BAYESIAN CONDITIONING IN POSSIBILITY THEORY

In this paper, possibility measures are viewed as upper bounds of ill- known probabilities, since a possibility distribution is a faithful en coding of a set of lower bounds of probabilities bearing on a nested c ollection of subsets. Two kinds of conditioning can be envisaged in th is framework, namely revision and focusing. On the one hand, revision by a sure event corresponds to adding an extra constraint enforcing th at this event is impossible. On the other hand, focusing amounts to a sensitivity analysis on the conditioned probability measures (induced by the lower bound constraints). When focusing on a particular situati on, the generic knowledge encoded by the probability bounds is applied to this situation, without aiming at modifying the generic knowledge. It contrasts with revision where the generic knowledge is modified by the new constraint. This paper proves that focusing applied to a poss ibility measure yields a possibility measure again, which means that t he conditioning of a family of probabilities, induced by lower bounds bearing on probabilities of nested events, can be faithfully handled o n the possibility representation itself. Relationships with similar re sults in the belief function setting are pointed out. Lastly the appli cation of possibilistic focusing to exception-tolerant inference is su ggested. (C) 1997 Elsevier Science B.V.