Progressive Defeat Paths in Abstract Argumentation Frameworks

Abstract argumentation systems are formalisms for defeasible reasoning where some components remain unspecified, the structure of arguments being the main abstraction. In the dialectical process carried out to identify accepted arguments in the system some controversial situations may appear. These relate to the reintroduction of arguments into the process which cause the onset of circularity. This must be avoided in order to prevent an infinite analysis. Some systems apply the sole restriction of not allowing the introduction of previously considered arguments in an argumentation line. However, repeating an argument is not the only possible cause for the risk mentioned. A more specific restriction needs to be applied considering the existence of subarguments. In this work, we introduce an extended argumentation framework where two kinds of defeat relation are present, and a definition for progressive defeat path.