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.
Consejo Nacional de Investigaciones Científicas y Técnicas（阿根廷国家科学技术研究委员会）；Department of Mathematics - Universidad Nacional de Santiago del Estero（圣地亚哥德埃斯特罗国立大学数学系）
Extension-ranking Semantics for Abstract Argumentation Preprint
Artificial Intelligence Group, University of Hagen, Hagen, Germany；Department of Advanced Computing Sciences, Maastricht University, The Netherlands；Department of Computer Science, Open Universiteit, The Netherlands；University of Cape Town, South Africa；Department of Computer Science, TU Dortmund, Dortmund, Germany
