# Robustness of Constraint Automata for Description Logics with Concrete Domains

arXiv: https://arxiv.org/abs/2601.19644 · HTML: https://mlsanity.com/paper/2601.19644/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 60 references that are in the map.
- First posted on arXiv 27 Jan 2026.

## Builds on (most cited first, 6 of 6)

- [Model Checking Constraint LTL over Trees](https://mlsanity.com/paper/1504.06105/) (2015)
- [An ExpTime Upper Bound for ALC with Integers (Extended Version)](https://mlsanity.com/paper/2006.02078/) (2020)
- [Realizability Problem for Constraint LTL](https://mlsanity.com/paper/2207.06708/) (2022)
- [Constraint Automata on Infinite Data Trees: From CTL(Z)/CTL*(Z) To Decision Procedures](https://mlsanity.com/paper/2302.05327/) (2023)
- [The Precise Complexity of Reasoning in ALC with ω-Admissible Concrete Domains (Extended Version)](https://mlsanity.com/paper/2405.19096/) (2024)
- [Concrete Domains Meet Expressive Cardinality Restrictions in Description Logics (Extended Version)](https://mlsanity.com/paper/2505.21103/) (2025)

## Abstract (arXiv)

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