On the strongest three-valued paraconsistent logic contained in classical logic and its dual

摘要

LP$^{supset,mathsf{F}}$ is a three-valued paraconsistent propositionallogic which is essentially the same as J3. It has most properties that havebeen proposed as desirable properties of a reasonable paraconsistentpropositional logic. However, it follows easily from already published resultsthat there are exactly 8192 different three-valued paraconsistent propositionallogics that have the properties concerned. In this note, properties concerningthe logical equivalence relation of a logic are used to distinguishLP$^{supset,mathsf{F}}$ from the others. As one of the bonuses of focussingon the logical equivalence relation, it is found that only 32 of the 8192logics have a logical equivalence relation that satisfies the identity,annihilation, idempotent, and commutative laws for conjunction and disjunction.