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  1. Remarks on Naive Set Theory Based on Lp.Hitoshi Omori - 2015 - Review of Symbolic Logic 8 (2):279-295.
    Dialetheism is the metaphysical claim that there are true contradictions. And based on this view, Graham Priest and his collaborators have been suggesting solutions to a number of paradoxes. Those paradoxes include Russell’s paradox in naive set theory. For the purpose of dealing with this paradox, Priest is known to have argued against the presence of classical negation in the underlying logic of naive set theory. The aim of the present paper is to challenge this view by showing that there (...)
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  • A Paraconsistent View on B and S5.Arnon Avron & Anna Zamansky - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 21-37.
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  • Classical Negation and Expansions of Belnap–Dunn Logic.Michael De & Hitoshi Omori - 2015 - Studia Logica 103 (4):825-851.
    We investigate the notion of classical negation from a non-classical perspective. In particular, one aim is to determine what classical negation amounts to in a paracomplete and paraconsistent four-valued setting. We first give a general semantic characterization of classical negation and then consider an axiomatic expansion BD+ of four-valued Belnap–Dunn logic by classical negation. We show the expansion complete and maximal. Finally, we compare BD+ to some related systems found in the literature, specifically a four-valued modal logic of Béziau and (...)
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  • N-Valued Maximal Paraconsistent Matrices.Adam Trybus - 2019 - Journal of Applied Non-Classical Logics 29 (2):171-183.
    ABSTRACTThe articles Maximality and Refutability Skura [. Maximality and refutability. Notre Dame Journal of Formal Logic, 45, 65–72] and Three-valued Maximal Paraconsistent Logics Skura and Tuziak [. Three-valued maximal paraconsistent logics. In Logika. Wydawnictwo Uniwersytetu Wrocławskiego] introduced a simple method of proving maximality of a given paraconsistent matrix. This method stemmed from the so-called refutation calculus, where the focus in on rejecting rather than accepting formulas. The article A Generalisation of a Refutation-related Method in Paraconsistent Logics Trybus [. A generalisation (...)
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  • Self-Extensional Three-Valued Paraconsistent Logics Have No Implications.Arnon Avron & Jean-Yves Beziau - 2017 - Logic Journal of the IGPL 25 (2):183-194.
    A proof is presented showing that there is no paraconsistent logics with a standard implication which have a three-valued characteristic matrix, and in which the replacement principle holds.
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  • Rexpansions of Nondeterministic Matrices and Their Applications in Nonclassical Logics.Arnon Avron & Yoni Zohar - 2019 - Review of Symbolic Logic 12 (1):173-200.
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  • Ideal Paraconsistent Logics.O. Arieli, A. Avron & A. Zamansky - 2011 - Studia Logica 99 (1-3):31-60.
    We define in precise terms the basic properties that an ‘ideal propositional paraconsistent logic’ is expected to have, and investigate the relations between them. This leads to a precise characterization of ideal propositional paraconsistent logics. We show that every three-valued paraconsistent logic which is contained in classical logic, and has a proper implication connective, is ideal. Then we show that for every n > 2 there exists an extensive family of ideal n -valued logics, each one of which is not (...)
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