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.

In 1995 N. C. A. da Costa and F. Doria proposed the modaltype elegant axiomatization of Jaśkowski's discussive logic D2. Yet his own problem which was formulated in 1975 in a following way: Is it possible to formulate natural and simple axiomatization for D2, employing classical disjunction and conjunction along with discussive implication and conjunction as the only primitive connectives?-still seems left open. The matter of fact is there are some axiomatizations of D2 proposed, e.g., by T. Furmanowski (1975), J. Kotas and N. C. A. da Costa (1979), G. Achtelik, L. Dubikajtus, E. Dudek and J. Konior (1981), satisfying da Costa's conditions, but they are rather looking very complicated and unnatural. An attempt is made to solve da Costa's problem. The new axiomatization of D2 is proposed essentially based on da Costa's-Doria axiomatization from 1995.

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