Inductive Definability and the Situation Calculus

We explore the situation calculus within the framework of inductive deenability. A consequence of this view of the situation calculus is to establish direct connections with diierent variants of the-First we show that the induction principle on situations Reiter, 1993] is implied by an inductive deenition of the set of situations. Then we consider the frame problem from the point of view of inductive deenability and by deening uents inductively we obtain essentially the same form of successor state axioms as Reiter, 1991]. Our approach allows extending this result to the case where ramiication constraints are present. Finally we demonstrate a method of applying inductive deenitions for computing xed point properties of GOLOG programs.