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| LANGUAGE IN ACTION, 130
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 Categories, Lambdas and Dynamic Logic
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By
J. van Benthem, University of Amsterdam, Institute for Logic, Language and Computation, Amsterdam, The Netherlands
Included in series
Studies in Logic and the Foundations of Mathematics, 130
Description
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.
Contents
Introduction.
Two Traditions. Lambda Calculus and Theory of Types. Categorial Grammar.
A Logical Perspective.
The Hierarchy
of Implicational Logics. Proofs, Terms, and Meanings.
Proof Theory.
Exploring Categorial Deduction. Cut Elimination and Decidability.
Recognizing Power.
Model Theory.
Enumerating Readings. Computing Denotational Constraints. Boolean Structure.
Variations and
Extensions.
Intensionality. Variable Polymorphism and Higher Type Theories.
Towards a Logic of Information.
Language Families.
Modal Logic of Information Patterns. Relational Algebra of Control. Dynamic Logic.
A Tour of Basic Logic.
Bibliography. Index.
Bibliographic & ordering Information
Hardbound, publication date: FEB-1991
ISBN-13: 978-0-444-89000-9
ISBN-10: 0-444-89000-9
Imprint: NORTH-HOLLAND
Price: Order form
EUR 106
USD 121
GBP 71
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Last update: 29 Aug 2008
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