In this work we introduce an extension of an structured argumentation system in which presumptions are fully integrated in the reasoning mechanism. A presumption is defined as a piece of information that is tentatively taken to be true, usually in the absence of acceptable reasons to the contrary. In Presumptive Defeasible Logic Programming (PreDeLP), arguments can be built from both facts and presumptions. We analyze several criteria to compare arguments in PreDeLP, and highlight one possibility that captures the semantic difference between presumptions and facts or defeasible rules. On top of PreDeLP we develop a defeasible approach to argumentation-based diagnostic reasoning. The use of presumptions permits to extend the reasoning beyond factual information, creating in this way a universe of possible scenarios that support or interfere with a claim. We characterize the set of possible scenarios for and against a claim and identify those that best explain the warrant status of the query.