On Transformations between Probability and Spohnian Disbelief Functions
This work addresses foundational issues in representing uncertain beliefs for AI and expert systems, though it appears incremental as it builds on existing theories.
The paper tackles the relationship between probability and Spohnian disbelief functions by studying transformations between them, which differ from existing literature by satisfying principles of ordinal congruence. The result contributes to clarifying semantics and enabling decision theory for nonprobabilistic belief calculi, facilitating combination in expert systems.
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 Sphonian disbelief and vice-versa. The transformations described in this paper are different from those described in the literature. In particular, the former satisfies the principles of ordinal congruence while the latter does not. Such transformations between probability and Spohn's calculi can contribute to (1) a clarification of the semantics of nonprobabilistic 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.