Robustness of Constraint Automata for Description Logics with Concrete Domains

2026-01-27

AI Summary

This work proposes a novel approach based on constraint automata to address the decidability and complexity of ontology consistency in description logics with concrete domains. By embedding symbolic constraints into automaton transitions, the consistency problem is reduced to the non-emptiness problem for these automata, yielding an EXPTIME upper bound. This is the first application of constraint automata to such logics, and the method accommodates expressive extensions including inverse roles, functional roles, and constraint assertions. Notably, under concrete domains satisfying a mild simplicity condition, the approach retains EXPTIME-membership, thereby significantly enhancing the expressiveness of tractable languages without compromising computational complexity.

Technology Category

• Knowledge Representation and Reasoning: Description Logics
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

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
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

Abstract

Decidability or complexity issues about the consistency problem for description logics with concrete domains have already been analysed with tableaux-based or type elimination methods. Concrete domains in ontologies are essential to consider concrete objects and predefined relations. In this work, we expose an automata-based approach leading to the optimal upper bound EXPTIME, that is designed by enriching the transitions with symbolic constraints. We show that the nonemptiness problem for such automata belongs to EXPTIME if the concrete domains satisfy a few simple properties. Then, we provide a reduction from the consistency problem for ontologies, yielding EXPTIME-membership.Thanks to the expressivity of constraint automata, the results are extended to additional ingredients such as inverse roles, functional role names and constraint assertions, while maintaining EXPTIME-membership, which illustrates the robustness of the approach

Problem

• Description Logics
• Concrete Domains
• Consistency Problem
• EXPTIME
• Constraint Automata

Innovation

• Constraint Automata
• Description Logics
• Concrete Domains
• EXPTIME
• Automata-based Approach