Hybrid Temporal Situation Calculus
This work addresses a foundational issue in AI reasoning for hybrid systems, but it is incremental as it builds directly on Reiter's existing axiomatization.
The paper tackles the problem of modeling continuous change in Reiter's temporal situation calculus by proposing an extension inspired by hybrid systems, adding a time argument to fluents to allow change due to time passage, and formally shows that the new theories capture hybrid automata.
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.