On the Relation between Kappa Calculus and Probabilistic Reasoning

TL;DR

This paper explores the relationship between kappa calculus and probabilistic reasoning in diagnosis, showing they often produce similar fault orderings and analyzing when they diverge, with implications for uncertainty modeling.

Contribution

It provides a formal comparison between kappa calculus and probabilistic reasoning, including conditions under which their fault orderings align or differ.

Findings

Fault orderings coincide when all causal relations are considered.

Differences occur in specific network structures.

Results impact the use of kappa rankings in knowledge engineering.

Abstract

We study the connection between kappa calculus and probabilistic reasoning in diagnosis applications. Specifically, we abstract a probabilistic belief network for diagnosing faults into a kappa network and compare the ordering of faults computed using both methods. We show that, at least for the example examined, the ordering of faults coincide as long as all the causal relations in the original probabilistic network are taken into account. We also provide a formal analysis of some network structures where the two methods will differ. Both kappa rankings and infinitesimal probabilities have been used extensively to study default reasoning and belief revision. But little has been done on utilizing their connection as outlined above. This is partly because the relation between kappa and probability calculi assumes that probabilities are arbitrarily close to one (or zero). The experiments in this paper investigate this relation when this assumption is not satisfied. The reported results have important implications on the use of kappa rankings to enhance the knowledge engineering of uncertainty models.