A paraconsistent logic is a logical system that attempts to deal sensibly with contradictions. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing paraconsistent (or "inconsistency-tolerant") systems of logic. (The term will be used in both ways in this article.)
Inconsistency-tolerant logics have been around since at least 1910 (and arguably much earlier, for example in the writings of Aristotle); however, the term paraconsistent ("beyond the consistent") was not coined until 1976, by the Peruvian philosopher Francisco Miró Quesada.