Towards State Update Axioms: Reifying Successor State Axioms

Successor state axioms are an optimal solution to the famous Frame Problem in reasoning about actions—but only as far as its representational aspect is concerned. We show how by gradually applying the principle of reification to these axioms, one can achieve gradual improvement regarding the inferential aspect without losing the representational merits. The resulting concept of state update axioms constitutes a novel version of what is known as the Fluent Calculus. We illustrate that under the provision that actions have no so-called open effects, any Situation Calculus specification can be transformed into an essentially equivalent Fluent Calculus specification, in which at the same time the representational and the inferential aspect of the Frame Problem are addressed. This alternative access to the Fluent Calculus both clarifies its role in relation to the most popular axiomatization paradigm and should help to enhance its acceptance.