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

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)