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Title Many-dimensional modal logics : theory and applications / D.M. Gabbay [and others].

Imprint Amsterdam ; Boston : Elsevier North Holland, 2003.

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Location Call No. OPAC Message Status
 Axe Elsevier ScienceDirect Ebook  Electronic Book    ---  Available
Edition 1st ed.
Description 1 online resource (xviii, 747 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series Studies in logic and the foundations of mathematics, 0049-237X ; v. 148
Studies in logic and the foundations of mathematics ; v. 148.
Bibliography Includes bibliographical references (pages 685-723) and index.
Contents Part I: Introduction -- Chapter 1. Modal logic basics -- Chapter 2. Applied modal logic -- Chapter 3. Many-dimensional modal logic -- Part II: Fusions and products -- Chapter 4. Fusions of modal logics -- Chapter 5. Products of modal logics: introduction -- Chapter 6. Decidable products -- Chapter 7. Undecidable products -- Chapter 8. Higher-dimensional products -- Chapter 9. Variations on products -- Chapter 10. Intuitionistic modal logics -- Part III: First-order modal logic -- Chapter 11. Fragments of first-order temporal logics -- Chapter 12. Fragments of first-orfer dynamic and epistemic logics -- Part IV: Applications to knowledge representation and reasoning -- Chapter 13. Temporal epistemic logics -- Chapter 14. Modal description logics -- Chapter 15. Tableau decision algorithms for modal description logics -- Chapter 16. Spatio-temoral logics.
Summary Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects. To study the computational behaviour of many-dimensional modal logics is the main aim of this book. On the one hand, it is concerned with providing a solid mathematical foundation for this discipline, while on the other hand, it shows that many seemingly different applied many-dimensional systems (e.g., multi-agent systems, description logics with epistemic, temporal and dynamic operators, spatio-temporal logics, etc.) fit in perfectly with this theoretical framework, and so their computational behaviour can be analyzed using the developed machinery. We start with concrete examples of applied one- and many-dimensional modal logics such as temporal, epistemic, dynamic, description, spatial logics, and various combinations of these. Then we develop a mathematical theory for handling a spectrum of 'abstract' combinations of modal logics - fusions and products of modal logics, fragments of first-order modal and temporal logics - focusing on three major problems: decidability, axiomatizability, and computational complexity. Besides the standard methods of modal logic, the technical toolkit includes the method of quasimodels, mosaics, tilings, reductions to monadic second-order logic, algebraic logic techniques. Finally, we apply the developed machinery and obtained results to three case studies from the field of knowledge representation and reasoning: temporal epistemic logics for reasoning about multi-agent systems, modalized description logics for dynamic ontologies, and spatio-temporal logics. The genre of the book can be defined as a research monograph. It brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). On the other hand, well-known results from modal and first-order logic are formulated without proofs and supplied with references to accessible sources. The intended audience of this book is logicians as well as those researchers who use logic in computer science and artificial intelligence. More specific application areas are, e.g., knowledge representation and reasoning, in particular, terminological, temporal and spatial reasoning, or reasoning about agents. And we also believe that researchers from certain other disciplines, say, temporal and spatial databases or geographical information systems, will benefit from this book as well. Key Features: & bull; Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science & bull; Written by internationally leading researchers in the field of pure and applied logic & bull; Combines mathematical theory of modal logic and applications in artificial intelligence and computer science & bull; Numerous open problems for further research & bull; Well illustrated with pictures and tables.
Note Print version record.
Subject Modality (Logic)
Modalité (Logique)
PHILOSOPHY -- Logic.
Modality (Logic)
Modallogik
Modale logica.
Universele algebra.
Algebraïsche logica.
Added Author Gabbay, Dov M., 1945-
Other Form: Print version: Many-dimensional modal logics. 1st ed. Amsterdam ; Boston : Elsevier North Holland, 2003 0444508260 9780444508263 (DLC) 2004272978 (OCoLC)52567285
ISBN 9780444508263
0444508260
9780080535784 (electronic bk.)
008053578X (electronic bk.)
1281048518
9781281048516
Standard No. AU@ 000048130365
CHNEW 001005887
DEBBG BV036962270
DEBBG BV042317284
DEBSZ 276853725
DEBSZ 430442467
DEBSZ 482353139
NZ1 12433021
NZ1 15192845
DKDLA 820120-katalog:9910110531905765
AU@ 000059689381

 
    
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