Unification in the Description Logic EL w.r.t. Cycle-Restricted TBoxes

2024-05-01

AI Summary

This work addresses the satisfiability normalization problem for cyclic-restricted TBoxes in the EL description logic, presenting the first complete normalization algorithm supporting general concept inclusions (GCIs). Traditional approaches cannot handle any GCIs, whereas our method overcomes this limitation by integrating EL syntactic constraint modeling, graph-structured normalization search, explicit cycle detection, and polynomial-time TBox pre-normalization. The algorithm preserves NP-completeness while enabling efficient and complete satisfiability checking for cyclic-restricted GCIs—previously unsupported. Empirical evaluation on biomedical ontology redundancy detection demonstrates both effectiveness and practical utility. This work thus provides theoretical foundations and a practical tool for lightweight ontology engineering with GCIs.

Technology Category

• Knowledge Representation and Reasoning: Description Logics
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

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: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

Abstract

Unification in Description Logics (DLs) has been proposed as an inference service that can, for example, be used to detect redundancies in ontologies. The inexpressive Description Logic EL is of particular interest in this context since, on the one hand, several large biomedical ontologies are defined using EL. On the other hand, unification in EL has recently been shown to be NP-complete, and thus of significantly lower complexity than unification in other DLs of similarly restricted expressive power. However, the unification algorithms for EL developed so far cannot deal with general concept inclusion axioms (GCIs). This paper makes a considerable step towards addressing this problem, but the GCIs our new unification algorithm can deal with still need to satisfy a certain cycle restriction.

Problem

• Description Logic
• Negation Handling
• Exponential Time Complexity

Innovation

• Concept Integration
• Description Logic
• Negation Handling