 One tradition concerns so-called relevant logics, designed to formulate a more demanding notion of implication than Lewis’s strict implication (cf. Meyer &amp; Routley 1973). The idea of relevant implication is based in large part on the idea that the antecedent and the consequent of an acceptable conditional \(A&gt;B\) must be connected in terms of topics. For example, a conditional of the form \((p \wedge \neg p) &gt; q\) need not be valid, despite having an impossible antecedent, since the consequent shares no content with the antecedent. Various constraints can be imposed on the idea of content-sharing, leading to various non-classical logics of so-called relevant implication (see Mares’s 2020 SEP entry on relevant logics for an overview, and Weiss 2019 on the use of analytic entailment to deal with Sextus’ so-called fourth conditional).