Acceptability semantics accounting for strength of attacks in argumentation

We consider argumentation systems with several attack relations of different strength. We focus on the impact of va rious strength attacks on the semantics of such systems. First, we refin the classical notion of defence, by comparing the strength o f an attack with the strength of a counter-attack. Then, we propose different ways to compare defenders, and sets of defenders. That enabl es us to define admissible sets offering a best defence for their elem ents. 1 Argumentation framework with attacks of various strength Argumentation is based on the evaluation of interacting arg uments (which support opinions, claims, decisions,... ) and the se l ction of acceptable sets of arguments. Most of the argumentation-ba sed proposals are instantiations of the Dung’s abstract system [2] , which is reduced to a set of arguments (completely abstract entiti s) and a binary attack relation, which captures the conflicts betwe n arguments. The increasing interest for the argumentation forma lis has led to numerous extensions of the basic abstract system, par ticul ly for making a distinction between various kinds of attacks [4 , 7, 8], and more precisely for taking into account the relative stre ngth of the attacks [3, 5, 7, 6]. Starting from the abstract argumentation system with varie dstrength attacks proposed by [6], we redefine the notion of de fenc and come to novel extensional semantics accounting for stre ngth of attacks. We consider the abstract system defined in [6]: Def 1 (Argumentation system with attacks of various strengt h – ASvs) An argumentation system with attacks of various strength is a triple 〈A,ATT, 〉 whereA is a finite set of arguments, ATT is a finite set of binary attack relations 〈 1 →, . . . , n → 〉 onA and is a binary relation onATT. The relation represents a relative strength between the attack relations. It is only assumed reflexive. The corresponding s trict relation is denoted by≻. AS denotes the classical system 〈A, S