On the strongest three-valued paraconsistent logic contained in classical logic

Por • 12 oct, 2018 • Sección: Opinion

A. Middelburg

LP⊃,F is a three-valued paraconsistent propositional logic which is essentially the same as J3. It has most properties that have been proposed as desirable properties of a reasonable paraconsistent propositional logic. However, it follows easily from already published results that there are exactly 8192 different three-valued paraconsistent propositional logics that have the properties concerned. In this note, properties concerning the logical equivalence relation of a logic are used to distinguish LP⊃,F from the others. As one of the bonuses of focussing on the logical equivalence relation, it is found that only 32 of the 8192 logics have a logical equivalence relation that satisfies the identity, annihilation, idempotent, and commutative laws for conjunction and disjunction.

arXiv:1702.03414v2 [cs.LO] 

Logic in Computer Science (cs.LO); Logic (math.LO)

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