In this talk, I recall the two classes of methods (extension semantics and gradual semantics) that were proposed in the literature. I analyze them against a set of rationality principles, and show that they are fundamentally different. This means that in concrete applications, they lead to different results. Namely, in case of reasoning with inconsistent information, extension semantics follow the same line of research as well-known syntactic approaches for handling inconsistency, while gradual semantics lead to novel and powerful ranking logics.