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We suggest a general formalism of four-valued reasoning, calledbiconsequence relations, intended to serve as a logical framework forreasoning with incomplete and inconsistent data. The formalism isbased on a four-valued semantics suggested by Belnap [3]. As for theclassical sequent calculus, any four-valued connective can be denedin biconsequence relations using suitable introduction and eliminationrules. In addition, various three-valued and partial logics are shownto be special ...

Biconsequence Relations: A Four-Valued Formalism of Reasoning with Inconsistency and Incompleteness