Integrating State Constraints and Obligations in Situation Calculus

Abstract

The ramiflcation problem concerns the characterisation of indirect efiects of actions. This problem arises when a theory of action is integrated with a set of state constraints. Thus integrating state constraints to a solution of the frame problem must deal with the ramiflcation problem. In the situation calculus a general solution to both the frame and ramiflcation problems has been proposed which includes the indirect efiects of actions in the successor state axioms. However, the notion of belief ∞uents has also been introduced into the situation calculus in order to distinguish between facts that hold in a situation and facts that are believed to hold in a situation. Hence in addition to the traditional frame and ramiflcation problems, a belief counterpart to each of these problems is considered. Building on these approaches, we propose a general solution to the belief frame and ramiflcation problems. The belief counterpart of the problems must deal with two types of constraints: the believed state constraints relating to physical laws and the constraints imposed by social conventions. These second kind of constraints are known in literature as obligations. A practical advantage is that the proposal is straightforward to implement.