Logical comparison of inconsistent perspectives using scoring functions

The language for describing inconsistency is underdeveloped. If a database (a set of formulae) is inconsistent, there is usually no qualification of that inconsistency. Yet, it would seem useful to be able to say how inconsistent a database is, or to say whether one database is "more inconsistent" than another database. In this paper, we provide a more general characterization of inconsistency in terms of a scoring function for each database Delta. A scoring function S is from the power set of Delta into the natural numbers defined so that S(Gamma) gives the number of minimally inconsistent subsets of Delta that would be eliminated if the subset Gamma was removed from Delta. This characterization offers an expressive and succinct means for articulating, in general terms, the nature of inconsistency in a set of formulae. We then compare databases using their scoring functions. This gives an intuitive ordering relation over databases that we can describe as "more inconsistent than". These techniques are potentially useful in a wide range of problems including monitoring progress in negotiations between a number of participants, and in comparing heterogeneous sources of information.