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

📝 Original Info

• Title: Can Uncertainty Management be Realized in a Finite Totally Ordered Probability Algebra?
• ArXiv ID: 1304.1535
• Date: 2013-04-08
• Authors: Researchers from original ArXiv paper

📝 Abstract

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.

💡 Deep Analysis

Deep Dive into 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 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.

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