Linking Iterated Belief Change Operations to Nonmonotonic Reasoning

The study of the exact relationships between belief revision and belief update, on one side, and belief revision and nonmonotonic reasoning, on the other, has raised considerable interest, but still, the picture is far from being complete. In this paper, we add some new details to this line of research by making a foundational contribution to the discussions on the very nature of belief change operations, and by introducing universal inference operations as a proper counterpart in nonmonotonic reasoning to iterated belief change. Belief change is investigated within an abstract framework of epistemic states and (qualitative or quantitative) conditionals here. We show how belief revision and belief update can be realized by one and the same generic change operator as simultaneous and successive change operations. We propose general postulates for revision and update that also apply to iterated change. The distinction between background knowledge and evidential information turns out to be a crucial feature in our framework, in order to analyse belief change in more depth.

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

[2]  William Harper,et al.  Causation in decision, belief change, and statistics , 1988 .

[3]  Didier Dubois,et al.  Non-standard theories of uncertainty of plausible reasoning , 1997 .

[4]  Peter Gärdenfors,et al.  Knowledge in Flux: Modeling the Dynamics of Epistemic States , 2008 .

[5]  Peter Gärdenfors,et al.  Relations between the logic of theory change and nonmonotonic logic , 1989, The Logic of Theory Change.

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

[7]  Pierre Marquis,et al.  Updating Epistemic States , 2001, Australian Joint Conference on Artificial Intelligence.

[8]  Gabriele Kern-Isberner.  Postulates for Conditional Belief Revision , 1999, IJCAI.

[9]  Gabriele Kern-Isberner,et al.  Conditionals in Nonmonotonic Reasoning and Belief Revision: Considering Conditionals as Agents , 2001 .

[10]  Gabriele Kern-Isberner,et al.  Characterizing the Principle of Minimum Cross-Entropy Within a Conditional-Logical Framework , 1998, Artif. Intell..

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

[12]  Jeff B. Paris,et al.  In defense of the maximum entropy inference process , 1997, Int. J. Approx. Reason..

[13]  David Makinson,et al.  General patterns in nonmonotonic reasoning , 1994 .

[14]  John E. Shore,et al.  Relative Entropy, Probabilistic Inference, and AI , 1985, UAI.

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

[16]  G. Brewka.  Principles of Knowledge Representation , 1996 .

[17]  Simon Parsons,et al.  Maximum Entropy and Variable Strength Defaults , 1999, IJCAI.

[18]  Gabriele Kern-Isberner,et al.  A Thorough Axiomatization of a Principle of Conditional Preservation in Belief Revision , 2004, Annals of Mathematics and Artificial Intelligence.

[19]  E. T. Jaynes,et al.  Where do we Stand on Maximum Entropy , 1979 .

[20]  Petr Hájek,et al.  Uncertain information processing in expert systems , 1992 .

[21]  Solomon Kullback,et al.  Information Theory and Statistics , 1970, The Mathematical Gazette.

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

[23]  Moisés Goldszmidt,et al.  A Maximum Entropy Approach to Nonmonotonic Reasoning , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  I. Csiszár.  $I$-Divergence Geometry of Probability Distributions and Minimization Problems , 1975 .

[25]  Aaron Hunter,et al.  Iterated Belief Change: A Transition System Approach , 2005, IJCAI.

[26]  R. Johnson,et al.  Properties of cross-entropy minimization , 1981, IEEE Trans. Inf. Theory.

[27]  Gabriele Kern-Isberner,et al.  Conditionals in Nonmonotonic Reasoning and Belief Revision , 2001, Lecture Notes in Computer Science.

[28]  Judea Pearl,et al.  Qualitative Probabilities for Default Reasoning, Belief Revision, and Causal Modeling , 1996, Artif. Intell..

[29]  Didier Dubois,et al.  Three Scenarios for the Revision of Epistemic States , 2008, J. Log. Comput..

[30]  E. T. Jaynes,et al.  Papers on probability, statistics and statistical physics , 1983 .

[31]  Didier Dubois,et al.  Iterated Revision as Prioritized Merging , 2006, KR.

[32]  Judea Pearl,et al.  On the Logic of Iterated Belief Revision , 1994, Artif. Intell..