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. Furmanowski, J. Kotas and N. (...) C. A. da Costa , G. Achtelik, L. Dubikajtus,E. Dudek and J. Konior , satisfying da Costa’s conditions, but they arerather looking very complicated and unnatural. An attempt is made to solveda Costa’s problem. The new axiomatization of D2 is proposed essentiallybased on da Costa’s-Doria axiomatization from 1995. (shrink)

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.

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.

. 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 shown that categorically the universe of universal logic turns out to be a topos and a paraconsistent complement topos. (shrink)

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 proposed. Some consequences of such an approach are investigated. (shrink)