Measuring and repairing inconsistency in knowledge bases with graded truth

In this paper we present a family of measures aimed at determining the amount of inconsistency in knowledge bases with graded truth, i.e., knowledge bases that consist of propositions along with a degree of truth or an interval of possible degrees of truth. Our approach to measuring inconsistency is also graded in the sense that we consider minimal adjustments in the truth degrees of the propositions necessary to make the knowledge base consistent within the frame of Łukasiewicz semantics. The computation of the family of measures we present here, in as much as it yields an adjustment in the truth degrees of each proposition that restores or brings consistency, provides the modeler with possible repairs of the knowledge base. Our motivation and case study for this paper is the fuzzy medical expert system CADIAG2.