Reasoning in the Defeasible Description Logic -computing standard inferences under rational and relevant semantics

The main contribution of this article is a kind of canonical model construction, which can be used to decide defeasible subsumption and instance queries in under rational and the stronger relevant entailment. Our so-called typicality models can reproduce the entailments obtained from materialisation-based rational and relevant closure and, more importantly, obtain stronger versions of rational and relevant entailment. These do not suffer from neglecting defeasible information for concepts appearing nested inside quantifications, which all materialisation-based approaches do. We also show the computational complexity of defeasible subsumption and instance checking in our stronger rational and relevant semantics.