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Two Genuine 3-Valued Paraconsistent Logics

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Towards Paraconsistent Engineering

Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 110))

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Abstract

In this paper we present two genuine three-valued paraconsistent logics, i.e. logics obeying neither \(p, \lnot p \vdash q\) nor \(\vdash \lnot (p \wedge \lnot p)\). We study their basic properties and their relations with other paraconsistent logics, in particular da Costa’s paraconsistent logics C1 and its extension \(C1+\).

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Dedicated to Jair Minoro Abe for his 60th birthday

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Notes

  1. 1.

    In [11] we have used k+ because we were also examining the possibilities where the third value was undesignated, using the notation k–.

  2. 2.

    \(\copyright \) can be implication. In the present paper we are studying logics without implication, so we are comparing these logics with the fragment of C1 without implication.

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Acknowledgments

This paper was written during a stay at University of Tel Aviv within the GeTFun exchange prorgram—Marie Curie project PIRSES-GA-2012-318986 funded by EU-FP7. Thanks to Arnon Avron for his useful comments.

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Authors and Affiliations

  1. UFRJ—Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

    Jean-Yves Beziau

  2. CNPq—Brazilian Research Council, Rio de Janeiro, Brazil

    Jean-Yves Beziau

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  1. Jean-Yves Beziau
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Correspondence to Jean-Yves Beziau .

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  1. Kawasaki, Japan

    Seiki Akama

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Beziau, JY. (2016). Two Genuine 3-Valued Paraconsistent Logics. In: Akama, S. (eds) Towards Paraconsistent Engineering. Intelligent Systems Reference Library, vol 110. Springer, Cham. https://doi.org/10.1007/978-3-319-40418-9_4

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  • DOI: https://doi.org/10.1007/978-3-319-40418-9_4

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