Business process models are abstractions of concrete operational procedures that occur in the daily business of organizations. To cope with the complexity of these models, business process model abstraction has been introduced recently. Its goal is to derive from a detailed process model several abstract models that provide a high-level understanding of the process. While techniques for constructing abstract models are reported in the literature, little is known about the relationships between process instances and abstract models. In this paper we show how the state of an abstract activity can be calculated from the states of related, detailed process activities as they happen. The approach uses activity state propagation. With state uniqueness and state transition correctness we introduce formal properties that improve the understanding of state propagation. Algorithms to check these properties are devised. Finally, we use behavioral profiles to identify and classify behavioral inconsistencies in abstract process models that might occur, once activity state propagation is used.