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.
This work has been partially funded by the CEC-ESPRIT III Basic Research Project 6156 (DRUMS II), and the Communauté Française de Belgique, ARC 92/97-160 (BELON).
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References
DEMPSTER A.P. (1967) Upper and lower probabilities induced by a multplevalued mapping. Ann. Math. Statistics 38:325–339.
DUBOIS D., GARBOLINO P., KYBURG H.E., PRADE H. and SMETS Ph. (1991) Quantified Uncertainty. J. Applied Non-Classical Logics 1:105–197.
JAFFRAY J.Y. (1992) Bayesian Updating and belief functions. IEEE Trans. SMC, 22:1144–1152.
KOHLAS J. and MONNEY P. A. (1990) Modeling and reasoning with hints. Technical Report. Inst. Automation and OR. Univ. Fribourg.
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.
EARL J. (1988) Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann Pub. San Mateo, Ca, USA.
RUSPINI E.H. (1986) The logical foundations of evidential reasoning. Technical note 408, SRI International, Menlo Park, Ca.
SHAFER G. (1976a) A mathematical theory of evidence. Princeton Univ. Press. Princeton, NJ.
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.
SHAFER G. and TVERSKY A. (1985) Laages and designs for probability. Cognitive Sc. 9:309–339.
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.
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.
SMETS P. (1992b) An axiomatic justifiaction for the use of belief function to quantify beliefs. IRIDIA-TR-92-11. To appear in IJCAI-93.
SMETS P. (1993a) Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem. Int. J. Approximate Reasoning.
SMETS P. (1993b) Probability od deducibility and belief functions. IRIDIA-TR-93-5/2
SMETS P. and KENNES R. (1990) The transferable belief model. Technical Report: IRIDIA-TR-90-14.
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Smets, P. (1993). Probability of deductibility and belief functions. In: Clarke, M., Kruse, R., Moral, S. (eds) Symbolic and Quantitative Approaches to Reasoning and Uncertainty. ECSQARU 1993. Lecture Notes in Computer Science, vol 747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028218
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DOI: https://doi.org/10.1007/BFb0028218
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