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Probability of deductibility and belief functions

  • Philippe Smets
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 747)

Abstract

We present an interpretation of Dempster-Shafer theory based on the probability of deducibility. We present two forms of revision (conditioning) that lead to the geometrical rule of conditioning and to Dempster rule of conditioning, respectively.

Keywords

Probability Measure Belief Function Geometrical Rule Plausibility Function Disjunctive Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. DEMPSTER A.P. (1967) Upper and lower probabilities induced by a multplevalued mapping. Ann. Math. Statistics 38:325–339.Google Scholar
  2. DUBOIS D., GARBOLINO P., KYBURG H.E., PRADE H. and SMETS Ph. (1991) Quantified Uncertainty. J. Applied Non-Classical Logics 1:105–197.Google Scholar
  3. JAFFRAY J.Y. (1992) Bayesian Updating and belief functions. IEEE Trans. SMC, 22:1144–1152.Google Scholar
  4. KOHLAS J. and MONNEY P. A. (1990) Modeling and reasoning with hints. Technical Report. Inst. Automation and OR. Univ. Fribourg.Google Scholar
  5. KRUSE R. and GEBHARDT J. (1993) Updating mechanisms for imprecise data. DRUMS II workshop on Belief Change. Duboie D. and Prade H. Eds., IRIT, Univ. Paul Sabatier, Toulouse, pg. 8–22.Google Scholar
  6. EARL J. (1988) Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann Pub. San Mateo, Ca, USA.Google Scholar
  7. RUSPINI E.H. (1986) The logical foundations of evidential reasoning. Technical note 408, SRI International, Menlo Park, Ca.Google Scholar
  8. SHAFER G. (1976a) A mathematical theory of evidence. Princeton Univ. Press. Princeton, NJ.Google Scholar
  9. SHAFER G. (1976b) A theory of statistical evidence, in Foundations of probability theory, statistical inference, and statistical theories of science. Harper and Hooker ed. Reidel, Doordrecht-Holland.Google Scholar
  10. SHAFER G. and TVERSKY A. (1985) Laages and designs for probability. Cognitive Sc. 9:309–339.Google Scholar
  11. SMETS P. (1988) Belief functions. in SMETS Ph, MAMDANI A., DUBOIS D. and PRADE H. eds. Non standard logics for automated reasoning. Academic Press, London p 253–286.Google Scholar
  12. SMETS P. (1991a) About updating. in D'Ambrosio B., Smets P., and Bonissone P.P. eds. Uncertainty in AI 91, Morgan Kaufmann, San Mateo, Ca, USA, 1991, 378–385.Google Scholar
  13. SMETS P. (1992b) An axiomatic justifiaction for the use of belief function to quantify beliefs. IRIDIA-TR-92-11. To appear in IJCAI-93.Google Scholar
  14. SMETS P. (1993a) Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem. Int. J. Approximate Reasoning.Google Scholar
  15. SMETS P. (1993b) Probability od deducibility and belief functions. IRIDIA-TR-93-5/2Google Scholar
  16. SMETS P. and KENNES R. (1990) The transferable belief model. Technical Report: IRIDIA-TR-90-14.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Philippe Smets
    • 1
  1. 1.IRIDIA, Université Libre de BruxellesBrusselsBelgium

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