Privacy-preserving process mining enables the analysis of business processes using event logs, while giving guarantees on the protection of sensitive information on process stakeholders. To this end, existing approaches add noise to the results of queries that extract properties of an event log, such as the frequency distribution of trace variants, for analysis.Noise insertion neglects the semantics of the process, though, and may generate traces not present in the original log. This is problematic. It lowers the utility of the published data and makes noise easily identifiable, as some traces will violate well-known semantic constraints.In this paper, we therefore argue for privacy preservation that incorporates a process semantics. For common trace-variant queries, we show how, based on the exponential mechanism, semantic constraints are incorporated to ensure differential privacy of the query result. Experiments demonstrate that our semantics-aware anonymization yields event logs of significantly higher utility than existing approaches.