 Both statements are such that the probability of the consequent given the antecedent is high. However, in (8)-b the antecedent does not increase the probability of the consequent, it is irrelevant in that sense, and the conditional may be called a “non-interference conditional”. Douven (2016) defines validity in terms of acceptability-preservation according to the EST criterion, for all thresholds \(t\in [0.5, 1)\). The resulting logic is weak, in particular it violates Modus Ponens, RW, AND, CMon, Cut, OR and Contraposition. Douven establishes the validity and invalidity of specific principles (see Douven 2016: Theorem 5.2.1), but a sound and complete axiomatization of his logic is still an open problem.