Another Useful Four-Valued Logic
We propose a four-valued logic with intuitive semantics by the connectives that is useful for understanding the contradictions in knowledge representation. The intuitive semantics reflects that any assertion has dual character by whose information for or against the judgment. The four-valued logic is weakly paraconsistent and has the weak consistency to capture whether or not the contradictions are reconcilable with information. The four-valued logic is a normal extension of classical logic in a sense that it contains the schemata of classical axioms. We then propose an axiomatization of the four-valued logic. The soundness and completeness of the axiomatization with respect to the semantics are proved. The usefulness of the four-valued logic is discussed.
KeywordsFour-valued logic Bilattice Paraconsistency Weak consistency Conflation