@article{Omori_Waragai_2009, title={On Béziau’s logic Z}, volume={17}, url={https://apcz.umk.pl/LLP/article/view/LLP.2008.017}, DOI={10.12775/LLP.2008.017}, abstractNote={In [1] Béziau developed the paraconsistent logic Z, which is definitionally equivalent to the modal logic S5 (cf. Remark 2.3), 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 (CPL) with the help of the new axiomatization of Z. Then we conclude the paper by making a remark on the paraconsistency of HZ.}, number={4}, journal={Logic and Logical Philosophy}, author={Omori, Hitoshi and Waragai, Toshiharu}, year={2009}, month={Mar.}, pages={305–320} }