4 found
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  1.  29
    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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  2.  38
    Sahlqvist Formulas Unleashed in Polyadic Modal Languages.Valentin Goranko & Dimiter Vakarelov - 2002 - In Frank Wolter, Heinrich Wansing, Maarten de Rijke & Michael Zakharyaschev (eds.), Advances in Modal Logic, Volume 3. World Scientific. pp. 221-240.
    We propose a generalization of Sahlqvist formulae to polyadic modal languages by representing modal polyadic languages in a combinatorial style and thus, in particular, developing what we believe to be the right approach to Sahlqvist formulae at all. The class of polyadic Sahlqvist formulae PSF defined here expands essentially the so far known one. We prove first-order definability and canonicity for the class PSF.
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  3.  38
    Hyperboolean Algebras and Hyperboolean Modal Logic.Valentin Goranko & Dimiter Vakarelov - 1999 - Journal of Applied Non-Classical Logics 9 (2):345-368.
    Hyperboolean algebras are Boolean algebras with operators, constructed as algebras of complexes (or, power structures) of Boolean algebras. They provide an algebraic semantics for a modal logic (called here a {\em hyperboolean modal logic}) with a Kripke semantics accordingly based on frames in which the worlds are elements of Boolean algebras and the relations correspond to the Boolean operations. We introduce the hyperboolean modal logic, give a complete axiomatization of it, and show that it lacks the finite model property. The (...)
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  4.  17
    Modal Logic and Universal Algebra I: Modal Axiomatizations of Structures.Valentin Goranko & Dimiter Vakarelov - 2000 - In Michael Zakharyaschev, Krister Segerberg, Maarten de Rijke & Heinrich Wansing (eds.), Advances in Modal Logic, Volume 2. CSLI Publications. pp. 265-292.
    We study the general problem of axiomatizing structures in the framework of modal logic and present a uniform method for complete axiomatization of the modal logics determined by a large family of classes of structures of any signature.
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