Relevance logic

As Relevance logics a family of non-classical logics is referred to that work with a more restrictive implication than standard systems. The primary goal is usually to avoid the so-called paradoxes of material implication. The basic idea is always that the antecedent for the consequent to be "relevant" ( hence the name).

All relevance logics are para consistent, that is, in them the ex falso quodlibet shall not, by which it is possible in most standard systems, of two contradictory propositions A, ¬ A or from a contradiction A ∧ ¬ A infer any statement.