A Medieval Controversy about Entailments between Categorical and 'Continuing' Propositions

The early thirteenth century tract Ars Meliduna deals with the issue whether categorical propositions entail, or are entailed by, 'continuing' propositions, i.e. by implications. From the perspective of modern logic, with implication interpreted as a material, truth-functional connective, the first question has to be answered in the affirmative because, e.g. beta entails (alpha $ \supset $ superset of beta). But conversely (alpha $ \supset $ superset of beta) 'normally' doesn't entail the truth (or the falsity) of any of the components alpha, beta; hence the second question should be answered in the negative. These results cannot, however, be directly transferred to medieval logic because implication was there usually interpreted as a strict implication. Yet, within the framework of modal logic, one obtains parallel results. In particular, whenever beta is necessary, then (alpha -> beta) must be true. Furthermore, if (alpha -> beta) is itself necessary, then it is entailed by alpha. Thus, in particular, 'Socrates is a man' entails the analytically true implication 'If Socrates is a man, Socrates is an animal', and the same premiss also entails the tautological consequent 'If Socrates is white, Socrates is white'.