FRONTIERS OF THE DISCURSIVE LOGIC
Janusz Ciuciura · 2008
In a discussion, the participants state opinions. There is an additional assump- tion that each opinion (or view) is consistent in itself, but we cannot exclude the possibility that some opinions might be inconsistent with one another. This is the main idea behind Jaskowski's discursive logic D2. The year of 1977 was one of the crucial points in the development of D2. It was the year when Da Costa, Dubikajtis and Kotas published their papers on the axiomatization of the discursive logic. The axiomatization was recognized, ever since, as a first real axiomatization of D2. The aim of this paper is to show that the claim is mistaken and next to introduce a correct axiomatization of Jaskowski's D2. We also present a direct (Kripke-type) semantics for the logic and prove some key metatheorems.