On Transformations between Probability and Spohnian Disbelief Functions
Phan Giang, Prakash Shenoy
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.
Keywords: spohn's epistemic belief, kappa calculus
PDF Link: /papers/99/p236-giang.pdf
AUTHOR = "Phan Giang
and Prakash Shenoy",
TITLE = "On Transformations between Probability and Spohnian Disbelief Functions",
BOOKTITLE = "Proceedings of the Fifteenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-99)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "1999",
PAGES = "236--244"