Belief Change and Dependence

It is a very natural requirement for belief change operations that formulas that are independent of a given update should be preserved. Such a proposal has already been made by Gardenfors (1990). In this perspective we study the links between belief change and the notion of dependence, our aim being to give dependence axioms able to characterize the AGM postulates. Proceeding exactly in the same way as Gardenfors (1988) did in the case of epistemic entrenchment, we show how a given dependence relation can be used to define a contraction operation, and the other way round we show how an independence relation can be obtained from a given contraction operation. The grande finale is a characterization theorem.

[1]  Peter Gärdenfors.  On the logic of relevance , 1978 .

[2]  A. N. Kolmogorov,et al.  Foundations of the theory of probability , 1960 .

[3]  James P. Delgrande,et al.  A Formal Approach to Relevance: Extended Abstract , 1994 .

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

[5]  Wolfgang Spohn,et al.  On the Properties of Conditional Independence , 1994 .

[6]  Luis Fariñas del Cerro,et al.  Sequents for dependence logics , 1991 .

[7]  Didier Dubois,et al.  Expressing Independence in a Possibilistic Framework and its Application to Default Reasoning , 1994, ECAI.

[8]  H. Jeffreys.  A Treatise on Probability , 1922, Nature.

[9]  Luis Fariñas del Cerro,et al.  An Ordinal View of Independence with Application to Plausible Reasoning , 1994, UAI.

[10]  Luis Fariñas del Cerro,et al.  Interference logic = conditional logic + frame axiom , 1994, Int. J. Intell. Syst..

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

[12]  Peter Gärdenfors.  Belief Revision and Relevance , 1990 .

[13]  Didier Dubois,et al.  Epistemic Entrenchment and Possibilistic Logic , 1991, Artif. Intell..

[14]  Luis Fariñas del Cerro,et al.  Possibility Theory and Independence , 1994, IPMU.

[15]  D. Dubois,et al.  Belief Revision: Belief change and possibility theory , 1992 .

[16]  Luis Fariñas del Cerro,et al.  Interference logic = conditional logic + frame axiom , 1993, Int. J. Intell. Syst..

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

[18]  Milan Studený.  Formal Properties of Conditional Independence in Different Calculi of AI , 1993, ECSQARU.

[19]  Luis Fariñas del Cerro,et al.  A Conditional Logic for Updating in the Possible Models Approach , 1994, KI.

[20]  Hans Rott,et al.  Logic, Action and Information , 1996 .

[21]  H. Jeffreys.  Logical Foundations of Probability , 1952, Nature.