Paracomplete logics which are dual to the paraconsistent logics L3A and L3B

LANMR 2019: Proceedings of the 12th Latin American Workshop on Logic/Languages, Algorithms and New Methods of Reasoning (2020)
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Abstract

In 2016 Beziau, introduce a more restricted concept of paraconsistency, namely the genuine paraconsistency. He calls genuine paraconsistent logic those logic rejecting φ, ¬φ |- ψ and |- ¬(φ ∧ ¬φ). In that paper the author analyzes, among the three-valued logics, which of these logics satisfy this property. If we consider multiple-conclusion consequence relations, the dual properties of those above mentioned are: |- φ, ¬φ, and ¬(ψ ∨ ¬ψ) |- . We call genuine paracomplete logics those rejecting the mentioned properties. We present here an analysis of the three-valued genuine paracomplete logics.

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Marcelo E. Coniglio
University of Campinas

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References found in this work

Paraconsistent Logic: Consistency, Contradiction and Negation.Walter Carnielli & Marcelo Esteban Coniglio - 2016 - Basel, Switzerland: Springer International Publishing. Edited by Marcelo Esteban Coniglio.
Multiple Conclusion Logic.D. J. Shoesmith & Timothy Smiley - 1978 - Cambridge, England / New York London Melbourne: Cambridge University Press. Edited by T. J. Smiley.
Paraconsistent logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
Reasoning with logical bilattices.Ofer Arieli & Arnon Avron - 1996 - Journal of Logic, Language and Information 5 (1):25--63.

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