Logic and Logical Philosophy 17 (4):305-320 (2008)

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
Keywords classical propositional logic  modal logic S5  paraconsistent logic Z
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Reprint years 2009
DOI 10.12775/LLP.2008.017
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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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