How Hard is it to Decide if a Fact is Relevant to a Query?

2026-04-24

AI Summary

This study addresses the problem of determining the relevance of a database fact to the answer of a Boolean conjunctive query—specifically, whether the fact belongs to a minimal subset of data sufficient to entail the query result. The authors identify self-joins as the primary source of the increased computational complexity of this relevance problem relative to query evaluation itself. By integrating techniques from database theory, computational complexity analysis, and structural restrictions such as hypertree width and ontology interaction width, they establish that relevance checking becomes no harder than query evaluation under bounded or absent self-joins: it is NP-complete in the absence of self-joins or when self-joins are bounded, and drops to LogCFL-complete for classes of bounded hypertree width and under DL-Lite_R ontologies.

Technology Category

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

Application Category

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

Abstract

We consider the following fundamental problem: given a database D, Boolean conjunctive query (CQ) q, and fact f in D, decide whether f is relevant to q wrt. D, i.e., does f belong to a minimal subset S of D such that S |= q. Despite being of central importance to query answer explanation, the combined complexity of deciding query relevance has not been studied in detail, leaving open what makes this problem hard, and which restrictions can yield lower complexity. Relevance has already been shown to be harder than query evaluation: namely, $Σ^p_2$-complete for CQs, even over a binary signature. We further observe that NP-hardness applies already to (acyclic) chain CQs. Our work identifies self-joins (multiple atoms with the same relation) as the culprit. Indeed, we prove that if we forbid or bound the occurrence of self-joins, then relevance has the same complexity as query evaluation, namely, NP (without structural restrictions) and LogCFL (for bounded hypertreewidth classes). In the ontology setting, we establish an analogous result for ontology-mediated queries consisting of a CQ and DL-Lite_R ontology, namely that relevance is no harder than query answering provided that we bound the interaction width (which generalizes both self-join width and a recently introduced 'interaction-free' condition). Our results thus pinpoint what makes relevance harder than query evaluation and identify natural classes of queries which admit efficient relevance computation.

Problem

• query relevance
• conjunctive query
• self-joins
• complexity
• minimal subset

Innovation

• query relevance
• self-joins
• combined complexity
• ontology-mediated queries
• interaction width