Integrating State Constraints and Obligations in Situation Calculus

The ramification problem concerns the characterisation of indirect effects of actions. This problem arises when a theory of action is integrated with a set of state constraints. So integrating state constraints to a solution of the frame problem must deal with the ramification problem. In the situation calculus a general solution to both the frame and ramification problems has been proposed. This solution includes the indirect effects of actions in the successor state axioms. On the other hand, in the situation calculus, the notion of belief fluents has been introduced in order to distinguish between facts that hold in a situation and facts that are believed to hold in a situation. So apart from the traditional frame and ramification problems, a belief counterpart of these problems is considered. The successor belief state axioms were proposed to address the belief frame problem. Inspired in the mentioned approaches, we propose a general solution to the belief frame and ramification problems. We consider two sorts of constraints: the believed state constraints relating to physical laws and the believed mental constraints relating to social laws. Constraints imposed by social laws are well know in literature as obligations. Automated reasoning based on the proposal could easily be implemented in Prolog.