This paper presents a novel unified account of three distinct non-material interpretations of "if... then...": the suppositional interpretation, the evidential interpretation, and the strict interpretation. We will spell out and compare these three interpretations within a single formal framework which rests on fairly uncontroversial assumptions, in that it requires nothing but propositional logic and the probability calculus. As we will show, each of the three intrerpretations exhibits specific logical features that deserve separate consideration. In particular, the evidential interpretation as we understand it — a precise and well defined version of it which has never been explored before — significantly differs both from the suppositional interpretation and from the strict interpretation
