No abstract

In this article, we propose a survey of the use of bipolarity in argumentation frameworks. On the one hand, the notion of bipolarity relies on the presence of two kinds of entities that have a diametrically opposed nature and that represent repellent forces (a positive entity and a negative entity). The notion exists in various domains (for example with the representation of preferences in artificial intelligence, or in cognitive psychology). On the other hand, argumentation process is a promising approach for reasoning, based on the construction and the comparison of arguments. It follows five steps: building the arguments, defining the interactions between these arguments, valuating the arguments, selecting the most acceptable arguments and, finally, drawing a conclusion. Using the nomenclature proposed by Dubois and Prade, this article shows on various applications, and with some formal definitions, that bipolarity appears in argumentation (in some cases if not always) and can be used in each step of this process under different forms. C 2008 Wiley Periodicals, Inc.

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.