Jeffrey's rule of conditioning generalized to belief functions

Jeffrey's rule of conditioning has been proposed in order to revise a probability measure by another probability function. We generalize it within the framework of the models based on belief functions. We show that several forms of Jeffrey's conditionings can be defined that correspond to the geometrical rule of conditioning and to Dempster's rule of conditioning, respectively.

[1]  Carl G. Wagner Generalizing Jeffrey Conditionalization , 1992, UAI.

[2]  G. Shafer Jeffrey's Rule of Conditioning , 1981, Philosophy of Science.

[3]  Philippe Smets,et al.  The Transferable Belief Model , 1994, Artif. Intell..

[4]  Philippe Smets About Updating , 1991, UAI.

[5]  Didier Dubois,et al.  Belief Revision and Updates in Numerical Formalisms: An Overview, with new Results for the Possibilistic Framework , 1993, IJCAI.

[6]  Philippe Smets,et al.  The Nature of the Unnormalized Beliefs Encountered in the Transferable Belief Model , 1992, UAI.

[7]  Didier Dubois,et al.  Focusing versus updating in belief function theory , 1994 .

[8]  B. Dahn Foundations of Probability theory, statistical inference, and statistical theories of science , 1978 .

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

[10]  Didier Dubois,et al.  On the unicity of dempster rule of combination , 1986, Int. J. Intell. Syst..

[11]  A. Hasman,et al.  Probabilistic reasoning in intelligent systems: Networks of plausible inference , 1991 .

[12]  David J. Goodman,et al.  Personal Communications , 1994, Mobile Communications.

[13]  P. Garbolino Quantified Uncertainty. A Bayesian Viewpoint , 1991 .

[14]  Hidetomo Ichihashi,et al.  Jeffrey-like rules of conditioning for the Dempster-Shafer theory of evidence , 1989, Int. J. Approx. Reason..

[15]  A. Tversky,et al.  Languages and designs for probability , 1985 .

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

[17]  Ronald Fagin,et al.  A new approach to updating beliefs , 1990, UAI.

[18]  G. Shafer A Theory of Statistical Evidence , 1976 .

[19]  Didier Dubois,et al.  Updating with belief functions, ordinal conditional functions and possibility measures , 1990, UAI.

[20]  E. Ruspini The Logical Foundations of Evidential Reasoning (revised) , 1987 .

[21]  I. Graham Non-standard logics for automated reasoning , 1990 .

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

[23]  Petr Hájek,et al.  On Belief Functions , 1992, Advanced Topics in Artificial Intelligence.

[24]  Glenn Shafer,et al.  Languages and Designs for Probability Judgment , 1985, Cogn. Sci..