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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.

03B53 Paraconsistent logics
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