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A quasi-discursive system $$ND_2^+$$. (English) Zbl 1113.03022
Summary: Discursive (or discussive) logic, $$D_2$$, introduced by Jaśkowski, is widely recognized as a first formal approach to paraconsistency. Jaśkowski applied a quite extraordinary technique at that time to describe his logic. He neither gave a set of the axiom schemata nor presented a direct semantics for $$D_2$$ but used a translation function to express his philosophical and logical intuitions. Discursive logic was defined by an interpretation in the language of $$S_5$$ of Lewis. The aim of this paper is to present a modified system of discursive logic that allows some of the weaker versions of Duns Scotus’s thesis to be valid. The initial idea is to consider a different characteristic of the connective of negation. We introduce both a direct semantics and an axiomatization of the new system, prove the key metatheorems, and describe labeled tableaux for the system.

##### MSC:
 03B53 Paraconsistent logics
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