An Argumentation System with Indirect Attacks

We discuss argumentation frameworks with indirect attacks, such as why-questions and supports. A whyquestion is regarded as a kind of attack relation, and a support is an answer to an un-presented why-question. Based on this idea, we construct an argumentation framework with why-questions from a pair of knowledge bases, as an instantiation of Dung’s abstract argumentation framework, and show that its extension is consistent. Next, we transform this argumentation framework into an argumentation framework with supports, and discuss its properties. The resulting framework is an instantiation of Bipolar Argumentation Framework (BAF), defined as a triple consisting of arguments, attack relations and support relations. We define an extension of BAF, and show that the framework defined in this paper has some nice properties.