  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.
