Can Uncertainty Management be Realized In a Finite Totally Ordered Probability Algebra?
Yang Xiang, Michael Beddoes, David Poole
In this paper, the feasibility of using finite totally ordered probability models under Alelinnas's Theory of Probabilistic Logic [Aleliunas, 1988] is investigated. The general form of the probability algebra of these models is derived and the number of possible algebras with given size is deduced. Based on this analysis, we discuss problems of denominator-indifference and ambiguity-generation that arise in reasoning by cases and abductive reasoning. An example is given that illustrates how these problems arise. The investigation shows that a finite probability model may be of very limited usage.
PDF Link: /papers/89/
AUTHOR = "Yang Xiang
and Michael Beddoes and David Poole",
TITLE = "Can Uncertainty Management be Realized In a Finite Totally Ordered Probability Algebra?",
BOOKTITLE = "Uncertainty in Artificial Intelligence 5 Annual Conference on Uncertainty in Artificial Intelligence (UAI-89)",
PUBLISHER = "Elsevier Science",
ADDRESS = "Amsterdam, NL",
YEAR = "1989",
PAGES = "41--57"