Notre Dame Journal of Formal Logic

Revisiting Z

Mauricio Osorio, José Luis Carballido, and Claudia Zepeda


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.

Article information

Notre Dame J. Formal Logic, Volume 55, Number 1 (2014), 129-155.

First available in Project Euclid: 20 January 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: X001 Y002
Secondary: Z003

paraconsistent logic logic $\mathbb{Z}$ modal logic nonmonotonic reasoning


Osorio, Mauricio; Carballido, José Luis; Zepeda, Claudia. Revisiting $\mathbb{Z}$. Notre Dame J. Formal Logic 55 (2014), no. 1, 129--155. doi:10.1215/00294527-2377905.

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