In this paper, we have introduced graduality in the two main related issues of argumentation systems:

Regarding the first issue, we have defined two formalisms introducing an interaction-based gradual valuation of arguments.

We have shown that each of these valuations induces a preordering on the set of the arguments, and we have brought to light the main differences between these two approaches.

Regarding the second issue, two distinct approaches have been proposed:

The first concept induces a refinement of the level of exi-accepted in two sublevels (cleanly-accepted arguments and only-exi-accepted arguments). The gradual valuation allows graduality inside each level of this collective acceptability.

The second concept induces two new levels of acceptability (well-defended arguments and not-well-defended arguments). The gradual valuation also allows graduality inside each level of this individual acceptability.

Regarding our initial purpose of introducing graduality in the definition of acceptability, we have adopted a basic principle:

Then, we have followed two different directions. One is based on a refinement of an existing partition and remains in the framework of Dung's work. The other one is based on the original concept of ``being well-defended'', and deserves further investigation, in particular from a computational point of view.

Marie-Christine Lagasquie 2005-02-04