Logic and Logical Philosophy 17 (4):305-320 (2008)
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| Abstract |
In [1] Béziau developed the paraconsistent logic Z, which is definitionally equivalent to the modal logic S5, and gave an axiomatization of the logic Z: the system HZ. In the present paper, we prove that some axioms of HZ are not independent and then propose another axiomatization of Z. We also discuss a new perspective on the relation between S5 and classical propositional logic with the help of the new axiomatization of Z. Then we conclude the paper by making a remark on the paraconsistency of HZ
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| Keywords | classical propositional logic modal logic S5 paraconsistent logic Z |
| Categories | (categorize this paper) |
| Reprint years | 2009 |
| DOI | 10.12775/LLP.2008.017 |
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References found in this work BETA
A Propositional Calculus for Inconsistent Deductive Systems.Stanisław Jaśkowski - 1999 - Logic and Logical Philosophy 7:35.
The Paraconsistent Logic Z. A Possible Solution to Jaśkowski's Problem.Jean-Yves Béziau - 2006 - Logic and Logical Philosophy 15 (2):99-111.
Citations of this work BETA
Revisiting $\mathbb{Z}$.Mauricio Osorio, José Luis Carballido & Claudia Zepeda - 2014 - Notre Dame Journal of Formal Logic 55 (1):129-155.
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