Belief Revision in Probability Theory

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 are 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.

[1]  A. Hasman,et al.  Probabilistic reasoning in intelligent systems: Networks of plausible inference , 1991 .

[2]  Gerhard Paass.  Second order probabilities for uncertain and conflicting evidence , 1990, UAI.

[3]  Henry E. Kyburg,et al.  Bayesian and Non-Bayesian Evidential Updating , 1987, Artificial Intelligence.

[4]  David Heckerman,et al.  An axiomatic framework for belief updates , 1986, UAI.

[5]  Kurt Weichselberger,et al.  A Methodology for Uncertainty in Knowledge-Based Systems , 1990, Lecture Notes in Computer Science.

[6]  Paul Weirich,et al.  Conditional Probabilities and Probabilities Given Knowledge of a Condition , 1983, Philosophy of Science.

[7]  Peter C. Cheeseman,et al.  In Defense of Probability , 1985, IJCAI.

[8]  Peter C. Cheeseman,et al.  Probabilistic vs. Fuzzy Reasoning , 1985, UAI.

[9]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[10]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[11]  Tod S. Levitt,et al.  Uncertainty in artificial intelligence , 1988 .

[12]  Nils J. Nilsson,et al.  Probabilistic Logic * , 2022 .

[13]  Isaac Levi,et al.  The Enterprise Of Knowledge , 1980 .

[14]  Gary James Jason,et al.  The Logic of Scientific Discovery , 1988 .

[15]  Judea Pearl,et al.  Fusion, Propagation, and Structuring in Belief Networks , 1986, Artif. Intell..

[16]  Didier Dubois,et al.  Updating with belief functions, ordinal conditional functions and possibility measures , 1990, UAI.

[17]  E KyburgHenry.  Bayesian and non-Bayesian evidential updating , 1987 .

[18]  Max Henrion,et al.  A Framework for Comparing Uncertain Inference Systems to Probability , 1985, UAI.

[19]  Judea Pearl,et al.  Bayesian decision methods , 1990 .

[20]  Theodore Hailperin,et al.  Probability logic , 1984, Notre Dame J. Formal Log..

[21]  Peter C. Cheeseman,et al.  An inquiry into computer understanding , 1988, Comput. Intell..