Logica Universalis 5 (1):165-176 (2011)

Does there exist any equivalence between the notions of inconsistency and consequence in paraconsistent logics as is present in the classical two valued logic? This is the key issue of this paper. Starting with a language where negation ( ${\neg}$ ) is the only connective, two sets of axioms for consequence and inconsistency of paraconsistent logics are presented. During this study two points have come out. The first one is that the notion of inconsistency of paraconsistent logics turns out to be a formula-dependent notion and the second one is that the characterization (i.e. equivalence) appears to be pertinent to a class of paraconsistent logics which have double negation property
Keywords Paraconsistent logic  non-explosiveness  inconsistency  double-negation
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DOI 10.1007/s11787-011-0029-2
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References found in this work BETA

Investigations Into Logical Deduction.Gerhard Gentzen - 1964 - American Philosophical Quarterly 1 (4):288 - 306.
Natural 3-Valued Logics—Characterization and Proof Theory.Arnon Avron - 1991 - Journal of Symbolic Logic 56 (1):276-294.
Star and Perp: Two Treatments of Negation.J. Michael Dunn - 1993 - Philosophical Perspectives 7:331-357.

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