Optimization of Answer Set Programs for Consistent Query Answering by Means of First-Order Rewriting

Abstract

Consistent Query Answering (CQA) with respect to primary keys is the following problem. Given a database instance that is possibly inconsistent with respect to its primary key constraints, define a repair as an inclusion-maximal consistent subinstance. Given a Boolean query q, the problem CERTAINTY(q) takes a database instance as input, and asks whether q is true in every repair. For every Boolean conjunctive query q, the complement of CERTAINTY(q) can be straightforwardly implemented in Answer Set Programming (ASP) by means of a generate-and-test approach: first generate a repair, and then test whether it falsifies the query. Theoretical research has recently revealed that for every self-join-free Boolean conjunctive query q, the complexity class of CERTAINTY(q) is one of FO, L-complete, or coNP-complete. Faced with this complexity trichotomy, one can hypothesize that in practice, the full power of generate-and-test is a computational overkill when CERTAINTY(q) is in the low complexity classes FO or L. We investigate part of this hypothesis within the context of ASP, by asking the following question: whenever CERTAINTY(q) is in FO, does a dedicated first-order algorithm exhibit significant performance gains compared to a generic generate-and-test implementation? We first elaborate on the construction of such dedicated first-order algorithms in ASP, and then empirically address this question.