How Many Inconsistencies Are In Your Database?

Measuring inconsistency is an approach that provides ways to quantify the severity of inconsistency and helps understanding the primary sources of conflicts. In this paper, we discuss inconsistency measures for indefinite databases, which allow for indefinite or partial information which is formally expressed by means of disjunctive tuples. We introduce inconsistency measures for indefinite databases with denial constraints, and explore the complexity of the problem of computing the value of the proposed inconsistency measures as well as of the problems of deciding whether the inconsistency value is lower than, greater than, or equal to a given threshold for indefinite and definite databases.