Belief Revision from Probability

TL;DR

This paper develops a question-relative probabilistic account of belief, analyzing its implications for belief dynamics and comparing it to traditional and other probabilistic theories.

Contribution

It introduces a weaker set of belief revision principles than AGM and compares this framework favorably to existing probabilistic belief theories.

Findings

Validated belief principles are weaker than AGM but stronger than Lockean theory.

Identified a class of models with additional natural principles.

Compared favorably to Leitgeb and Lin-Kelly probabilistic accounts.

Abstract

In previous work ("Knowledge from Probability", TARK 2021) we develop a question-relative, probabilistic account of belief. On this account, what someone believes relative to a given question is (i) closed under entailment, (ii) sufficiently probable given their evidence, and (iii) sensitive to the relative probabilities of the answers to the question. Here we explore the implications of this account for the dynamics of belief. We show that the principles it validates are much weaker than those of orthodox theories of belief revision like AGM, but still stronger than those valid according to the popular Lockean theory of belief, which equates belief with high subjective probability. We then consider a restricted class of models, suitable for many but not all applications, and identify some further natural principles valid on this class. We conclude by arguing that the present framework compares favorably to the rival probabilistic accounts of belief developed by Leitgeb and by Lin and Kelly.