**Topic:**

**PARACONSISTENCY**

## ON THE DA COSTA, DUBIKAJTIS AND KOTAS' SYSTEM OF THE DISCURSIVE LOGIC, D

*_{2}

By Janusz CiuciuraIn the late forties, Stanislaw Jaskowski published two papers on the

discursive(ordiscussive)sentential calculus, D. He provided a definition of it by an interpretation in the language of S5 of Lewis. The known axiomatization of D_{2}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_{2}realJa?›kowski's calculus. In fact, they built a new system, D*for short, that differs from D_{2}in many respects. The aim of this paper is to introduce a direct_{2}Kripke-typesemantics 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, D, paraconsistent logic, labelled tableaux._{2}

Published inLogic and Logical Philosophy, Volume 14 (2005), 235-252