Starting from the framework proposed by Dung in 1995, our purpose is to introduce ``graduality'' in the selection of the best arguments, i.e. to be able to partition the set of the arguments in more than the two usual subsets of ``selected'' and ``non-selected'' arguments in order to represent different levels of selection.
Our basic idea is that an argument is all the more acceptable if it can be preferred to its attackers. First, we discuss general principles underlying a ``gradual'' valuation of arguments based on their interactions. Following these principles, we define several valuation models for an abstract argumentation system. Then, we introduce ``graduality'' in the concept of acceptability of arguments. We propose new acceptability classes and a refinement of existing classes taking advantage of an available ``gradual'' valuation.