Adaptivity in Process Management Systems (PMS) is key to their successful applicability in pratice. Approaches have already been developed to ensure the system correctness after arbitrary process changes at the syntactical level. However, still errors may be caused at the semantical level. Therefore, the integration of application knowledge will flag a milestone in the development of process management technology. In this paper, we introduce a framework for defining semantic constraints over processes in such a way that they can express real-world application knowledge. On the other hand, these constraints are still manageable concerning the effort for maintenance and semantic process verification. This can be used, for example, to detect semantic conflicts when applying process changes (e.g., drug incompatibilities). In order to enable the PMS to deal with such semantic conflicts we also introduce a notion of semantic correctness and discuss how to (efficiently) verify semantic correc...