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7Aristotle on the relation between logic and ontologyRUDN Journal of Philosophy 21 (2): 192-198. 2017.
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Vasiliev’s Clue to Mourdoukhay-Boltovskoy’s HypersyllogisticIn Dmitry Zaitsev & Vladimir Markin (eds.), The Logical Legacy of Nikolai Vasiliev and Modern Logic, Springer Verlag. 2017.
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43The Bibinary Semantics for R and Lℵ0Bulletin of the Section of Logic 15 (3): 109-114. 1986.The ternary, not binary, Kripke-type relation on a set of possible worlds is an essential part of the semantics of entailment by Routley-Meyer [2]. The unpopularity of such approach among many logicians is due to its intuitive vague content and complexity. An attempt is made to use not one ternary relation but two binary relations and necessity of bibinarness is demonstrated. It is shown that both semantics are equal hence the soundness and completeness of the system R of entailment can be estab…Read more
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17Implicative Logics, Sequential Deductive Systems and Exponential MulticategoriesBulletin of the Section of Logic 29 (1-2): 13-25. 2000.
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248In Memoriam: Vladimir Aleksandrovich Smirnov 1931–1996Bulletin of Symbolic Logic 2 (3): 371-372. 1996.
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67The completeness of the factor semantics for łukasiewicz's infinite-valued logicsStudia Logica 52 (1). 1993.In [12] it was shown that the factor semantics based on the notion ofT-F-sequences is a correct model of the ukasiewicz's infinite-valued logics. But we could not consider some important aspects of the structure of this model because of the short size of paper. In this paper we give a more complete study of this problem: A new proof of the completeness of the factor semantic for ukasiewicz's logic using Wajsberg algebras [3] (and not MV-algebras in [1]) and Symmetrical Heyting monoids [7] is pro…Read more
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6Non-Elementary Exegesis of Twardowski's Theory of PresentationIn Katarzyna Kijania-Placek & Jan Woleński (eds.), The Lvov-Warsaw school and contemporary philosophy, Kluwer Academic Publishers. pp. 153--167. 1998.
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54Antidiodorean logics and the brentano-husserl's conception of timeAxiomathes 4 (3): 373-388. 1993.In some systems of Legniewskian Ontology were introduced as a toolkit for Husserl's and Meinong's theory of objects. Here such consi- deration is extended to Brentano-Husserl's theory of time. So-called antidiodo- rean logics are used as the foundations of the approach undertaken.
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T-f-toposes For Lukasiewicz's Infinite-valued LogicsBulletin of the Section of Logic 17 (3-4): 182-187. 1988.The interpretation of the Lukasiewicz’s ℵ0-infinite-valued logic Lℵ0 in topoi is proposed. The construction of the T-F-topos of functors Set Σ is defined by means of infinite T-F-sequences and then it is used for the interpretation of Lℵ0 in this topos. The equivalency of factor-semantics and T-F-toposes semantics for Lℵ0 is proved
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6Categorial semantics for ajdukievvicz-Lambek calculusIn Vito Sinisi & Jan Woleński (eds.), The heritage of Kazimierz Ajdukiewicz, Rodopi. pp. 40--321. 1995.
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85Paraconsistency in Categories: Case of Relevance LogicStudia Logica 98 (3): 429-443. 2011.Categorical-theoretic semantics for the relevance logic is proposed which is based on the construction of the topos of functors from a relevant algebra (considered as a preorder category endowed with the special endofunctors) in the category of sets Set. The completeness of the relevant system R of entailment is proved in respect to the semantic considered
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53Structuring the universe of universal logicLogica Universalis 1 (2): 277-294. 2007.. How, why and what for we should combine logics is perfectly well explained in a number of works concerning this issue. But the interesting question seems to be the nature and the structure of the general universe of possible combinations of logical systems. Adopting the point of view of universal logic in the paper the categorical constructions are introduced which along with the coproducts underlying the fibring of logics describe the inner structure of the category of logical systems. It is…Read more
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61A new axiomatization of Jaśkowski's discussive logicLogic and Logical Philosophy 9 (n/a): 35. 2001.In 1995 N. C. A. da Costa and F. Doria proposed the modaltype elegant axiomatization of Jaśkowski’s discussive logic D2. Yet his ownproblem which was formulated in 1975 in a following way: Is it possible toformulate natural and simple axiomatization for D2, employing classical disjunction and conjunction along with discussive implication and conjunctionas the only primitive connectives? — still seems left open. The matter of factis there are some axiomatizations of D2 proposed, e.g., by T. Furma…Read more
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