Consistent Query Answering for Primary Keys and Conjunctive Queries with Negated Atoms.

This paper studies query answering on databases that may be inconsistent with respect to primary key constraints. A repair is any consistent database that is obtained by deleting a minimal set of tuples. Given a Boolean query q, the problem CERTAINTY(q) takes a database as input and asks whether q is true in every repair of the database. A significant complexity classification task is to determine, given q, whether CERTAINTY(q) is first-order definable (and thus solvable by a single SQL query). This problem has been extensively studied for self-join-free conjunctive queries. An important extension of this class of queries is to allow negated atoms. It turns out that if negated atoms are allowed, CERTAINTY(q) can express some classical matching problems. This paper studies the existence and construction of first-order definitions for CERTAINTY(q) for q in the class of self-join-free conjunctive queries with negated atoms.