ID-logic and the Ramification Problem for the Situation Calculus

The goal of this paper is to extend the general solution to the ramification problem for the situation calculus to the case where causal rules specifying indirect effects of actions may form cycles or cycles through negation. We formulate causal dependencies as rules of inductive definitions. Then we give a semantics to a logic for representing inductive definitions (ID-logic) by translating definitions to sentences of fixed-point logic. We describe a regression-based procedure for generating successor state axioms from inductive rules, and consider several benchmark examples. Finally, we show that boundedness is a sufficient condition for translating causal theories to successor state axioms.