From Situation Calculus to Fluent Calculus: State Update Axioms as a Solution to the Inferential Frame Problem

Successor state axioms provide a solution to the famous Frame Problem as far as the representational aspect is concerned. Solving in classical, monotonic logic the additional inferential Frame Problem, on the other hand, was the major motivation for the development of the Fluent Calculus a decade or so ago. Yet the expressiveness of the latter in comparison to the Situation Calculus remained a largely open question until today. In this note, we derive a novel version of the Fluent Calculus by gradually applying the principle of reification to successor state axioms in order to address the inferential Frame Problem without losing the representational merits. Our approach results in a fully mechanic method for the generation of state update axioms from any collection of Situation Calculus-style effect axioms for deterministic actions, provided the actions do not have potentially infinitely many effects. The axiomatization thus obtained is proved essentially equivalent to the corresponding axiomatization which uses successor state axioms.