Open Access
2014 Revisiting Z
Mauricio Osorio, José Luis Carballido, Claudia Zepeda
Notre Dame J. Formal Logic 55(1): 129-155 (2014). DOI: 10.1215/00294527-2377905

Abstract

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.

Citation

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Mauricio Osorio. José Luis Carballido. Claudia Zepeda. "Revisiting Z." Notre Dame J. Formal Logic 55 (1) 129 - 155, 2014. https://doi.org/10.1215/00294527-2377905

Information

Published: 2014
First available in Project Euclid: 20 January 2014

zbMATH: 1326.03033
MathSciNet: MR3161417
Digital Object Identifier: 10.1215/00294527-2377905

Subjects:
Primary: X001 , Y002
Secondary: Z003

Keywords: logic $\mathbb{Z}$ , modal logic , nonmonotonic reasoning , paraconsistent logic

Rights: Copyright © 2014 University of Notre Dame

Vol.55 • No. 1 • 2014
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