Consistent Query Answering for Primary Keys

We study the complexity of consistent query answering with respect to primary key violations, for self-join-free conjunctive queries. A repair of a possibly inconsistent database is obtained by selecting a maximal number of tuples without selecting two distinct tuples with the same primary key value. For any Boolean query q, CERTAINTY(q) is the problem that takes a database as input, and asks whether q is true in every repair of the database. The complexity of this problem has been extensively studied for q ranging over the class of self-join-free Boolean conjunctive queries. A research challenge is to determine, given q, whether CERTAINTY(q) belongs to complexity classes FO, P, or coNP-complete. We show that for any self-join-free Boolean conjunctive query q, it can be decided whether or not CERTAINTY(q) is in FO. Further, CERTAINTY(q) is either in P or coNP-complete, and the complexity dichotomy is effective. This settles a research question of practical relevance that has been open for ten years.