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.
