Combined Approximations for Uniform Operational Consistent Query Answering

TL;DR

This paper investigates the feasibility of approximating the percentage of repairs that entail a query in operational consistent query answering, focusing on specific query classes and introducing a new counting complexity class.

Contribution

It establishes the existence of efficient approximation schemes for certain classes of conjunctive queries and introduces the $ ext{SpanTL}$ complexity class for counting problems in this context.

Findings

Efficient approximation schemes exist for self-join-free conjunctive queries with bounded generalized hypertreewidth.

Such schemes are unlikely for queries outside these syntactic restrictions.

The paper introduces the $ ext{SpanTL}$ complexity class and demonstrates its relevance to approximation problems in CQA.

Abstract

Operational consistent query answering (CQA) is a recent framework for CQA based on revised definitions of repairs, which are built by applying a sequence of operations (e.g., fact deletions) starting from an inconsistent database until we reach a database that is consistent w.r.t. the given set of constraints. It has been recently shown that there is an efficient approximation for computing the percentage of repairs that entail a given query when we focus on primary keys, conjunctive queries, and assuming the query is fixed (i.e., in data complexity). However, it has been left open whether such an approximation exists when the query is part of the input (i.e., in combined complexity). We show that this is the case when we focus on self-join-free conjunctive queries of bounded generelized hypertreewidth. We also show that it is unlikely that efficient approximation schemes exist once we give up one of the adopted syntactic restrictions, i.e., self-join-freeness or bounding the generelized hypertreewidth. Towards the desired approximation, we introduce a counting complexity class, called $\mathsf{SpanTL}$, show that each problem in it admits an efficient approximation scheme by using a recent approximability result about tree automata, and then place the problem of interest in $\mathsf{SpanTL}$.