Reasoning about Probabilities in Dynamic Systems using Goal Regression

Reasoning about degrees of belief in uncertain dynamic worlds is fundamental to many applications, such as robotics and planning, where actions modify state properties and sensors provide measurements, both of which are prone to noise. With the exception of limited cases such as Gaussian processes over linear phenomena, belief state evolution can be complex and hard to reason with in a general way. This paper proposes a framework with new results that allows the reduction of subjective probabilities after sensing and acting to questions about the initial state only. We build on an expressive probabilistic first-order logical account by Bacchus, Halpern and Levesque, resulting in a methodology that, in principle, can be coupled with a variety of existing inference solutions.