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A well-known procedure of this kind is that related to the enlargement of a probability assessment, given on a class of (conditional) events {Hi , E|Hi } (with incompatible and exhaustive Hi = Hi |Ω, where Ω is the sure event), to the events {Hi |E} through Bayes’ theorem. The attractiveness 17 ch02 June 2,2008 10:50 18 spi-b560 Uncertainty and Intelligent Information Systems 9in x 6in G. Busanello et al. and the relevant success of this specific case is due mainly to its simplicity and to the uniqueness of the answer.
The second edition was reprinted by the State Publishing House, Moscow (1959). 9. -A. Cournot, Exposition de la th´eorie des chances et des probabilit´es. Hachette, Paris, 1843. Reprinted in 1984 as Vol. I (B. ) of Ref. 1, 10. -A. Cournot, Euvres compl`etes. Vrin, Paris, 1973–1984. Vols. 10, with an eleventh to appear. 11. A. P. Dawid, Statistical theory: The prequential approach (with discussion). Journal of the Royal Statistical Society. Series A, 147, 278–292 (1984). 12. B. de Finetti, Recent suggestions for the reconciliation of theories of probability.
1. Introduction During the knowledge acquisition process (as in decision theory), a fundamental role is played by the problem of enlarging the domain of events of interest and the ensuing relevant values of the reference measure (such as uncertainty or information measure). This process is usually referred to as “inferential process”. A well-known procedure of this kind is that related to the enlargement of a probability assessment, given on a class of (conditional) events {Hi , E|Hi } (with incompatible and exhaustive Hi = Hi |Ω, where Ω is the sure event), to the events {Hi |E} through Bayes’ theorem.