Hierarchical Evidence and Belief Functions

TL;DR

This paper explores how belief rules in automated reasoning can be transformed into joint belief functions for propagation, highlighting the impact of different representations on inferred beliefs.

Contribution

It introduces a method to convert belief rules into joint belief functions and analyzes how different representations affect belief propagation.

Findings

Different joint belief functions can be consistent with the same rules.

Representation choices influence the resulting beliefs on hypotheses.

Transforming rules into joint belief functions enables belief propagation in reasoning systems.

Abstract

Dempster/Shafer (D/S) theory has been advocated as a way of representing incompleteness of evidence in a system's knowledge base. Methods now exist for propagating beliefs through chains of inference. This paper discusses how rules with attached beliefs, a common representation for knowledge in automated reasoning systems, can be transformed into the joint belief functions required by propagation algorithms. A rule is taken as defining a conditional belief function on the consequent given the antecedents. It is demonstrated by example that different joint belief functions may be consistent with a given set of rules. Moreover, different representations of the same rules may yield different beliefs on the consequent hypotheses.