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Dimiter Vakarelov

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  •  117
    Dynamic Modalities
    Studia Logica 100 (1-2): 385-397. 2012.
    A new modal logic containing four dynamic modalities with the following informal reading is introduced: $${\square^\forall}$$ – always necessary , $${\square^\exists}$$ – sometimes necessary , and their duals – $${\diamondsuit^\forall}$$ – always possibly , and $${\diamondsuit^\exists}$$ – sometimes possibly . We present a complete axiomatization with respect to the intended formal semantics and prove decidability via fmp
    Logic and Philosophy of LogicModal and Intensional Logic
  •  970
    Hyperboolean Algebras and Hyperboolean Modal Logic
    with Valentin Goranko
    Journal of Applied Non-Classical Logics 9 (2): 345-368. 1999.
    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 i…Read more
    Modal LogicSemantics for Modal Logic
  •  107
    Many-dimensional arrow logics
    Journal of Applied Non-Classical Logics 6 (4): 303-345. 1996.
    ABSTRACT The notion of n-dimensional arrow structure is introduced, which for n = 2 coincides with the notion of directed multi-graph. In part I of the paper several first-order and modal languages connected with arrow structures are studied and their expressive power is compared. Part II is devoted to the axiomatization of some arrow logics. At the end some further perspectives of ?arrow approach? are discussed
  •  103
    A duality between Pawlak's knowledge representation systems and bi-consequence systems
    Studia Logica 55 (1). 1995.
    A duality between Pawlak's knowledge representation systems and certain information systems of logical type, called bi-consequence systems is established. As an application a first-order characterization of some informational relations is given and a completeness theorem for the corresponding modal logic INF is proved. It is shown that INF possesses finite model property and hence is decidable.
    Logic and Philosophy of Logic