Fixed-Domain Reasoning for Description Logics

After decades of fruitful research, description logics (DLs) have evolved into a de facto standard in logic-based knowledge representation. In particular, they serve as the formal basis of the standardized and very popular web ontology language (OWL), which also comes with the advantage of readily available user-friendly modeling tools and optimized reasoning engines. In the course of the wide-spread adoption of OWL and DLs, situations have been observed where logically less skilled practitioners are (ab)using these formalisms as constraint languages adopting a closed-world assumption, contrary to the open-world semantics imposed by the classical definitions and the standards. To provide a clear theoretical basis and inferencing support for this often practically reasonable “off-label use” we propose an alternative formal semantics reflecting the intuitive understanding of such scenarios. To that end, we introduce the fixed-domain semantics and argue that this semantics gives rise to an interesting new inferencing task: model enumeration. We describe how the new semantics can be axiomatized in very expressive DLs. We thoroughly investigate the complexities for standard reasoning as well as query answering under the fixed-domain semantics for a wide range of DLs. Further, we present an implementation of a fixed-domain DL reasoner based on a translation into answer set programming (ASP) which is competitive with alternative approaches for standard reasoning tasks and provides the added functionality of model enumeration.