Many-dimensional modal logics: theory and applications
type: Item
instance of: scholarly article
title: Many-dimensional modal logics: theory and applications
zbMATH Open document ID: 1051.03001
published in: Studies in Logic and the Foundations of Mathematics
publication date: 2004-02-17T00:00:00Z
review text: Many-dimensional modal logics result from combining different kinds of modal logical systems, each one of which involves a dimension that the other system(s) does (do) not involve, as, for instance, the logical systems yielded by mixing epistemic logic with temporal and/or spatial logic. This book is a research monograph on the construction of such modal logics, their properties with respect to their component logics (e.g., completeness, decidability and computational complexity) as well as directions of future investigations. The book mainly aims at researchers who use logic in computer science and artificial intelligence, but there are many parts of the book which would be of interest for pure logicians. The methods employed are basically semantical. The book initially presents the motivation, syntax, semantics and applications of basic propositional modal logic. The semantic systems characterized are constituted by possible world semantic frames and models, though a brief description of algebraic semantics is also offered. Applications of basic modal logic include temporal logic, interval temporal logic, epistemic logic, dynamic logic, description logic, spatial logic and intuitionistic logic. The authors prove several theorems concerning the computational reductions (more precisely, polynomial reductions) between these different logics. We should note that first-order modal logic is not dealt with in this introductory part of the book but rather in later chapters, extensively and within the context of many-dimensional logics. In this connection, we should mention that the authors present a number of recent results concerning undecidable as well as decidable and axiomatizable fragments of first-order modal and temporal logics. And for several of these decidable fragments the authors determine their computational complexity. Following the exposition of basic material, the authors consider two ways of constructing many-dimensional logic, namely: by fusions and by p…
Mathematics Subject Classification ID: 03-02
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03B70
Mathematics Subject Classification ID: 03B42
Mathematics Subject Classification ID: 03B44
Mathematics Subject Classification ID: 03B20
Mathematics Subject Classification ID: 03B25
Mathematics Subject Classification ID: 68T30
zbMATH DE Number: 2043957
zbMATH Keywords: semantics for many-dimensional modal logics
zbMATH Keywords: computational complexity of modal logics
zbMATH Keywords: decidability of modal logics
zbMATH Keywords: undecidable modal logics
author: Dov Gabbay
author: Agi Kurucz
author: F. Wolter
author: Michael Zakharyaschev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2043957