low-level event of the same type to be of high-level type *Eating*. Note that for some traces high-level annotations might be available, in which case its events contain the *label* attribute, while other traces might not be annotated. High-level interpretations of unannotated traces, by inferring the *label* attribute based on information that is present in the annotated traces, allow the use of unannotated traces for process discovery and conformance checking on a high level.

Petri nets
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A process modeling notation frequently used as output of process discovery techniques is the Petri net. Petri nets are directed bipartite graphs consisting of transitions and places, connected by arcs. Transitions represent activities, while places represent the status of the system before and after execution of a transition. Labels are assigned to transitions to indicate the type of activity that they represent. A special label $\tau$ is used to represent invisible transitions, which are only used for routing purposes and do not represent any real activity.

\[def:lpn\] A labeled Petri net is a tuple $N=(P,T,F,R,\ell)$ where $P$ is a finite set of places, $T$ is a *finite set* of transitions such that $P \cap T = \emptyset$, and $F \subseteq (P \times T) 