Reasoning About Indefinite Actions

In this paper, we view planning as a special case of reasoning about indefinite actions. We treat actions as predicates defined over a linear temporal order. This formalism permits the representation of concurrent activity. Suppose we have a set of abstract actions defined by Horn clauses from a set of basic actions. Let us assume that an abstract action ψ has occurred, and ask whether a given condition φ is entailed by all the basic actions that constitute ψ. A countermodel to this hypothetical implication is then a plan for “doing ψ and avoiding φ.” We propose a formalization of this problem using circumscription, and argue that this is the correct formalization if our action definitions include recursive rules. We then investigate two techniques for solving the problem: (1) a special type of inductive proof procedure, which is sound but not complete; and (2) a decision procedure that works for an interesting subclass of the general problem. Because of the use of recursive rules in our action definitions, we can use these techniques to reason about an abstract action that consists of “doing ψ some finite number of times.” We demonstrate the techniques on a simple example involving concurrent, repetitive actions.