Cancellation, negation, and rejection

•We diagnose whether the Relevance Effect belongs to the semantics or pragmatics of indicative conditionals.•Four Experiments investigate whether it is produced by (a) a conversational implicature, (b) a (probabilistic) presupposition failure, or (c) a conventional implicature.•Experiment 1 finds that the reason-relation reading of indicative conditionals is not cancellable without contradiction (unlike conversational implicatures).•Experiment 2 finds that the reason-relation reading of indicative conditionals does not project under embeddings of negation operators (unlike presuppositions) In this paper, new evidence is presented for the assumption that the reason-relation reading of indicative conditionals ('if A, then C') reflects a conventional implicature. In four experiments, it is investigated whether relevance effects found for the probability assessment of indicative conditionals (Skovgaard-Olsen, Singmann, & Klauer, 2016a) can be classified as being produced by (a) a conversational implicature, (b) a (probabilistic) presupposition failure, or (c) a conventional implicature. After considering several alternative hypotheses, and the accumulating evidence from other studies as well, we conclude that the evidence is most consistent with the Relevance Effect being the outcome of a conventional implicature. This finding indicates that the reason-relation reading is part of the semantic content of indicative conditionals, albeit not part of their primary truth-conditional content.