Full Idea
Priest and Routley have developed paraconsistent relevant logic. 'Relevant' logics insist on there being some sort of connection between the premises and the conclusion of an argument. 'Paraconsistent' logics allow contradictions.
Gist of Idea
A logic is 'relevant' if premise and conclusion are connected, and 'paraconsistent' allows contradictions
Source
report of Graham Priest (works [1998]) by Michèle Friend - Introducing the Philosophy of Mathematics 6.8
Book Reference
Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.160
A Reaction
Relevance blocks the move of saying that a falsehood implies everything, which sounds good. The offer of paraconsistency is very wicked indeed, and they are very naughty boys for even suggesting it.