Notre Dame Journal of Formal Logic 47 (3):371-384 (2006)

Janusz Ciuciura
University of Lodz
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
Keywords discursive (discussive) logic   D2   paraconsistent logic
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DOI 10.1305/ndjfl/1163775444
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References found in this work BETA

On the Theory of Inconsistent Formal Systems.Newton C. A. Costa - 1972 - Recife, Universidade Federal De Pernambuco, Instituto De Matemática.
On the Theory of Inconsistent Formal Systems.Newton C. A. da Costa - 1974 - Notre Dame Journal of Formal Logic 15 (4):497-510.
Paraconsistent Logic From a Modal Viewpoint.Jean-Yves Béziau - 2005 - Journal of Applied Logic 3 (1):7-14.

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