A Unifying Framework for Probabilistic Belief Revision

In this paper we provide a general, unifying framework for probabilistic belief revision. We first introduce a probabilistic logic called p-logic that is capable of representing and reasoning with basic probabilistic information. With p-logic as the background logic, we define a revision function called p-revision that resembles partial meet revision in the AGM framework. We provide a representation theorem for p-revision which shows that it can be characterised by the set of basic AGM revision postulates. P-revision represents an “all purpose” method for revising probabilistic information that can be used for, but not limited to, the revision problems behind Bayesian conditionalisation, Jeffrey conditionalisation, and Lewis’s imaging. Importantly, p-revision subsumes the above three approaches indicating that Bayesian conditionalisation, Jeffrey conditionalisation, and Lewis’ imaging all obey the basic principles of AGM revision. As well our investigation sheds light on the corresponding operation of AGM expansion in the probabilistic setting.

[1]  D. Lewis.  Probabilities of Conditionals and Conditional Probabilities , 1976 .

[2]  Marcelo Finger,et al.  Consolidating Probabilistic Knowledge Bases via Belief Contraction , 2016, KR.

[3]  Thomas Andreas Meyer,et al.  On Revision of Partially Specified Convex Probabilistic Belief Bases , 2016, ECAI.

[4]  C. Aitken,et al.  The logic of decision , 2014 .

[5]  Abdul Sattar,et al.  Probabilistic Belief Contraction Using Argumentation , 2015, IJCAI.

[6]  Peter Gärdenfors,et al.  On the logic of theory change: Partial meet contraction and revision functions , 1985, Journal of Symbolic Logic.

[7]  Ronald Fagin,et al.  A logic for reasoning about probabilities , 1988, [1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science.

[8]  Gabriele Kern-Isberner,et al.  Revising and Updating Probabilistic Beliefs , 2001 .

[9]  James P. Delgrande,et al.  Revising beliefs on the basis of evidence , 2012, Int. J. Approx. Reason..

[10]  Andrew Coles,et al.  Proceedings of the 22nd European Conference on Artificial Intelligence (ECAI 2016) , 2016, ECAI 2016.

[11]  F. J. Pelletier,et al.  316 Notre Dame Journal of Formal Logic , 1982 .

[12]  Sven Ove Hansson,et al.  A textbook of belief dynamics - theory change and database updating , 1999, Applied logic series.

[13]  Frans Voorbraak,et al.  Probabilistic Belief Change: Expansion, Conditioning and Constraining , 1999, UAI.

[14]  Peter Gärdenfors,et al.  Revisions of Knowledge Systems Using Epistemic Entrenchment , 1988, TARK.

[15]  Joseph Y. Halpern.  Reasoning about uncertainty , 2003 .

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

[17]  J. E. Creighton,et al.  The Philosophical Review , 1901 .

[18]  Mehmet A. Orgun,et al.  Belief Erasure Using Partial Imaging , 2010, Australasian Conference on Artificial Intelligence.

[19]  Abdul Sattar,et al.  Probabilistic Belief Revision via Imaging , 2014, PRICAI.

[20]  Joseph Y. Halpern,et al.  Updating Sets of Probabilities , 1998, UAI.

[21]  P G rdenfors,et al.  Knowledge in flux: modeling the dynamics of epistemic states , 1988 .