The traces of process executions are a strategic source of information, from which a model of the process can be mined. In our recent work, we have proposed SIM (semantic interactive miner), an innovative process mining tool to discover the process model incrementally: it supports the interaction with domain experts, who can selectively merge parts of the model to achieve compactness, generalization, and reduced redundancy. We now propose a substantial extension of SIM, making it able to exploit (both automatically and interactively) pre-encoded taxonomic knowledge about the refinement (ISA relations) and composition (part-of relations) of process activities, as is available in many domains. The extended approach allows analysts to move from a process description where activities are reported at the ground level to more user-interpretable/compact descriptions, in which sets of such activities are abstracted into the "macro-activities" subsuming them or constituted by them. An experimental evaluation based on a real-world setting (stroke management) illustrates the advantages of our approach.