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Traditional process mining considers only one single case notion anddiscovers and analyzes models based on this. However, a single case notion isoften not a realistic assumption in practice. Multiple case notions mightinteract and influence each other in a process. Object-centric process miningintroduces the techniques and concepts to handle multiple case notions. So far,such event logs have been standardized and novel process model discoverytechniques were proposed. However, notions for evaluating the quality of amodel are missing. These are necessary to enable future research on improvingobject-centric discovery and providing an objective evaluation of modelquality. In this paper, we introduce a notion for the precision and fitness ofan object-centric Petri net with respect to an object-centric event log. Wegive a formal definition and accompany this with an example. Furthermore, weprovide an algorithm to calculate these quality measures. We discuss ourprecision and fitness notion based on an event log with different models. Ourprecision and fitness notions are an appropriate way to generalize qualitymeasures to the object-centric setting since we are able to consider multiplecase notions, their dependencies and their interactions.

Precision and Fitness in Object-Centric Process Mining