Pragmatic presupposition is explored as grounded on an implicit reasoning process based on a range of presumptions, which can determine cultural differences. The basic condition for presupposing a proposition is represented as a reasoning criterion, to wit reasonableness. Presuppositions, on this view, need to be reasonable, namely they need to be the reasonable conclusions of an underlying presumptive reasoning, which does not or may not contain contradictions with other presumptions. Presumptions are in turn explored considering their nature and their hierarchy, namely their subject matter and their possible contextual backing, which removes some of their possible defaults. This assay of presupposition reveals the relationship between misunderstandings deriving from presuppositional failures and the underlying system of presumptions. This approach is applied to the exploration of communicative issues within the medical context, and more precisely doctor-patient communication in diabetes cases.