A new introduction to modal logic. (English) Zbl 0855.03002

Hughes, G. E.; Cresswell, M. J.

London: Routledge. x, 421 p. £13.99/pbk, £40.00/hbk (1996).

This book is intended to serve as a replacement for the authors’ earlier books “An introduction to modal logic” (1968; Zbl 0205.00503) and “A companion to modal logic” (1984; Zbl 0625.03005). It is a very elementary introduction to Kripke semantics of modal propositional and predicate logics. As its predecessors, this textbook deals with a few particular modal systems and shows how to establish their completeness with respect to Kripke or finite frames. Simple examples of incomplete logics are also presented.
The book is clearly and well written; it can be recommended as a textbook for beginners. It seems, however, that the level of concepts used in the book is too low (even such a basic notion as \(p\)-morphism is mentioned only in a footnote) to reflect the development of modal logic in the last 25 years.

Reviewer: M.Zakharyaschev (Berlin)

MSC:

03-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations
03B45	Modal logic (including the logic of norms)

Keywords:

propositional logic; predicate logic; Kripke semantics; textbook; frames; modal logic

Citations:

Zbl 0205.00503; Zbl 0625.03005