Abstract The following activity recognition problem is considered: a description of the action capabilities of an agent being observed is given. This includes the preconditions and effects of atomic actions and of the activities (sequences of actions) the agent may execute. Given this description and a set of propositions, called history, about action occurrences, intended actions and properties of the world all at various points in time, the problem is to complete the picture as much as possible and determine what has already happened, what the intentions of the agent are, and what may happen as a result of the agent acting on those intentions. We present a framework to solve these activity recognition problems based on a formal language for reasoning about actions that includes a notion of intended actions, and a corresponding formalization in answer set programming