Fitting Description Logic Ontologies to ABox and Query Examples

2025-08-11

AI Summary

This paper investigates the ontology fitting problem in description logic, given positive and negative ABox-query examples—where positives are ABoxes entailed by the ontology together with the query, and negatives are not. The goal is to construct a logically consistent ALC or ALCI ontology satisfying these constraints. We provide the first precise complexity characterizations for the existence of such ontologies: for atomic queries (AQ) and full conjunctive queries (CQ), the problem is CO-NP-complete; for general CQs and unions of CQs (UCQs), it is 2EXPTIME-complete—both in ALC and ALCI. Furthermore, we establish a unified satisfiability characterization and decision framework applicable across multiple query languages. This work delivers the first formal foundation for ontology-driven automated knowledge acquisition that is both theoretically complete and expressive across a broad spectrum of query languages.

Technology Category

• Knowledge Representation and Reasoning: Description Logics
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Data Mining & Knowledge Management: Intelligent Query Processing

Application Category

• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

We study a fitting problem inspired by ontology-mediated querying: given a collection of positive and negative examples of the form $(mathcal{A},q)$ with $mathcal{A}$ an ABox and $q$ a Boolean query, we seek an ontology $mathcal{O}$ that satisfies $mathcal{A} cup mathcal{O} vDash q$ for all positive examples and $mathcal{A} cup mathcal{O} otvDash q$ for all negative examples. We consider the description logics $mathcal{ALC}$ and $mathcal{ALCI}$ as ontology languages and a range of query languages that includes atomic queries (AQs), conjunctive queries (CQs), and unions thereof (UCQs). For all of the resulting fitting problems, we provide effective characterizations and determine the computational complexity of deciding whether a fitting ontology exists. This problem turns out to be ${small CO}NP$ for AQs and full CQs and $2E{small XP}T{small IME}$-complete for CQs and UCQs. These results hold for both $mathcal{ALC}$ and $mathcal{ALCI}$.

Problem

• Fitting ontologies to ABox and query examples
• Satisfying positive and negative logical entailments
• Determining computational complexity of ontology existence

Innovation

• Fitting ontologies to ABox and query examples
• Using description logics ALC and ALCI
• Characterizing computational complexity for query languages