Combined approaches have become a successful technique for CQ answering over ontologies. Existing algorithms, however, are restricted to the logics underpinning the OWL 2 profiles. Our goal is to make combined approaches applicable to a wider range of ontologies. We focus on RSA: a class of Horn ontologies that extends the profiles while ensuring tractability of standard reasoning. We show that CQ answering over RSA ontologies without role composition is feasible in NP. Our reasoning procedure generalises the combined approach for ELHO and DL-LiteR using an encoding of CQ answering into fact entailment w.r.t. a logic program with function symbols and stratified negation. Our results have significant practical implications since many out-of-profile Horn ontologies are RSA.

In the search for knowledge graph embeddings that could capture ontological knowledge, geometric models of existential rules have been recently introduced. It has been shown that convex geometric regions capture the so-called quasi-chained rules. Attributed description logics (DL) have been defined to bridge the gap between DL languages and knowledge graphs, whose facts often come with various kinds of annotations that may need to be taken into account for reasoning. In particular, temporally attributed DLs are enriched by specific attributes whose semantics allows for some temporal reasoning. Considering that geometric models and (temporally) attributed DLs are promising tools designed for knowledge graphs, this paper investigates their compatibility, focusing on the attributed version of a Horn dialect of the DL-Lite family. We first adapt the definition of geometric models to attributed DLs and show that every satisfiable ontology has a convex geometric model. Our second contribution is a study of the impact of temporal attributes. We show that a temporally attributed DL may not have a convex geometric model in general but we can recover geometric satisfiability by imposing some restrictions on the use of the temporal attributes.

Combined approaches have become a successful technique for CQ answering over ontologies. Existing algorithms, however, are restricted to the logics underpinning the OWL 2 profiles. Our goal is to make combined approaches applicable to a wider range of ontologies. We focus on RSA: a class of Horn ontologies that extends the profiles while ensuring tractability of standard reasoning. We show that CQ answering over RSA ontologies without role composition is feasible in NP. Our reasoning procedure generalises the combined approach for ELHO and DL-LiteR using an encoding of CQ answering into fact entailment w.r.t. a logic program with function symbols and stratified negation. Our results have significant practical implications since many out-of-profile Horn ontologies are RSA.

Rewriting-based approaches for answering queries over an OWL 2 DL ontology have so far been developed mainly for Horn fragments of OWL 2 DL. In this paper, we study the possibilities of answering queries over non-Horn ontologies using datalog rewritings. We prove that this is impossible in general even for very simple ontology languages, and even if PTIME = NP. Furthermore, we present a resolution-based procedure for SHI ontologies that, in case it terminates, produces a datalog rewriting of the ontology. We also show that our procedure necessarily terminates on DL-Lite Bool H,+ ontologies — an extension of OWL 2 QL with transitive roles and Boolean connectives.

Consequence-based ontology reasoning procedures have so far been known only for Horn ontology languages. A difficulty in extending such procedures is that non-Horn axioms seem to require reasoning by case, which causes non-determinism in tableau-based procedures. In this paper we present a consequence-based procedure for ALCH that overcomes this difficulty by using rules similar to ordered resolution to deal with disjunctive axioms in a deterministic way; it retains all the favourable attributes of existing consequence-based procedures, such as goal-directed “one pass” classification, optimal worst-case complexity, and “pay-asyou- go” behaviour. Our preliminary empirical evaluation suggests that the procedure scales well to non-Horn ontologies.