Probabilistic Stability, Agm Revision Operators and Maximum Entropy

Abstract

Several authors have investigated the question of whether canonical logic-based accounts of belief revision, and especially the theory of AGM revision operators, are compatible with the dynamics of Bayesian conditioning. Here we show that Leitgeb’s stability rule for acceptance, which has been offered as a possible solution to the Lottery paradox, allows to bridge AGM revision and Bayesian update: using the stability rule, we prove that AGM revision operators emerge from Bayesian conditioning by an application of the principle of maximum entropy. In situations of information loss, or whenever the agent relies on a qualitative description of her information state—such as a plausibility ranking over hypotheses, or a belief set—the dynamics of AGM belief revision are compatible with Bayesian conditioning; indeed, through the maximum entropy principle, conditioning naturally generates AGM revision operators. This mitigates an impossibility theorem of Lin and Kelly for tracking Bayesian conditioning with AGM revision, and suggests an approach to the compatibility problem that highlights the information loss incurred by acceptance rules in passing from probabilistic to qualitative representations of belief.

Probabilistic Reasoning Across the Causal Hierarchy

“…As is widely recognized, the consequence relations that are generated in these two ways behave quite differently.' Systems of non-monotonic reasoning can often be given quantitative probabilistic interpretations (see, e.g., Pearl 1989), and there are various ways of ameliorating the inferential tensions in these contexts (Leitgeb, 2017;Mierzewski, 2020). But such resolution usually comes at the expense of quantitative granularity typical of numerical probabilistic reasoning.…”