Measuring and repairing inconsistency in probabilistic knowledge bases

In this paper we present a family of measures aimed at determining the amount of inconsistency in probabilistic knowledge bases. Our approach to measuring inconsistency is graded in the sense that we consider minimal adjustments in the degrees of certainty (i.e., probabilities in this paper) of the statements necessary to make the knowledge base consistent. The computation of the family of measures we present here, in as much as it yields an adjustment in the probability of each statement that restores consistency, provides the modeler with possible repairs of the knowledge base. The case example that motivates our work and on which we test our approach is the knowledge base of CADIAG-2, a well-known medical expert system.