Combined Approximations for Uniform Operational Consistent Query Answering

2025-08-16

AI Summary

This paper addresses the problem of efficiently approximating the repair ratio—the fraction of repairs satisfying a given union of conjunctive queries (UCQ)—over an inconsistent database with primary key constraints, under operational consistency query answering (CQA). The method introduces a new counting complexity class, SpanTL, and integrates tree-automata-based approximability theory, generalized hypertree decompositions (GHDs), and an extension of the SpanL function class to devise the first polynomial-time approximation scheme for UCQs of bounded generalized hypertree width. The result is tight: relaxing either the primary key constraint or the bounded-GHD-width condition renders approximation intractable unless P = NP. This work establishes the first efficient approximation framework for operational repair semantics that provides both rigorous theoretical guarantees and practical tractability bounds.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Data Mining & Knowledge Management: Intelligent Query Processing

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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 $mathsf{SpanTL}$.

Problem

• Efficient approximation for operational CQA in combined complexity
• Focus on self-join-free conjunctive queries with bounded hypertreewidth
• Investigate existence of approximation schemes under syntactic restrictions

Innovation

• Combined complexity approximation for CQA
• Self-join-free bounded hypertreewidth queries
• SpanTL class with efficient approximation schemes