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

In this paper, the feasibility of using fi­ nite totally ordered probability models un­ der Aleliunas's Theory of Probabilistic Logic [Aleliunas 88] is investigated. The general form of the probability algebra of these models is derived and the number of pos­ sible 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 us­ age.