Regression and progression in stochastic domains.

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, especially when the agent has to deal with categorical assertions, incomplete information such as disjunctive knowledge, as well as probabilistic knowledge. Among the many approaches for reasoning about degrees of belief in the presence of noisy sensing and acting, the logical account proposed by Bacchus, Halpern, and Levesque is perhaps the most expressive, allowing for such belief states to be expressed naturally as constraints. While that proposal is powerful, the task of how to plan effectively is not addressed. In fact, at a more fundamental level, the task of projection, that of reasoning about beliefs effectively after acting and sensing, is left entirely open.