Property Persistence in the Situation Calculus

Ryan F. Kelly, Adrian R. Pearce

We develop an algorithm for reducing universally quantified situation calculus queries to a form more amenable to automated reasoning. Universal quantification in the situation calculus requires a second-order induction axiom, making automated reasoning difficult for such queries. We show how to reduce queries about property persistence, a common family of universally-quantified query, to an equivalent form that does not quantify over situations. The algorithm for doing so utilizes only first-order reasoning. We give several examples of important reasoning tasks that are facilitated by our approach, including checking for goal impossibility and reasoning about knowledge with partial observability of actions.