The Nondeterministic Situation Calculus

The standard situation calculus assumes that atomic actions are deterministic. But many domains involve nondeterministic actions, with problems such as fully observable nondeterministic (FOND) planning and high-level program execution requiring solutions. Various approaches have been proposed to accommodate nondeterminism on top of the standard situation calculus language, for instance by introducing nondeterministic programs as in Golog and ConGolog. But a key problem in these approaches is that they don’t clearly distinguish between choices that can be made by the agent and choices that are made by the environment, i.e., angelic vs. devilish nondeterminism. In this paper, we propose a simple extension to the standard situation calculus that accommodates nondeterministic actions and preserves Reiter’s solution to the frame problem and answering projection queries through regression. We also provide a formalization of FOND planning and show how ConGolog high-level program execution in nondeterministic domains can be defined.