Probabilistic Belief Revision via Imaging

While Bayesian conditioning fits in nicely with probabilistic belief expansion, its use is problematic in the context of non-trivial belief revision. Lewis’ use of imaging based on closeness between possible worlds offers a way to overcome this limitation in the context of belief update (in a dynamic environment). In this paper, we explore the use of imaging as a means to construct probabilistic belief revision. Specifically, we present explicit constructions of three candidates strategies, dubbed Naive, Gullible and Cunning, that are based on imaging, and investigate their properties.

[1]  Mukesh Dalal,et al.  Investigations into a Theory of Knowledge Base Revision , 1988, AAAI.

[2]  Philippe Smets The transferable belief model and other interpretations of Dempster-Shafer's model , 1990, UAI.

[3]  Peter G¿rdenfors,et al.  Belief Revision , 2003 .

[4]  Didier Dubois,et al.  Timed possibilistic logic , 1991, Fundam. Informaticae.

[5]  Abhaya C. Nayak,et al.  Probabilistic Belief Contraction , 2012, Minds and Machines.

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

[7]  Andreas Herzig,et al.  Propositional Belief Base Update and Minimal Change , 1999, Artif. Intell..

[8]  Karl Schlechta,et al.  Distance semantics for belief revision , 1996, Journal of Symbolic Logic.

[9]  D. Dubois,et al.  Belief Change Rules in Ordinal and Numerical Uncertainty Theories , 1998 .

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

[11]  Craig Boutilier,et al.  On the Revision of Probabilistic Belief States , 1995, Notre Dame J. Formal Log..

[12]  Dov M. Gabbay,et al.  Handbook of logic in artificial intelligence and logic programming (vol. 1) , 1993 .

[13]  Jérôme Lang,et al.  Belief Update Revisited , 2007, IJCAI.

[14]  Sébastien Konieczny,et al.  Logic Based Merging , 2011, J. Philos. Log..

[15]  Pavlos Peppas,et al.  Handbook of Knowledge Representation Edited Belief Revision Pavlos Peppas 8.1 Introduction , 2022 .

[16]  Adam J. Grove,et al.  Two modellings for theory change , 1988, J. Philos. Log..

[17]  Wlodzimierz Rabinowicz,et al.  On probabilistic representation of non-probabilistic belief revision , 1989, J. Philos. Log..

[18]  Eduardo L. Fermé,et al.  Belief Revision , 2007, Inteligencia Artif..

[19]  H. Prade,et al.  Possibilistic logic , 1994 .

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

[21]  Hirofumi Katsuno,et al.  On the Difference between Updating a Knowledge Base and Revising It , 1991, KR.

[22]  Wolfgang Spohn,et al.  Ordinal Conditional Functions: A Dynamic Theory of Epistemic States , 1988 .

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

[24]  Peter Gärdenfors,et al.  Knowledge in Flux , 1988 .

[25]  Abhaya C. Nayak,et al.  Is Revision a Special Kind of Update? , 2011, Australasian Conference on Artificial Intelligence.