On Transformations between Probability and Spohnian Disbelief Functions

Abstract

In this paper, we analyze the relationship between probability and Spohn's theory for representation of uncertain beliefs. Using the intuitive idea that the more probable a proposition is, the more believable it is, we study transformations from probability to Spohnian disbelief and vice-versa. The transformations described in this paper are different from those described in the literature. In particular, the former satisfies the principle of ordinal congurence while the latter does not. Such transformations between probability and Spohn's calculi can contribute to (1) a clarification of the semantics of non-probabilistic degree of uncertain belief, and (2) to a construction of a decision theory for such calculi. In practice, the transformations will allow a meaningful combination of more than one calculus in different stages of using an expert system such as knowledge acquisition, inference, and interpretation of results.