Integrating actions and state constraints: A closed-form solution to the ramification problem (sometimes)

Our general concern is with how to integrate a representation of action into an existing set of state constraints. As has been observed in the literature, state constraints implicitly define indirect effects of actions as well as indirectly imposing further preconditions on the performance of actions. Thus, any representation scheme we propose must address the ramification and qualification problems, as well as the frame problem. In this paper we achieve such a representation for a syntactically restricted class of situation calculus theories. This paper presents two major technical contributions. The first contribution is provision of an axiomatic closed-form solution to the frame, ramification and qualification problems for a common class of ramification constraints. The solution is presented in the form of an automatable procedure that compiles a syntactically restricted set of situation calculus ramification constraints and effect axioms into a set of successor state axioms. The second major contribution of this paper is provision of an independent semantic justification for this closed-form solution. In particular, we present a semantic specification for a solution to the frame and ramification problems in terms of a prioritized minimization policy, and show that the successor state axioms of our closed-form solution adhere to this specification. Observing that our minimization policy is simply an instance of prioritized circumscription, we exploit results of Lifschitz on computing circumscription [6] to show that computing the prioritized circumscription yields our successor state axioms. In the special case where there are no ramification constraints, computing the circumscription yields Reiter’s earlier successor state axiom solution to the frame problem [17].