Hybrid Temporal Situation Calculus

The ability to model continuous change in Reiter's temporal situation calculus action theories has attracted a lot of interest. In this paper, we propose a new development of his approach, which is directly inspired by hybrid systems in control theory. Specifically, while keeping the foundations of Reiter's axiomatization, we propose an elegant extension of his approach by adding a time argument to all fluents that represent continuous change. Thereby, we insure that change can happen not only because of actions, but also due to the passage of time. We present a systematic methodology to derive, from simple premises, a new group of axioms which specify how continuous fluents change over time within a situation. We study regression for our new temporal basic action theories and demonstrate what reasoning problems can be solved. Finally, we formally show that our temporal basic action theories indeed capture hybrid automata.