Language in Action: Categories, Lambdas and Dynamic Logic

Softcover

ISBN 10: 0444548807 ISBN 13: 9780444548801

Publisher: North Holland, 2011

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.

From the Back Cover:

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 addendum 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.

About 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. E-mail: johan@fwi.uva.nl, johan@csli.stanford.edu