The paper considers two kinds of medieval obligational disputations and the medieval genre of sophismata in relation to the kinds of inferences accepted in them. The main texts discussed are the anonymous Obligationes parisienses from the early 13th century and Richard Kilvington’s Sophismata from the early 14th century. Four different kinds of warranted transition from an antecedent to a consequent become apparent in the medieval discussions: the strong logical validity of basic propositional logic, analytic validity based on conceptual containment, merely (...) semantic impossibility of the antecedent being true without the consequent, and intuitively true counterfactual conditionals. As these different kinds of consequences are spelled out by means of obligational disputations, it appears that the genre of obligations is indeed useful for the “knowledge of consequences,” as the anonymous Obligationes parisienses claims. (shrink)