  We extend description logics (DLs) with non-monotonic reasoning features. We
start by investigating a notion of defeasible subsumption in the spirit of
defeasible conditionals as studied by Kraus, Lehmann and Magidor in the
propositional case. In particular, we consider a natural and intuitive
semantics for defeasible subsumption, and investigate KLM-style syntactic
properties for both preferential and rational subsumption. Our contribution
includes two representation results linking our semantic constructions to the
set of preferential and rational properties considered. Besides showing that
our semantics is appropriate, these results pave the way for more effective
decision procedures for defeasible reasoning in DLs. Indeed, we also analyse
the problem of non-monotonic reasoning in DLs at the level of entailment and
present an algorithm for the computation of rational closure of a defeasible
ontology. Importantly, our algorithm relies completely on classical entailment
and shows that the computational complexity of reasoning over defeasible
ontologies is no worse than that of reasoning in the underlying classical DL
ALC.
