In many data-centric applications it is desirable to use OWL as an expressive schema language where one expresses constraints that need to be satisfied by the (instance) data. However, some features of OWL's semantics, specifically the Open World Assumption (OWL) and not having a Unique Name Assumption (UNA), make it hard to use OWL for this task. What would trigger a constraint violation in a closed world system like a relational database leads to new inferences in OWL. In this paper, we explore how OWL can be extended to accommodate integrity constraints and discuss several alternatives for the syntax and semantics of such an extension. We primarily focus on applications in the Supply Chain Management (SCM) domain but we are also gathering use cases and requirements from many other application areas to assess which of these alternatives provides the best solution.