Reasoning about Motion Kinematics with Continuous Uncertainty in the Situation Calculus

Motion kinematics and probabilistic state estimation tasks are fundamental reasoning concerns in robotic applications, where the world is uncertain, and sensors and effectors are noisy. Most systems make various assumptions about the dependencies between state variables, and especially about how these dependencies change as a result of actions. Building on a general framework by Bacchus, Halpern and Levesque for reasoning about degrees of belief in the situation calculus, and a recent extension to it for continuous domains, in this paper we investigate the above reasoning concerns in the presence of a rich theory of actions using an example. We also show that while actions might affect prior distributions in nonstandard ways, suitable posterior beliefs are nonetheless entailed as a side-effect of the overall specification.