Robustness of Constraint Automata for Description Logics with Concrete Domains
This work addresses decidability and complexity issues in ontologies with concrete domains, offering a robust method for researchers in knowledge representation and logic, though it is incremental as it builds on existing automata techniques.
The paper tackles the consistency problem for description logics with concrete domains by proposing an automata-based approach, achieving an optimal EXPTIME upper bound and extending results to include features like inverse roles and constraint assertions.
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