Dialetheism http://plato.stanford.edu/entries/dialetheism/
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.
Paraconsistent Logic http://plato.stanford.edu/entries/logic-paraconsistent/
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.