Defeasible description logics (DDLs) support nonmonotonic reasoning by admitting defeasible concept inclusions in the knowledge base. Early reasoning methods for subsumption did not always use defeasible information for objects in the scope of nested quantifiers and thus neglected un-defeated information. The reasoning approach employing typicality models for the DDL EL_⊥ overcomes this effect for existentially quantified objects.

In this extended abstract we report on how to lift typicality model-based reasoning to the DDL ELI_⊥, which extends EL_⊥ with inverse roles. These can capture a form of universal quantification and extend expressivity of the DDL substantially. Reasoning in DDLs often employs rational closure according to the propositional KLM postulates. We can show that the proposed subsumption algorithm yields more entailments than rational propositional entailment.