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.