On the Consistent Rewriting of Conjunctive Queries Under Primary Key Constraints

Abstract

This article deals with the computation of consistent answers to queries on relational databases that violate primary key constraints. A repair of such inconsistent database is obtained by selecting a maximal number of tuples from each relation without ever selecting two distinct tuples that agree on the primary key. We are interested in the following problem: Given a Boolean conjunctive query q, compute a Boolean first-order (FO) query ψ such that for every database db, ψ evaluates to true on db if and only if q evaluates to true on every repair of db. Such ψ is called a consistent FO rewriting of q. We use novel techniques to characterize classes of queries that have a consistent FO rewriting. In this way, we are able to extend previously known classes and discover new ones. Finally, we use an Ehrenfeucht-Fraisse game to show the non-existence of a consistent FO rewriting for (the existential closure of) R(x, y) ∧ R(y, c), where c is a constant and the first coordinate of R is the primary key.