Relative inconsistency measures

摘要

The literature on inconsistency measures has ignored a distinction, that is, differentiating absolute measures and relative measures. An absolute measure gives the total amount of inconsistency in the knowledge base but a relative measure computes, by some criteria, the proportion of the base that is inconsistent. To compare the inconsistency measures, researchers have proposed postulates for such measures. We split these postulates into three groups: ones (including two new postulates) that relative measures should satisfy, ones inappropriate for relative measures, and ones that relative measures may satisfy. We obtain some new results upon the relationships between these groups of postulates. On these grounds, we introduce a formal definition for relative inconsistency measures. We consider some relative measures previously proposed and define several new ones that serve as examples. We show that all of these measures satisfy the new formal definition.