Reasoning about Noisy Sensors in the Situation Calculus

Agents interacting with an incompletely known dynamic world need to be able to reason about the effects of their actions, and to gain further information about that world using sensors of some sort. Unfortunately, sensor information is inherently noisy, and in general serves only to increase the agent’s degree of confidence in various propositions. Building on a general logical theory of action formalized in the situation calculus, developed by Reiter and others, we propose a simple axiomatization of the effect on an agent’s state of belief of taking a reading from a noisy sensor. By exploiting Reiter’s solution to the frame problem, we automatically obtain that these sensor actions leave the rest of the world unaffected, and further, that non-sensor actions change the state of belief of the agent in appropriate ways.