Consistent Query Answering for Primary Keys in Datalog

Abstract

We study the complexity of consistent query answering on databases that may violate primary key constraints. A repair of such a database is any consistent database that can be obtained by deleting a minimal set of tuples. For every Boolean query q, CERTAINTY(q) is the problem that takes a database as input and asks whether q evaluates to true on every repair. In Koutris and Wijsen (ACM Trans. Database Syst. 42(2), 9:1–9:45, 2017), the authors show that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either in P or coNP-complete, and it is decidable which of the two cases applies. In this article, we sharpen this result by showing that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either expressible in symmetric stratified Datalog (with some aggregation operator) or coNP-complete. Since symmetric stratified Datalog is in L, we thus obtain a complexity-theoretic dichotomy between L and coNP-complete. Another new finding of practical importance is that CERTAINTY(q) is on the logspace side of the dichotomy for queries q where all join conditions express foreign-to-primary key matches, which is undoubtedly the most common type of join condition.