Inconsistency Measures for Relational Databases

In this paper, building on work done on measuring inconsistency in knowledge bases, we introduce inconsistency measures for databases. In particular, focusing on databases with denial constraints, we first consider the natural approach of virtually transforming a database into a propositional knowledge base and then applying well-known measures. However, using this method, tuples and constraints are equally considered in charge of inconsistencies. Then, we introduce a version of inconsistency measures blaming database tuples only, i.e., treating integrity constraints as irrefutable statements. We analyze the compliance of database inconsistency measures with standard rationality postulates and find interesting relationships between measures. Finally, we investigate the complexity of the inconsistency measurement problem as well as of the problems of deciding whether the inconsistency is lower than, greater than, or equal to a given threshold.