A new axiomatization of Jaśkowski's discussive logic

Vladimir L. Vasyukov

DOI: http://dx.doi.org/10.12775/LLP.2001.003

Abstract


In 1995 N.C.A. da Costa and F. Doria proposed the modal-type 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 D 2 is proposed essentially based on da Costa’s-Doria axiomatization from 1995.

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References


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