A dialetheia is a true contradiction, a statement, A, such that both it and its negation, A, are true. Hence, dialeth(e)ism is the view that there are true contradictions. Dialetheism opposes the so-called Law of Non-Contradiction. By Graham Priest, from the Stanford Encyclopedia.
The development of paraconsistent logic was initiated in order to challenge the logical principle that anything follows from contradictory premises, ex contradictione quodlibet. By Koji Tanaka, from the Stanford Encyclopedia.