 Disjunctive Syllogism (DS) states that we can infer \(\psi\) from \( (\phi \vee \psi) \) and \(\neg \phi\). DS, which is valid in classical logic, but also in intuitionistic logic and in the multi-valued logics discussed in the previous section (with the exception of PL), has however been rejected in relevance logics (Anderson and Belnap 1962, 1975). Relevance logics are non-classical logical systems developed to avoid the paradoxes of material and strict implication (see the entry on  relevance logic).  These are classically valid principles, like \(p \to (q \vee \neg q)\), which however strike us as counterintuitive. This is so because, according to the relevantist, they involve a fallacy of relevance: in these cases the antecedent is typically irrelevant to the consequent. Belnap’s formal criteria of relevance (also known as variable sharing principle) is that in any provable implication, the antecedent and the consequent should share at least one propositional variable, and that no inference can be shown valid if the premises and conclusion do not share at least one propositional variable.