**Dept. of Computer and Information science, Linköping University**

## IDA Technical Reports: abstract

*Generated: Tue, 27 Jan 2015 17:50:54 *

Driankov, D. (1986).
**Inference with Consistent Probabilities in Expert Systems**.
Technical Report LiTH-IDA-R-86-12, Department of Computer and Information
Science, Linköping University, Sweden.
Also in Proc. of IJCAI-87.
(bibtex),

**Abstract: **The objective of the present paper is twofold:
first, to provide an algorithm which helps in eliciting consistent, with
respect to the axioms of the probability theory, a priori and conditional
probabilities as well as higher order conditional and joint probabilities for
a set of events representing pieces of evidence and hypotheses in the context
of a rule based expert system. The algorithm proposed, utilizes the least
possible number of a priori and conditional probabilities as input in order
to obtain all the remaining ones and then, proceeds further by producing the
lower and upper bounds for particular higher order conditional and joint
probabilities so that these be consistent with the input provided. In the
case, when inconsistent lower and upper bounds are obtained, it is shown how
the latter can be turned into consistent ones by changing the values of only
these input-probabilities which are directly representing the higher order
probability expressions under consideration.Secondly, a number of typical
cases with respect to the problems of aggregation and propagation of
uncertainty in expert systems is presented and it is shown how these can be
modelled using the results of the algorithm proposed. For this purpose no
global assumptions for independence of evidence and for mutual exclusiveness
of hypotheses are required since the presence of independent and/or dependent
pieces of evidence as well as the presence of mutually exclusive hypotheses
is explicitly encoded in the input-probabilities and thus, such a presence is
automatically taken care of by the algorithm when obtaining higher order
probabilities.

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