Many-dimensional modal logics : theory and applications / D.M. Gabbay, A. Kurucz, F. Wolter,... [et al.]

Auteur secondaire : Gabbay, Dov M., 1945-, Editeur scientifique • Kurucz, György, Editeur scientifique • Wolter, Frank, 1972-, Editeur scientifiqueType de document : MonographieCollection : Studies in logic and the foundations of mathematics, 148Langue : anglais.Pays: Pays Bas.Éditeur : Amsterdam : Elsevier, 2003Description : 1 vol. (747 p.) : ill. ; 23 cmISBN: 9780444508263.ISSN: 0049-237X.Bibliographie : Bibliogr. p. 685-723. Index.Sujet MSC : 03B45, General logic, Modal logic (including the logic of norms)
03B70, General logic, Logic in computer science
03B42, General logic, Logics of knowledge and belief (including belief change)
03B44, General logic, Temporal logic
03B25, General logic, Decidability of theories and sets of sentences
68T30, Computer science - Artificial intelligence, Knowledge representation
En-ligne : Zentralblatt | MathSciNet
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Bibliogr. p. 685-723. Index

... 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. ... (Zentralblatt)

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