Logica Universalis 11 (3):297-315 (2017)

Abstract
A logic \ is called self-extensional if it allows to replace occurrences of a formula by occurrences of an \-equivalent one in the context of claims about logical consequence and logical validity. It is known that no three-valued paraconsistent logic which has an implication can be self-extensional. In this paper we show that in contrast, there is exactly one self-extensional three-valued paraconsistent logic in the language of \ for which \ is a disjunction, and \ is a conjunction. We also investigate the main properties of this logic, determine the expressive power of its language, and provide a cut-free Gentzen-type proof system for it.
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DOI 10.1007/s11787-017-0173-4
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References found in this work BETA

The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
On the Theory of Inconsistent Formal Systems.Newton C. A. Costa - 1972 - Recife, Universidade Federal De Pernambuco, Instituto De Matemática.
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A Calculus for Antinomies.F. G. Asenjo - 1966 - Notre Dame Journal of Formal Logic 16 (1):103-105.
A Paraconsistent 3-Valued Logic Related to Godel Logic G3.G. Robles & J. M. Mendez - 2014 - Logic Journal of the IGPL 22 (4):515-538.

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Citations of this work BETA

Compositional Meaning in Logic.Carlos Caleiro & Luca Viganò - 2017 - Logica Universalis 11 (3):283-295.

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