Sur les fonctions ordinales conditionnelles transfinies

Ordinal Conditional Functions (OCFs) are one of the predominant frameworks to define belief change operators. In his original paper Spohn defines OCFs as functions from the set of worlds to the set of ordinals. But in subsequent paper by Spohn and others, OCFs are just used as functions from the set of worlds to natural numbers (plus eventually +∞). The use of transfinite ordinals in this framework has never been studied. This paper opens this way. We study generalisations of transmutations operators to transfinite ordinals. Using transfinite ordinals allows to represent different “levels of beliefs”, that naturally appear in real applications. This can be viewed as a generalisation of the usual “two levels of beliefs” framework : knowledge versus beliefs ; or rules base versus facts base, issued from expert systems works.