Finite Query Answering in Expressive Description Logics with Transitive Roles
This addresses a theoretical challenge in knowledge representation for settings without finite controllability, such as those with transitive roles, but is incremental as it extends known decidability results to specific fragments.
The paper tackled the problem of finite ontology mediated query answering (FOMQA) in description logics with transitive roles, which is undecidable in general, and showed decidability for three fragments (SOI, SOF, SIF) by developing automata-based procedures with optimal complexity bounds.
We study the problem of finite ontology mediated query answering (FOMQA), the variant of OMQA where the represented world is assumed to be finite, and thus only finite models of the ontology are considered. We adopt the most typical setting with unions of conjunctive queries and ontologies expressed in description logics (DLs). The study of FOMQA is relevant in settings that are not finitely controllable. This is the case not only for DLs without the finite model property, but also for those allowing transitive role declarations. When transitive roles are allowed, evaluating queries is challenging: FOMQA is undecidable for SHOIF and only known to be decidable for the Horn fragment of ALCIF. We show decidability of FOMQA for three proper fragments of SOIF: SOI, SOF, and SIF. Our approach is to characterise models relevant for deciding finite query entailment. Relying on a certain regularity of these models, we develop automata-based decision procedures with optimal complexity bounds.