Computing Minimal Projection Modules for$$\mathcal{ELH}^{r}$$ -Terminologies

For the development of large-scale representations of knowledge, the application of methodologies and design principles becomes relevant. The knowledge may be organized in ontologies in a modular and hierarchical fashion. An upper-level (reference) ontology typically provides specifications of requirements, functions, design or standards that are to be complied with by domain ontologies for a specific task on a lower level (task ontology) in the hierarchy. Verifying whether and how specifications have been implemented by a task ontology becomes a challenge when relevant axioms of the domain ontology need to be inspected. We consider specifications to be defined using entailments of certain queries over a given vocabulary. For selecting the relevant axioms from task ontologies, we propose a novel module notion called projection module that entails the queries that follow from a reference ontology. We develop algorithms for computing minimal projection modules of Description Logic terminologies for subsumption, instance and conjunctive queries.