The Influence of Defeated Arguments in Defeasible Argumentation

Formal defeasible argumentation is currently the subject of active research. Formalisms of defeasible argumentation are characterized by a notion of defeasible argument. The influence of arguments on which conclusions can be drawn distinguishes formalisms of defeasible argumentation from nonmonotonic logics. This influence occurs for two reasons: by the structure of an argument, and by interaction with other arguments. In the process of argumentation not all arguments are available at once. At each stage of argumentation new arguments are taken into account. In defeasible argumentation, where arguments can be defeated by other arguments, this results in the possible change of the status of arguments, depending on which arguments have been considered. Existing formalisms of defeasible argumentation do not provide a process view on argumentation, or overlook the influence on this process of the defeated arguments that have been taken into account. In this paper we argue that a model of the process of argumentation requires that the arguments that are defeated at some stage of argumentation cannot simply be ignored. Otherwise, different stages of argumentation cannot be distinguished, and orders of argumentation can disappear.