Decidable Reasoning About Time in Finite-Domain Situation Calculus Theories

arXiv:2402.03164v3 Announce Type: replace 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 function 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 when the domain contains only finitely many 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. With this restriction, we can show that the reachability problem for finite-domain basic action theories is decidable. Finally, we apply our results to Golog program realization by presenting a decidable procedure for determining an action sequence that is a successful execution of a given program.

Source: arXiv cs.AI | 2026-10-15

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