The Ex Contradictione Quodlibet-rule of traditional logic claims that from false premises everything can be deducted. Paraconsistent Logic challenges this claim.

(Work in progress)

Quote: Logics in which it is generally false that contradictions imply any and every proposition. Contradictory statements (p·~p) are both true and false, as opposed to simply false. Hence the principle of excluded middle is affirmed, while the principle of non-contradiction denied. Paraconsistent logics can be "lived" if one vows to accept all truths, but does not insist on rejecting all falsehood. Paraconsistent logics do not hold that all paradoxes can be "solved" and urges that they be recognized as contradictions.