Sampling-Based Belief Revision

Michael Thielscher

Abstract: Model sampling has proved to be a practically viable method for decision-making under uncertainty, for example in imperfect-information games with large state spaces. In this paper, we examine the logical foundations of sampling-based belief revision. We show that it satisfies six of the standard AGM postulates but not Vacuity nor Subexpansion. We provide a corresponding representation theorem that generalises the standard result from a single to a family of faithful assignments for a given belief set. We also provide a formal axiomatisation of sampling-based belief revision in the Situation Calculus as an alternative way of reasoning about actions, sensing, and beliefs.