A Simple and Tractable Extension of Situation Calculus to Epistemic Logic

The frame problem and the representation of knowledge change have deserved a lot of works. In particular, at the Cognitive Robotics Group, at Toronto, several researchers in the last ten years have produced quite interesting papers in a uni- form logical framework based on Situation Calulus [Rei91, SL93, LR94, LL98]. In [Rei91] Reiter has proposed a simple solution to the frame problem. Scherl and Levesque in [SL93] have defined an extension to Epistemic Logic to represent knowledge dynamics in contexts where some actions may produce knowledge, like, for instance, sensing actions for a robot. This approach has been extended by Lakemeyer and Levesque in [LL98] to modal operators of the kind “I know and only know”. Also, they have given a formal semantics and axiomatics, and they proved soundness and completeness of the axiomatics.