Data Cleaning and Query Answering with Matching Dependencies and Matching Functions

TL;DR

This paper introduces a formal framework for data cleaning and query answering using matching dependencies and functions, establishing a lattice structure and semantics for clean answers, with complexity analysis and approximation methods.

Contribution

It formalizes the process of data cleaning with matching dependencies, introduces a lattice structure on attribute domains, and defines semantics for clean query answering including approximation techniques.

Findings

Clean query answering is intractable in some cases.

Monotone queries allow for under/over approximation of clean answers.

Non-monotone positive queries can be relaxed into monotone queries.

Abstract

Matching dependencies were recently introduced as declarative rules for data cleaning and entity resolution. Enforcing a matching dependency on a database instance identifies the values of some attributes for two tuples, provided that the values of some other attributes are sufficiently similar. Assuming the existence of matching functions for making two attributes values equal, we formally introduce the process of cleaning an instance using matching dependencies, as a chase-like procedure. We show that matching functions naturally introduce a lattice structure on attribute domains, and a partial order of semantic domination between instances. Using the latter, we define the semantics of clean query answering in terms of certain/possible answers as the greatest lower bound/least upper bound of all possible answers obtained from the clean instances. We show that clean query answering is intractable in some cases. Then we study queries that behave monotonically wrt semantic domination order, and show that we can provide an under/over approximation for clean answers to monotone queries. Moreover, non-monotone positive queries can be relaxed into monotone queries.