Belief Revision in Probability Theory
This work addresses a foundational issue in probabilistic reasoning systems, highlighting an incremental theoretical gap that affects AI and ML methodologies relying on Bayesian methods.
The paper argues that Bayes' theorem and Jeffrey's rule are not generally applicable for belief revision in probability theory, as they fail to distinguish explicit and implicit conditions, revealing a fundamental limitation in the Bayesian approach.
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.