Revisiting Z
Mauricio Osorio, José Luis Carballido, Claudia Zepeda · Notre Dame Journal of Formal Logic · 2014
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. Omori and Waragai proved that some axioms of HZ are not independent and then proposed another axiomatization for Z that includes two inference rules and helps to understand the relation between S5 and classical propositional logic. In the present paper, we analyze logic Z in detail; in the process we also construct a family of paraconsistent logics that are characterized by different properties that are relevant in the study of logics.