Algorithms and application in decision-making for the finest splitting of a set of formulae

Belief revision, as one central problem in artificial intelligence, is of interest in decision-making and game theory. To deal with local belief change that is a desirable property for belief revision, a novel notion - the finest splitting was proposed by Parikh, Kourousias and Makinson, respectively. But it was not clear how to construct the finest splitting of a propositional theory (a closed set of propositional formulae). In this paper, we propose a constructive method, that is intractable generally, to compute the finest splitting of a propositional theory. We also propose a polynomial time algorithm to compute the finest splitting of a propositional theory consisting of clauses. As an application in the diagnosis theory, we show that, given a diagnosis system (SD,COMP,OBS), it is quite easy to compute all of its diagnosis if the splitting of SD@?OBS is pre-computed. Additionally, in terms of this approach, we can have more specific reason to interpret observation than the original one.

[1]  Huaiqing Wang,et al.  A framework of fuzzy diagnosis , 2004, IEEE Transactions on Knowledge and Data Engineering.

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

[3]  R. Parikh.  Beliefs, belief revision, and splitting languages , 1999 .

[4]  Sheila A. McIlraith,et al.  The Role of Redundant Clauses in Solving Satisfiability Problems , 2005, CP.

[5]  Hans Rott,et al.  Change, choice and inference - a study of belief revision and nonmonotonic reasoning , 2001, Oxford logic guides.

[6]  Ephraim Nissan,et al.  Belief Revision as Applied within a Descriptive Model of Jury Deliberations , 2001 .

[7]  David Makinson,et al.  Parallel interpolation, splitting, and relevance in belief change , 2007, Journal of Symbolic Logic.

[8]  David Makinson.  Friendliness for Logicians , 2005, We Will Show Them!.

[9]  Rohit Parikh,et al.  Relevance Sensitive Non-Monotonic Inference on Belief Sequences , 2000, J. Appl. Non Class. Logics.

[10]  M. de Rijke,et al.  Logic, language and computation, vol. 2 , 1999 .

[11]  David Makinson.  Propositional Relevance through Letter-Sharing: Review and Contribution , 2007, Formal Models of Belief Change in Rational Agents.

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

[13]  Dongmo Zhang,et al.  Reasoning about Bargaining Situations , 2007, AAAI.

[14]  Dongmo Zhang,et al.  Representation Theorems for Multiple Belief Changes , 1997, IJCAI.

[15]  Maonian Wu,et al.  A Constructive Method of the Finest Splitting of Belief Set , 2008 .

[16]  Efraim Turban,et al.  Decision support systems and intelligent systems , 1997 .

[17]  Yan Zhang,et al.  An Ordinal Bargaining Solution with Fixed-Point Property , 2008, J. Artif. Intell. Res..

[18]  Rohit Parikh,et al.  Relevance sensitive belief structures , 2000, Annals of Mathematics and Artificial Intelligence.

[19]  Raymond Reiter,et al.  A Theory of Diagnosis from First Principles , 1986, Artif. Intell..

[20]  Kenneth H. Rosen,et al.  Discrete Mathematics and its applications , 2000 .

[21]  Norman Y. Foo,et al.  Negotiation as Mutual Belief Revision , 2004, AAAI.

[22]  Norman Y. Foo,et al.  Distance Semantics for Relevance-Sensitive Belief Revision , 2004, KR.

[23]  Andrew B. Whinston,et al.  Decision Support Systems: A Knowledge Based Approach : , 1996 .