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37Review: Maarten Marx, Yde Venema, Multi-Dimensional Modal Logic (review)Bulletin of Symbolic Logic 6 (4): 490-495. 2000.
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26Intuitive semantics for some three-valued logics connected with information, contrariety and subcontrarietyStudia Logica 48 (4). 1989.Four known three-valued logics are formulated axiomatically and several completeness theorems with respect to nonstandard intuitive semantics, connected with the notions of information, contrariety and subcontrariety is given.
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33An application of Rieger-Nishimura formulas to the intuitionistic modal logicsStudia Logica 44 (1). 1985.The main results of the paper are the following: For each monadic prepositional formula which is classically true but not intuitionistically so, there is a continuum of intuitionistic monotone modal logics L such that L+ is inconsistent.There exists a consistent intuitionistic monotone modal logic L such that for any formula of the kind mentioned above the logic L+ is inconsistent.
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68Non-Classical Negation in the Works of Helena Rasiowa and Their Impact on the Theory of NegationStudia Logica 84 (1): 105-127. 2006.The paper is devoted to the contributions of Helena Rasiowa to the theory of non-classical negation. The main results of Rasiowa in this area concerns–constructive logic with strong (Nelson) negation.
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32A Proximity Approach to Some Region-Based Theories of SpaceJournal of Applied Non-Classical Logics 12 (3-4): 527-559. 2002.This paper is a continuation of [VAK 01]. The notion of local connection algebra, based on the primitive notions of connection and boundedness, is introduced. It is slightly different but equivalent to Roeper's notion of region-based topology [ROE 97]. The similarity between the local proximity spaces of Leader [LEA 67] and local connection algebras is emphasized. Machinery, analogous to that introduced by Efremovi?c [EFR 51],[EFR 52], Smirnov [SMI 52] and Leader [LEA 67] for proximity and local…Read more
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413Elementary canonical formulae: extending Sahlqvist’s theoremAnnals of Pure and Applied Logic 141 (1): 180-217. 2006.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…Read more
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16Rough polyadic modal logicsJournal of Applied Non-Classical Logics 1 (1): 9-35. 1991.Rough polyadic modal logics, introduced in the paper, contain modal operators of many arguments with a relational semantics, based on the Pawlak's rough set theory. Rough set approach is developed as an alternative to the fuzzy set philosophy, and has many applications in different branches in Artificial Intelligence and theoretical computer science.
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36Lattices related to Post algebras and their applications to some logical systemsStudia Logica 36 (1-2): 89-107. 1977.
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9An application of the Rieger-Nishimura formulas to the intuitionistic modal logicsBulletin of the Section of Logic 13 (3): 120-122. 1984.We proved in [1] that there exist a continuum consistent monotone intuitionistic modal logics which do not admit the law of the excluded middle p ∨ ¬p. Rieger [2] and Nishimura [3] introduced a sequence of formulas ϕ0, ϕ1, . . . , ϕω of one variable p such that for any intuitionistic formula ϕi containing only the variable p there exists a formula ϕi from this sequence equivalent to ϕ in the intuitionistic propositional logic . In [5] V. Tselkov has proved that for each i ≥ 4 there exist at leas…Read more
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21Dynamic extensions of arrow logicAnnals of Pure and Applied Logic 127 (1-3): 1-15. 2004.This paper is devoted to the complete axiomatization of dynamic extensions of arrow logic based on a restriction of propositional dynamic logic with intersection. Our deductive systems contain an unorthodox inference rule: the inference rule of intersection. The proof of the completeness of our deductive systems uses the technique of the canonical model
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57Nelson's Negation on the Base of Weaker Versions of Intuitionistic NegationStudia Logica 80 (2): 393-430. 2005.Constructive logic with Nelson negation is an extension of the intuitionistic logic with a special type of negation expressing some features of constructive falsity and refutation by counterexample. In this paper we generalize this logic weakening maximally the underlying intuitionistic negation. The resulting system, called subminimal logic with Nelson negation, is studied by means of a kind of algebras called generalized N-lattices. We show that generalized N-lattices admit representation form…Read more
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50Dynamic ModalitiesStudia 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
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296Hyperboolean Algebras and Hyperboolean Modal LogicJournal 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
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18Representation Theorems for Semi-Boolean Algebras and Semantics for Heyting-Brower Predicate LogicProceedings of the XVth World Congress of Philosophy 5 127-130. 1975.