Many-Dimensional Modal Logics
Theory and Applications
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Many-Dimensional Modal Logics by Dov M. Gabbay
Book DescriptionModal 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 include: integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science; written by internationally leading researchers in the field of pure and applied logic; combines mathematical theory of modal logic and applications in artificial intelligence and computer science; numerous open problems for further research; and well illustrated with pictures and tables.
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Book DetailsISBN: 9780444508263
(229mm x 166mm x 34mm)
Publisher: Elsevier Science & Technology
Publish Date: 21-Oct-2003
Country of Publication: United States
Books By Author Dov M. Gabbay
Philosophy of Statistics, Hardback (May 2011)
Statisticians and philosophers of science have many common interests but restricted communication with each other. This book provides research in the area of Philosophy of Statistics. It presents work in the field without bias toward any particular statistical paradigm.
Inductive Logic, Hardback (May 2011)
Covers the rich history of scientific turning points in Inductive Logic, including probability theory and decision theory. This book is suitable for senior undergraduates, graduate students and researchers in the history of logic, and the history of philosophy.
Logic, Hardback (June 2010)
Brings together the development of logic in modern techniques of historical and interpretative scholarship. This title covers in depth the notion of logical consequence. It discusses the central concept in logic of modality.
Quantification in Nonclassical Logic, Hardback (June 2009)» View all books by Dov M. Gabbay
Quantification and modalities have always been topics of great interest for logicians. These two themes emerged from philosophy and language in ancient times. This title emphasises on model-theoretic and it concentrates on descriptions of different sound semantics and completeness problem.
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Author Biography - Dov M. Gabbay
Dov M. Gabbay is Augustus De Morgan Professor Emeritus of Logic at the Group of Logic, Language and Computation, Department of Computer Science, King's College London. He has authored over four hundred and fifty research papers and over thirty research monographs. He is editor of several international Journals, and many reference works and Handbooks of Logic.
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