Inconsistency Measures for Relational Databases

TL;DR

This paper introduces and analyzes inconsistency measures for relational databases, focusing on how to quantify and understand data conflicts, especially with denial constraints, and explores their theoretical properties and computational complexity.

Contribution

It proposes new inconsistency measures that focus solely on database tuples, ignoring constraints, and analyzes their rationality and computational complexity.

Findings

Measures comply with rationality postulates

Relationships between different inconsistency measures are identified

Complexity results for measuring and comparing inconsistencies are provided

Abstract

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.