Hybrid Temporal Situation Calculus

TL;DR

This paper extends Reiter's temporal situation calculus to model continuous change inspired by hybrid systems, enabling reasoning about both actions and the passage of time in dynamic environments.

Contribution

It introduces a novel extension of the temporal situation calculus by adding time arguments to fluents, capturing continuous change and relating it to hybrid automata.

Findings

Formalizes continuous change within the situation calculus framework

Provides a systematic methodology for deriving axioms of continuous change

Demonstrates that the extended theories capture hybrid automata behaviors

Abstract

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.