On the Relation between Kappa Calculus and Probabilistic Reasoning
  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.
