First-order under-approximations of consistent query answers

Abstract

Consistent Query Answering (CQA) is a principled approach for answering queries on inconsistent databases. The consistent answer to a query q on an inconsistent database db is the intersection of the answers to q on all repairs, where a repair is any consistent database that is maximally close to db. Unfortunately, computing consistent answers under primary key constraints has already exponential data complexity for very simple conjunctive queries, and is therefore completely impracticable.In this paper, we propose a new framework for divulging an inconsistent database to end users, which adopts two postulates. The first postulate complies with CQA and states that inconsistencies should never be divulged to end users. Therefore, end users should only get consistent query answers. The second postulate states that only those queries can be answered whose consistent answers can be obtained with low data complexity (i.e., by a polynomial-time algorithm or even a first-order logic query). User queries that exhibit a higher data complexity will be rejected.A significant problem in this framework is as follows: given a rejected query, find other queries, called under-approximations, that are accepted and whose consistent answers are contained in those of the rejected query. We provide solutions to this problem for the special case where the constraints are primary keys and the queries are self-join-free conjunctive queries.