Reasoning about Probabilities in Dynamic Systems using Goal Regression

By Vaishak Belle, Hector J. Levesque. 2013

19 citations recorded by the source corpus.

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, both in discrete and continuous domains, 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.

Subfields: Artificial Intelligence

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Citations in the corpus

Logic meets Probability: Towards Explainable AI Systems for Uncertain Worlds (2017, background): “Nonetheless, given queries about outcomes after actions, as needed for automated planning, we have shown that actions can be either “compiled” away, or “injected” to the current state [Belle and Levesque, 2013b; 2014a].”
Reasoning about Probabilities in Unbounded First-Order Dynamical Domains (2017, background): “Our sense is that earlier results for the BHL scheme [Belle and Levesque, 2013b; 2014] can be reformulated forDS with some effort.”
A Logical Theory of Localization (2015, background): “In very recent work [6,8], we have investigated ways to address the problem of projection in our framework, where one is interested in the properties that hold after actions.”
PREGO: An Action Language for Belief-Based Cognitive Robotics in Continuous Domains (2014, methodology): “See (Bacchus, Halpern, and Levesque 1999; Belle and Levesque 2013a) for more discussions.”
How to Progress Beliefs in Continuous Domains (2014, background): “BL deal with this issue using regression: beliefs are regressed to the initial state where (P3) does hold, and all the actual belief calculations can be done in the initial state (Belle and Levesque 2013b).”
A logical theory of robot localization (2014, background): “Recently, we [5] have shown how regression can be formulated for degrees of belief, by means of which projection queries reduce to formulas about the initial situation.”