Inductive Definability and the Situation Calculus

We explore the situation calculus within the framework of inductive definability. A consequence of this view of the situation calculus is to establish direct connections with different variants of the Μ-calculus [Par70,HP73,Pra81,Koz83,EC80], structural operational semantics of concurrent processes [Plo81], and logic programming [Apt90]. First we show that the induction principle on situations [Rei93] is implied by an inductive definition of the set of situations. Then we consider the frame problem from the point of view of inductive definability and by defining fluents inductively we obtain essentially the same form of successor state axioms as [Rei91]. Our approach allows extending this result to the case where ramification constraints are present. Finally we demonstrate a method of applying inductive definitions for computing fixed point properties of GOLOG programs.

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