Possibility and Innnitary Nondeterminism in the Situation Calculus Nondeterminism and Possibility in the Situation Calculus

This paper presents a version of the Situation Calculus with improved capabilities in formalizing and reasoning about nondeterministic actions. Instead of describing the eeects of such actions by posting constraints on their possible outcomes , as is typically done in the common Situation Calculus, we provide means of describing actions by the set of their possible total eeects. An important advantage of this approach is its allowing for reasoning about the possible (as opposed to the necessary) postconditions of actions. Furthermore, our method does not require enumerating the possible outcomes of an action, so that actions with innnitary effects , like randomly picking an object from a bag containing unknown objects, can be modeled without diiculty. Based on our version of the Situation Calculus, we present a high-level rst-order language for specifying queries about the possible courses of given action sequences and a simple regression procedure for evaluating such queries.