Salem Benferhat, Didier Dubois, Henri Prade
This paper offers a detailed analysis of the structure of this family of possibility distributions by exploiting two different orderings between them: Yager’s specificity ordering and a new refinement ordering. It is shown that from a representation point of view, it is sufficient to consider the subset of linear possibility distributions which corresponds to all the possible completions of the default knowledge in agreement with the constraints. There also exists a semantics for system P in terms of infinitesimal probabilities. Surprisingly, it is also shown that a standard probabilistic semantics can be equivalently given to System P, without referring to infinitesimals, by using a special family of probability measures, that two of the authors have called acceptance functions, and that has been also recently considered by Snow in that perspective.