Principle of explosion

The principle of explosion is a logical rule of inference. According to the rule, from a set of premises in which a sentence "A" and its negation "-A" are both true (i.e., a contradiction is true), any sentence "B" may be inferred. It is also known by its Latin name ex contradictione quodlibet, meaning from a contradiction anything follows, or ECQ for short. Since a contradiction is always false, another Latin term is ex falso quodlibet. In layman's terms, if you start with two contradictory premises, you can actually deduce literally anything.

Classical logic accepts the principle of explosion; but in paraconsistent logic it is rejected. It is also rejected in relevance logic, since relevance logic is based on the competing principle that the premises must be relevant to the conclusion. (All relevance logics are paraconsistent, but not all paraconsistent logics are relevant.)