Language in action. Categories, lambdas and dynamic logic. (English) Zbl 0717.03001

van Benthem, Johan

Studies in Logic and the Foundations of Mathematics, 130. Amsterdam etc.: North-Holland. x, 349 p. (1991).

This book aims to set out the basic ideas of logicl syntax and semantics relating categorial grammar and lambda calculus, the former of which plays a prominent role in computational processing of natural languages, and the latter of which has a conspicuous relationship with the semantics of programming languages. The exposition has a considerably wide perspective, pertaining to mathematics, linguistics, and computer science, though the author’s concern lies more in a unifying logical treatment for a number of disciplines than in a thorough exploitation of each ingredient. He touches upon various logical paradigms such as relevant logic, modal logic, linear logic,... from a standpoint of information processing.

Reviewer: H.Nishimura

MSC:

03-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations
03B65	Logic of natural languages
03B40	Combinatory logic and lambda calculus
03B70	Logic in computer science
68T50	Natural language processing
68Q55	Semantics in the theory of computing
03B45	Modal logic (including the logic of norms)
03B47	Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)

Keywords:

dynamic logic; syntax; semantics; categorial grammar; lambda calculus; computational processing of natural languages; semantics of programming languages; relevant logic; modal logic; linear logic