  Argumentation is based on the exchange and valuation of interacting
arguments, followed by the selection of the most acceptable of them (for
example, in order to take a decision, to make a choice). 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.
