On the tractability and intractability of consistent conjunctive query answering

Abstract

The consistent query answering framework has received considerable attention since it was first introduced as an alternative to coping with inconsistent databases. The framework was defined based on two notions: repairs and consistent query answers. Informally, a repair is a consistent database that minimally differs from the inconsistent database. The consistent answers to a query are those tuples that appear in the intersection of the answer sets of the query when evaluated over all possible repairs. Here we study the complexity of the problem of consistent query answering for the class of acyclic conjunctive queries without self-joins, under primary key constraints. The problem is known to be coNP-complete in general for this class. Our goal is to determine the boundary between tractability and intractability, by establishing a dichotomy to the effect that, every conjunctive query in this class is either in PTIME or coNP-complete. In the PTIME direction, previous work has identified the queries for which consistent answers can be computed via first-order rewriting. In fact, for the class of acyclic conjunctive queries without self-joins, under primary key constraints, the boundary between first-order rewritable and not first-order rewritable queries has already been determined. Hence, our focus is on queries for which there is no first-order rewriting. We present a technique for computing in polynomial time the consistent query answers to several not first-order rewritable queries. We hope this technique may lay the foundations for a more general algorithm that handles all PTIME not first-order rewritable queries. In the hardness direction, we identify several representative queries of the class, for which we show that the problem is coNP-hard.This work is done under the supervision of Prof. Phokion G. Kolaitis and Prof. Wang-Chiew Tan.