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Self-Extensional Three-Valued Paraconsistent Logics

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Abstract

A logic \(\mathbf{L}\) is called self-extensional if it allows to replace occurrences of a formula by occurrences of an \(\mathbf{L}\)-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 \(\{\lnot ,\wedge ,\vee \}\) for which \(\vee \) is a disjunction, and \(\wedge \) is a conjunction. We also investigate the main properties of this logic, determine the expressive power of its language (in the three-valued context), and provide a cut-free Gentzen-type proof system for it.

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  1. School of Computer Science, Tel-Aviv University, Tel-Aviv, Israel

    Arnon Avron

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  1. Arnon Avron
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Correspondence to Arnon Avron.

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Avron, A. Self-Extensional Three-Valued Paraconsistent Logics. Log. Univers. 11, 297–315 (2017). https://doi.org/10.1007/s11787-017-0173-4

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  • DOI: https://doi.org/10.1007/s11787-017-0173-4

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