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arXiv · 2402.03164

Decidable Reasoning About Time in Finite-Domain Situation Calculus Theories

Till Hofmann·Stefan Schupp·Gerhard Lakemeyer
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Abstract

Representing time is crucial for cyber-physical systems and has been studied extensively in the Situation Calculus. The most commonly used approach represents time by adding a real-valued fluent $\mathit{time}(a)$ that attaches a time point to each action and consequently to each situation. We show that in this approach, checking whether there is a reachable situation that satisfies a given formula is undecidable, even if the domain of discourse is restricted to a finite set of objects. We present an alternative approach based on well-established results from timed automata theory by introducing clocks as real-valued fluents with restricted successor state axioms and comparison operators. %that only allow comparisons against fixed rationals. With this restriction, we can show that the reachability problem for finite-domain basic action theories is decidable. Finally, we apply our results on Golog program realization by presenting a decidable procedure for determining an action sequence that is a successful execution of a given program.

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Till Hofmann, Stefan Schupp, Gerhard Lakemeyer. 2024-02-05. Decidable Reasoning About Time in Finite-Domain Situation Calculus Theories. https://arxiv.org/abs/2402.03164

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