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

TL;DR

This paper explores the potential and limitations of finite totally ordered probability models within Aleliunas's probabilistic logic, analyzing their algebraic structure and practical applicability.

Contribution

It derives the general form of these probability algebras, counts possible algebras of given size, and discusses inherent reasoning problems.

Findings

Finite probability models may have limited practical use.

Problems of denominator-indifference and ambiguity-generation are identified.

An illustrative example demonstrates these issues.

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.