Consistent Query Answering for Primary Keys on Path Queries

We study the data complexity of consistent query answering (CQA) on databases that may violate the primary key constraints. A repair is a maximal consistent subset of the database. For a Boolean query q, the problem CERTAINTY(q) takes a database as input, and asks whether or not each repair satisfies the query q. It is known that for any self-join-free Boolean conjunctive query q, CERTAINTY(q) is in FO, L-complete, or coNP-complete. In particular, CERTAINTY(q) is in FO for any self-join-free Boolean path query q. In this paper, we show that if self-joins are allowed, then the complexity of CERTAINTY(q) for Boolean path queries q exhibits a tetrachotomy between FO, NL-complete, PTIME-complete, and coNP-complete. Moreover, it is decidable, in polynomial time in the size of the query q, which of the four cases applies.