Theory and Decision

, Volume 53, Issue 2, pp 95–135 | Cite as

Can Bayes' Rule be Justified by Cognitive Rationality Principles?

  • Bernard Walliser
  • Denis Zwirn


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 but 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 Miller–Popper 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.

Bayes rule belief revision cognitive rationality probability revising probability updating 


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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Bernard Walliser
    • 1
  • Denis Zwirn
    • 1
  1. 1.ENPCParisFrance

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