The capability to store data about Business Process (BP) executions in so-called Event Logs has brought to the identification of a range of key reasoning services (consistency, compliance, runtime monitoring, prediction) for the analysis of process executions and process models. Tools for the provision of these services typically focus on one form of reasoning alone. Moreover, they are often very rigid in dealing with forms of incomplete information about the process execution. While this enables the development of ad hoc solutions, it also poses an obstacle for the adoption of reasoning-based solutions in the BP community. In this paper, we introduce the notion of Structured Processes with Observability and Time (SPOT models), able to support incompleteness (of traces and logs), and temporal constraints on the activity duration and between activities. Then, we exploit the power of abduction to provide a flexible, yet computationally effective framework able to reinterpret key reasoning services in terms of incompleteness and observability in a uniform way.