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  1. Modal Logic.Alexander Chagrov - 1997 - Oxford University Press.
    For a novice this book is a mathematically-oriented introduction to modal logic, the discipline within mathematical logic studying mathematical models of reasoning which involve various kinds of modal operators. It starts with very fundamental concepts and gradually proceeds to the front line of current research, introducing in full details the modern semantic and algebraic apparatus and covering practically all classical results in the field. It contains both numerous exercises and open problems, and presupposes only minimal knowledge in mathematics. A specialist (...)
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  • On the Strength and Scope of DLS.Willem Conradie - 2006 - Journal of Applied Non-Classical Logics 16 (3-4):279-296.
    We provide syntactic necessary and sufficient conditions on the formulae reducible by the second-order quantifier elimination algorithm DLS. It is shown that DLS is compete for all modal Sahlqvist and Inductive formulae, and that all modal formulae in a single propositional variable on which DLS succeeds are canonical.
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  • An Undecidable Problem in Correspondence Theory.L. A. Chagrova - 1991 - Journal of Symbolic Logic 56 (4):1261-1272.
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  • An Algebraic Theory of Normal Forms.Silvio Ghilardi - 1995 - Annals of Pure and Applied Logic 71 (3):189-245.
    In this paper we present a general theory of normal forms, based on a categorial result for the free monoid construction. We shall use the theory mainly for proposictional modal logic, although it seems to have a wider range of applications. We shall formally represent normal forms as combinatorial objects, basically labelled trees and forests. This geometric conceptualization is implicit in and our approach will extend it to other cases and make it more direct: operations of a purely geometric and (...)
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  • Elementary Canonical Formulae: Extending Sahlqvist’s Theorem.Valentin Goranko & Dimiter Vakarelov - 2006 - Annals of Pure and Applied Logic 141 (1):180-217.
    We generalize and extend the class of Sahlqvist formulae in arbitrary polyadic modal languages, to the class of so called inductive formulae. To introduce them we use a representation of modal polyadic languages in a combinatorial style and thus, in particular, develop what we believe to be a better syntactic approach to elementary canonical formulae altogether. By generalizing the method of minimal valuations à la Sahlqvist–van Benthem and the topological approach of Sambin and Vaccaro we prove that all inductive formulae (...)
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  • Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2002 - Cambridge University Press.
    This modern, advanced textbook reviews modal logic, a field which caught the attention of computer scientists in the late 1970's.
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  • The Computational Complexity of Hybrid Temporal Logics.C. Areces, P. Blackburn & M. Marx - 2000 - Logic Journal of the IGPL 8 (5):653-679.
    In their simplest form, hybrid languages are propositional modal languages which can refer to states. They were introduced by Arthur Prior, the inventor of tense logic, and played an important role in his work: because they make reference to specific times possible, they remove the most serious obstacle to developing modal approaches to temporal representation and reasoning. However very little is known about the computational complexity of hybrid temporal logics.In this paper we analyze the complexity of the satisfiability problem of (...)
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  • On Modal Μ-Calculus with Explicit Interpolants.G. D'Agostino & G. Lenzi - 2006 - Journal of Applied Logic 4 (3):256-278.
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