Brief Revision on Generalized Ajoint Characterization of Bayes’ Rules and Jeffrey’s Rules
[1]
Kishwer Naheed, Department of Mathematics, Virtual University of Pakistan, Lahore, Punjab, Pakistan.
[2]
Nafeesa Rehman, Department of Mathematics, Virtual University of Pakistan, Lahore, Punjab, Pakistan.
[3]
Kamran Ayub, Department of Mathematics, Riphah International University, Islamabad, Pakistan.
[4]
Qazi Mahmood Ul-Hassan, Department of Mathematics, University of Wah, Wah, Pakistan.
We present a general framework for representing belief-revision rules and use it to characterize Bayes’ rule as a classical example and Jeffrey’s rule as a non-classical one. In Jeffrey’s rule, the input to a belief revision is not simply the information that some event has occurred, as in Bayes’ rule, but a new assignment of probabilities to some events. Despite their differences, Bayes’ and Jeffrey’s rules can be characterized in terms of the same axioms: responsiveness, which requires that revised beliefs incorporate what has been learnt, and conservativeness, which requires that beliefs on which the learnt input is ‘silent’ do not change.
Belief Revision, Subjective Probability, Bayes’ and Jeffrey’s Rules, Axiomatic Foundations, Fine-Grained Versus Coarse-Grained Beliefs, Unawareness
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