Consistent Query Answers in the Presence of Universal Constraints

TL;DR

This paper studies the complexity of consistent query answers under universal constraints, introducing an extended conflict hypergraph and polynomial algorithms for certain classes, while identifying intractable cases.

Contribution

It proposes a new hypergraph-based framework for repairs, provides polynomial algorithms for specific constraints, and characterizes complexity boundaries for consistent query answering.

Findings

Repair checking is in PTIME for full tuple-generating dependencies and denial constraints.

A polynomial repair algorithm is presented that is both sound and complete.

Consistent query answering becomes intractable for more general classes of constraints.

Abstract

The framework of consistent query answers and repairs has been introduced to alleviate the impact of inconsistent data on the answers to a query. A repair is a minimally different consistent instance and an answer is consistent if it is present in every repair. In this article we study the complexity of consistent query answers and repair checking in the presence of universal constraints. We propose an extended version of the conflict hypergraph which allows to capture all repairs w.r.t. a set of universal constraints. We show that repair checking is in PTIME for the class of full tuple-generating dependencies and denial constraints, and we present a polynomial repair algorithm. This algorithm is sound, i.e. always produces a repair, but also complete, i.e. every repair can be constructed. Next, we present a polynomial-time algorithm computing consistent answers to ground quantifier-free queries in the presence of denial constraints, join dependencies, and acyclic full-tuple generating dependencies. Finally, we show that extending the class of constraints leads to intractability. For arbitrary full tuple-generating dependencies consistent query answering becomes coNP-complete. For arbitrary universal constraints consistent query answering is \Pi_2^p-complete and repair checking coNP-complete.