Can Uncertainty Management be Realized in a Finite Totally Ordered Probability Algebra?
This work addresses theoretical limitations in probabilistic logic for researchers in AI and logic, but it is incremental as it builds on existing theory to analyze specific issues.
The paper investigates the feasibility of finite totally ordered probability models under Aleliunas's Theory of Probabilistic Logic, deriving their general form and counting possible algebras, and shows that such models have limited usage due to problems like denominator-indifference and ambiguity-generation in reasoning tasks.
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.