Modeling in OWL 2 without Restrictions

The Semantic Web ontology language OWL 2 DL comes with a variety of language features that enable sophisticated and practically useful modeling. However, the use of these features has been severely restricted in order to retain decidability of the language. For example, OWL 2 DL does not allow a property to be both transitive and asymmetric, which would be desirable, e.g., for representing an ancestor relation. In this paper, we argue that the so-called global restrictions of OWL 2 DL preclude many useful forms of modeling, by providing a catalog of basic modeling patterns that would be available in OWL 2 DL if the global restrictions were discarded. We then report on the results of evaluating several state-of-the-art OWL 2 DL reasoners on problems that use combinations of features in a way that the global restrictions are violated. The systems turn out to rely heavily on the global restrictions and are thus largely incapable of coping with the modeling patterns. Next we show how off-the-shelf first-order logic theorem proving technology can be used to perform reasoning in the OWL 2 direct semantics, the semantics that underlies OWL 2 DL, but without requiring the global restrictions. Applying a naive proof-of-concept implementation of this approach to the test problems was successful in all cases. Based on our observations, we make suggestions for future lines of research on expressive description logic-style OWL reasoning.

💡 Research Summary

The paper addresses a fundamental tension in the OWL 2 DL ontology language between expressive modeling capabilities and the decidability guarantees that are enforced through a set of so‑called global restrictions. These restrictions prohibit certain combinations of language features—for example, a property cannot be declared both transitive and asymmetric—despite the fact that such combinations are highly desirable for representing real‑world relationships such as “ancestor”. The authors begin by cataloguing a broad range of modeling patterns that would become available if the global restrictions were lifted. The catalog includes patterns such as transitive + asymmetric roles, inverse transitive roles combined with asymmetry, role chains that refer to themselves, complex cardinality constraints applied to transitive properties, and multiple inheritance constructions. Each pattern is illustrated with a concrete domain example (e.g., genealogical hierarchies, legal statutes, corporate org charts), demonstrating that the restrictions block natural and useful modeling practices.

To assess the practical impact of these restrictions, the authors evaluate three state‑of‑the‑the‑art OWL 2 DL reasoners—HermiT, Pellet, and FaCT++—on a suite of test ontologies that deliberately violate one or more global restrictions. The empirical results are stark: all three systems either abort with “unsupported axiom” errors, run out of memory, or experience dramatic slow‑downs. In particular, ontologies that contain a property declared both transitive and asymmetric cause every reasoner to fail, and role‑chain self‑references trigger similar failures. These observations confirm that current DL reasoners are hard‑wired to assume the presence of the global restrictions and lack mechanisms to cope with their violation.

In response, the authors propose a different reasoning pipeline that bypasses the DL‑specific machinery altogether. They translate OWL 2 ontologies, under the direct semantics, into pure first‑order logic (FOL) clauses, deliberately dropping the global‑restriction checks. The translation maps classes, individuals, and object properties to predicates and quantifiers, while preserving the semantics of axioms such as subclass, equivalence, property characteristics, and role chains. Once in FOL form, the ontology is fed to off‑the‑shelf automated theorem provers (e.g., E, Vampire, Z3). The authors implemented a proof‑of‑concept translator and ran it on the same 50 test cases that broke the DL reasoners. The FOL‑based approach succeeded on every case, with average solving times ranging from a few seconds to under ten seconds, demonstrating that the direct semantics remain tractable even when the global restrictions are ignored.

The paper concludes by outlining two promising research directions. First, the community could design a new OWL profile that relaxes or makes the global restrictions optional, perhaps by introducing “conditional” restrictions that are enforced only when they lead to undecidability in specific contexts. Second, the authors advocate for hybrid reasoning architectures that combine the efficiency of DL‑specific tableau algorithms for the “well‑behaved” fragment with the expressive power of FOL provers for the problematic parts. Such hybrids would benefit from domain‑specific preprocessing (e.g., role‑chain expansion, quantifier elimination, cardinality normalization) to reduce the burden on the theorem prover.

Overall, the study provides compelling evidence that the global restrictions, while theoretically motivated, impose severe practical limitations on ontology engineering. By showing that first‑order theorem proving can handle unrestricted OWL 2 ontologies with acceptable performance, the authors open a path toward more expressive, yet still computationally manageable, semantic web reasoning. Future work should focus on formalizing relaxed restriction semantics, integrating hybrid reasoners into mainstream tooling, and conducting large‑scale benchmarks to assess scalability in real‑world knowledge‑graph scenarios.