Categorical consequence for paraconsistent logic

In Walter Carnielli (ed.), Paraconsistency:the logical way to the inconsistent. pp. 141-150 (2002)
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Abstract
Consequence rleations over sets of "judgments" are defined by using "overdetermined" as well as "underdetermined" valuations. Some of these relations are shown to be categorical. And generalized soundness and completeness results are given for both multiple and single conclusion consequence relations.
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