Belief Revision in Probability Theory

TL;DR

This paper critically examines the limitations of Bayesian methods for belief revision, emphasizing the importance of distinguishing belief revision from belief updating, and argues that Bayesian approaches are insufficient for general belief revision.

Contribution

It clarifies the conceptual differences between belief revision and updating, and demonstrates that Bayesian probability functions lack the necessary information for revision.

Findings

Bayes' theorem is not a universal belief revision rule.

Jeffrey's rule is also not a true revision rule.

Bayesian approach cannot perform general belief revision.

Abstract

In a probability-based reasoning system, Bayes' theorem and its variations are often used to revise the system's beliefs. However, if the explicit conditions and the implicit conditions of probability assignments `me properly distinguished, it follows that Bayes' theorem is not a generally applicable revision rule. Upon properly distinguishing belief revision from belief updating, we see that Jeffrey's rule and its variations are not revision rules, either. Without these distinctions, the limitation of the Bayesian approach is often ignored or underestimated. Revision, in its general form, cannot be done in the Bayesian approach, because a probability distribution function alone does not contain the information needed by the operation.