Can Uncertainty Management be Realized in a Finite Totally Ordered Probability Algebra?

In this paper, the feasibility of using finite totally ordered probability models under Aleliunas’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.

• Type: Conference
• Year: 1989
• Where: UAI
• Authors: Yang Xiang, Michael P. Beddoes, David Poole
• Keywords: Probability Algebra, Probability Model, UAI 1989, UAI 2008, finite Probability Model