How to Progress Beliefs in Continuous Domains

When Lin and Reiter introduced the progression of basic action theories in the situation calculus, they were essentially motivated by long-lived robotic agents functioning over thousands of actions. However, their account does not deal with probabilistic uncertainty about the initial situation nor with effector or sensor noise, as often needed in robotic applications. In this paper, we obtain results on how to progress continuous degrees of belief against continuous effector and sensor noise in a semantically correct fashion. Most significantly, and perhaps surprisingly, we identify conditions under which our account is not only as efficient as the filtering mechanisms commonly used in robotics, but considerably more general.