Robustness of Constraint Automata for Description Logics with Concrete Domains

TL;DR

This paper introduces an automata-based method for reasoning in description logics with concrete domains, achieving optimal EXPTIME complexity and handling various expressive features.

Contribution

It presents a novel automata-based approach with symbolic constraints that maintains EXPTIME complexity for complex description logics.

Findings

Automata nonemptiness problem is in EXPTIME for certain concrete domains.

Reduction from ontology consistency problem also in EXPTIME.

Method extends to inverse roles, functional roles, and constraints while preserving complexity.

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