Language in Action: Categories, Lambdas and Dynamic Logic (Volume 130) (Studies in Logic and the Foundations of Mathematics, Volume 130)

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. Content: Edited by Page iii Copyright page Page iv Dedication Page v Preface Pages ix-x I Introduction Pages 1-33 II A Logical Perspective Pages 35-69 III Proof Theory Pages 71-109 IV Model Theory Pages 111-154 V Variations and Extensions Pages 155-183 VI Toward a Logic of Information Pages 185-270 VII A Tour of Basic Logic Pages 271-325 Bibliography Pages 327-344 Index Pages 345-349