There are several proposals to deal with inconsistencies in DL ontologies through argumentation. Different from existing approaches, in this paper, we consider the scenario that our knowledge is both uncertain and inconsistent and/or incoherent, and wepropose a logic-based argumentation framework to deal with incomplete and conflicting DL ontologies. We do so by adopting a distinct notion of attack [3, 4] among arguments to encompass different forms of conflicts in DL ontologies. The paper presents the following major contributions: (1) a general framework for reasoning with uncertain, inconsistent and/or incoherent ontologies with the use of logic-based argumentation; (2) a general labelling method, sensitive to the numbers of attacks and the weights of arguments, with different interesting instantiations to identify the justification statuses of each argument; and (3) a number of inference relations derived from our framework in order to obtain meaningful answers without increasing the computational complexity of the reasoning process compared to classical DL reasoning. We also study thelogical properties of these new entailment relations.