Well-Foundedness in Weighted Argumentation Frameworks

We revise classical properties of Abstract Argumentation Frameworks in presence of weights on attacks. We focus on the notion of well-foundedness originally provided by P. M. Dung in his pioneering work. We generalise it by considering sequences of Set-maximal Attack sets, instead of a plain sequence of arguments: such sets include all the arguments attacking a previous set in the sequence. By using a parametric framework based on an algebraic structure, we are able to study different proposals of weighted defence in the literature, and consequently relate their well-foundedness. We generalise such a property to any weighted defence, but also to original Dung's defence. Finally, we provide conditions for the uniqueness of the preferred and existence of the stable extensions.