The use of interval probability theory (IPT) for uncertain inference i
s demonstrated. The general inference rule adopted is the theorem of t
otal probability. This enables information on the relevance of the ele
ments of the power set of evidence to be combined with the measures of
the support for and dependence between each item of evidence. The app
roach recognises the importance of the structure of inference problems
and yet is an open world theory in which the domain need not be compl
etely specified in order to obtain meaningful inferences. IPT is used
to manipulate conflicting evidence and to merge evidence on the depend
ability of a process with the data handled by that process. Uncertain
inference using IPT is compared with Bayesian inference. (C) 1998 Else
vier Science Inc. All rights reserved.