Mathematical Logic Quarterly 52 (5):478-493 (2006)

Abstract
We introduce a family of matrices that define logics in which paraconsistency and/or paracompleteness occurs only at the level of literals, that is, formulas that are propositional letters or their iterated negations. We give a sound and complete axiomatization for the logic defined by the class of all these matrices, we give conditions for the maximality of these logics and we study in detail several relevant examples
Keywords Paraconsistency  Leibniz relation‐operator  paracompleteness  logical matrix
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DOI 10.1002/malq.200510044
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Natural 3-Valued Logics—Characterization and Proof Theory.Arnon Avron - 1991 - Journal of Symbolic Logic 56 (1):276-294.

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