 In this program, an agreed upon necessary (though, in general, not sufficient) condition for a conditional to be logically valid is that there be some connection between antecedent and consequent. Historically, this has often been phrased via a requirement called the Variable Sharing Property (VSP): \(A \rightarrow B\) is valid only when \(A\) and \(B\) share some sentential variable or parameter (cf. Anderson &amp; Belnap 1975: 32–3). VSP delivers hyperintensional distinctions: conditionals with (classically) impossible antecedents and necessary consequents are not all trivially valid or true. The infamous ex falso quodlibet, \((A \land \neg A) \rightarrow B\), for instance, fails (it’s not the case that anything is implied by a contradiction); whereas \((A \land \neg A) \rightarrow A\) holds in most mainstream relevant systems (plausibly, a conjunction relevantly implies its conjuncts).