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2006 A Quasi-Discursive System $ND_2^+$
Janusz Ciuciura
Notre Dame J. Formal Logic 47(3): 371-384 (2006). DOI: 10.1305/ndjfl/1163775444


Discursive (or discussive) logic, D₂, 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 D₂ but used a translation function to express his philosophical and logical intuitions. Discursive logic was defined by an interpretation in the language of S₅ of Lewis. The aim of this paper is to present a modified system of the 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.


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Janusz Ciuciura. "A Quasi-Discursive System $ND_2^+$." Notre Dame J. Formal Logic 47 (3) 371 - 384, 2006.


Published: 2006
First available in Project Euclid: 17 November 2006

zbMATH: 1113.03022
MathSciNet: MR2264706
Digital Object Identifier: 10.1305/ndjfl/1163775444

Primary: 03B53

Rights: Copyright © 2006 University of Notre Dame


Vol.47 • No. 3 • 2006
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