes the substructural logics driving the dynamics of natural language syntax and semantics. This is a general type-theoretic approach that lends itself easily to proof-theoretic and semantic studies in tandem with standard logic. The emphasis is on a broad landscape of substructural categorial logics and their proof-theoretical and semantic peculiarities.
This provides a systematic theory for natural language understanding, admitting of significant mathematical results. Moreover, the theory makes possible dynamic interpretations that view natural languages as programming formalisms for various cognitive activities.

The MIT Press

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Editorial Reviews

Booknews
First published by Elsevier Science in 1991, this study demonstrates the viability of mathematical research into the foundations of categorial grammar, a topic at the border between logic and linguistics. It presents the categorial processing of syntax and semantics as a central component in a more general dynamic logic of information flow, in tune with computational developments in artificial intelligence and cognitive science. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780262720243
  • Publisher: MIT Press
  • Publication date: 6/28/1995
  • Edition description: 1st MIT Press ed
  • Edition number: 1
  • Pages: 377
  • Product dimensions: 6.00 (w) x 9.00 (h) x 1.00 (d)

Meet the Author

Johan van Benthem is University Professor of Pure and Applied Logic at the University of
Amsterdam and Henry Waldgrave Stuart Professor of Philosophy at Stanford University. He is the author of Language in Action: Categories, Lambdas, and Dynamic Logic (MIT
Press), Exploring Logical Dynamics, Logical Dynamics of Information and
Interaction
, and other books.
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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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