Can Bayes' Rule Be Justified by Cognitive Rationality Principles

The justification of Bayes' rule by cognitive rationality principles is undertaken by extending the propositional axiom systems usually proposed in two contexts of belief change: revising and updating. Probabilistic belief change axioms are introduced, either by direct transcription of the set-theoretic ones, or in a stronger way nevertheless in the spirit of the underlying propositional principles. Weak revising axioms are shown to be satisfied by a General Conditioning rule, extending Bayes' rule but also compatible with others, and weak updating axioms by a General Imaging rule, extending Lewis rule. Strong axioms (equivalent to the Popper-Miller axiom system) are necessary to justify Bayes' rule in a revising context, and justify in fact an extended Bayes' rule which applies even if the message has zero probability.