This paper presents an argumentation framework for reasoning and management in (inconsistent or incoherent) description logic ontologies which contain conflicts. First, a new argumentation framework obtained by combining Besnard and Hunter's framework with binary argumentation is introduced to frame the inner relation over axioms in an ontology. A dialogue mechanism, based on this framework, is then presented to derive meaningful consequences from inconsistent ontologies. Three novel operators are developed to repair those axioms or assertions which cause inconsistency or incoherency of ontologies by using this framework. Within this framework, an inconsistency is neither directly assigned a contradictory value nor roughly removed but ...