Axiomatizing a Minimal Discussive Logic

Grigoriev, O.; Nasieniewski, M.; Mruczek-Nasieniewska, K.; Petrukhin, Y.; Shangin, V.

Авторы: Grigoriev Oleg, Nasieniewski Marek, Mruczek-Nasieniewska Krystyna, Petrukhin Yaroslav, Shangin Vasily
Журнал: Studia Logica
Том: 111
Номер: 5
Год издания: 2023
Издательство: Springer Nature
Местоположение издательства: Switzerland
Первая страница: 855
Последняя страница: 895
DOI: 10.1007/s11225-023-10042-9
Аннотация: In the paper we analyse the problem of axiomatizing the minimal variant of discussive logic denoted as D0. Our aim is to give its axiomatization that would correspond to a known axiomatization of the original discussive logic D2. The considered system is minimal in a class of discussive logics. It is defined similarly, as Jaśkowski’s logic D2 but with the help of the deontic normal logic D. Although we focus on the smallest discussive logic and its correspondence to D2, we analyse to some extent also its formal aspects, in particular its behaviour with respect to rules that hold for classical logic. In the paper we propose a deductive system for the above recalled discussive logic. While formulating this system, we apply a method of Newton da Costa and Lech Dubikajtis—a modified version of Jerzy Kotas’s method used to axiomatize D2. Basically the difference manifests in the result—in the case of da Costa and Dubikajtis, the resulting axiomatization is pure modus ponens-style. In the case of D0, we have to use some rules, but they are mostly needed to express some aspects of positive logic. D0 understood as a set of theses is contained in D2. Additionally, any non-trivial discussive logic expressed by means of Jaśkowski’s model of discussion, applied to any regular modal logic of discussion, contains D0.
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