Many medical information systems record data about the executed process instances in the form of an event log. In this paper, we present a framework, able to convert actions in the event log into higher level concepts, at different levels of abstraction, on the basis of domain knowledge. Abstracted traces are then provided as an input to trace comparison and semantic process discovery. Our abstraction mechanism is able to manage non trivial situations, such as interleaved actions or delays between two actions that abstract to the same concept. Trace comparison resorts to a similarity metric able to take into account abstraction phase penalties, and to deal with quantitative and qualitative temporal constraints in abstracted traces. As for process discovery, we rely on classical algorithms embedded in the framework ProM, made semantic by the capability of abstracting the actions on the basis of their conceptual meaning. The approach has been tested in stroke care, where we adopted abstraction and trace comparison to cluster event logs of different stroke units, to highlight (in)correct behavior, abstracting from details. We also provide process discovery results, showing how the abstraction mechanism allows to obtain stroke process models more easily interpretable by neurologists.