A Logic of Acting, Sensing, Knowing, and Only Knowing

This work is motivated by the existence of two useful but quite different knowledge representation formalisms, the situation calculus due to McCarthy, and the logic of only knowing due to Levesque. In this paper, we propose the logic , which combines both approaches in a clean and natural way. We present a semantics for which generalizes the semantics of to account for actions, and a sound and complete set of axioms for which generalizes the Lin and Reiter foundational axioms of the situation calculus to account for only knowing. The logic is compatible with earlier work on knowledge and action in that the solution to the frame problem for knowledge proposed by Scherl and Levesque becomes now a theorem of . We also demonstrate that the logic avoids certain anomalies present in related work by Lakemeyer. Finally we provide a mapping from into such that a sentence of is valid iff its mapping is a theorem of , thus providing, for the first time, a complete axiomatic characterization of .