Paraconsistent logic

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Paraconsistent logic is a type of non-classical logic that allows for the coexistence of contradictory statements without leading to a logical explosion, where anything can be proven true. Specifically, paraconsistent logic is the subfield of logic that is concerned with studying and developing "inconsistency-tolerant" systems of logic, purposefully excluding the principle of explosion.

Inconsistency-tolerant logics have been discussed since at least 1910 (and arguably much earlier, for example in the writings of Aristotle);^[1] however, the term paraconsistent ("beside the consistent") was first coined in 1976, by the Peruvian philosopher Francisco Miró Quesada Cantuarias.^[2] The study of paraconsistent logic has been dubbed paraconsistency,^[3] which encompasses the school of dialetheism.