Argumentation abstraite et concepts formels A formal concept view of abstract argumentation

This paper for the first time presents a parallel between two important theories for the treatment of information which address questions that are apparently completely different and that are studied by research communities that are fully distinct : the formal concept analysis theory on the one hand and the abstract theory of argumentation on the other hand. These two theories exploit a binary relation expressing a link object-property for the first one, and the attack of an argument by another argument for the second one. The parallel becomes more accurate when considering the complementary relation “does not attack”. Then, it appears that the notion of stable extension which is at the basis of the semantics for argumentation corresponds to the idea of formal concept. The paper proposes a preliminary study of the parallel between abstract argumentation theory and formal concept analysis, itself enriched with operators other than the one at the basis of formal concepts thanks to an analogy with possibility theory. This parallel appears to be of interest for providing a richer view of the abstract theory of argumentation in the case where the relation is bi-valued, as in the case where the relation is fuzzy. A cube of oppositions between eight remarkable sets of arguments is thus obtained.