This paper proposes a novel family of argumentation-based logics for handling inconsistency. Starting with a base logic, it builds arguments and attack relations between them. The novelty of the approach lies in the fact that arguments are evaluated using a ranking semantics which rank-orders arguments from the most acceptable to the least acceptable ones. Naturally, a second novelty is that the conclusions to be drawn are ranked with regard to plausibility. We provide a couple of axioms that such logics should enjoy and illustrate the approach with a particular ranking semantics. We show that the new logics are more discriminating than existing argumentation-based logics. Moreover, they are good candidates for measuring inconsistency in knowledge bases. Categories and Subject Descriptors I.2.3 [Deduction and Theorem Proving]: Nonmonotonic reasoning and belief revision; I.2.11 [Distributed Artificial Intelligence]: Intelligent agents General Terms Human Factors, Theory Keywords Handl...