ON THE DA COSTA, DUBIKAJTIS AND KOTAS' SYSTEM OF THE DISCURSIVE LOGIC, D*2
By Janusz Ciuciura
In the late forties, Stanislaw Jaskowski published two papers on the discursive (or discussive) sentential calculus, D2. He provided a definition of it by an interpretation in the language of S5 of Lewis. The known axiomatization of D2 with discursive connectives as primitives was introduced by da Costa, Dubikajtis and Kotas in 1977. It turns out, however, that one of the axioms they used is not a thesis of the real Ja?›kowski's calculus. In fact, they built a new system, D*2 for short, that differs from D2 in many respects. The aim of this paper is to introduce a direct Kripke-type semantics for the system, axiomatize it in a new way and prove soundness and completeness theorems. Additionally, we present labeled tableaux for D*2.
Keywords: discursive (discussive) logic, D2, paraconsistent logic, labelled tableaux.
Published in Logic and Logical Philosophy, Volume 14 (2005), 235-252