Argumentation framework with weighted argument structure

Theory of argumentation constitutes a general framework for reasoning and has been widely applied in computational intelligence problems such as nonmonotonic reasoning, decision making and logic programming. To capture the internal structure of arguments, each argument is assigned with a weight, which represents the argument´s credibility, to construct a numeric argumentation framework. Within this framework, attacks and preferences are endowed with strengths which are determined by the weights of arguments related. Inspired by the majority rule, properties of attacks or preferences sharing the same target are also explored. The notion of acceptability and extended theory retain the basic machinery of Dung´s theory. Finally, an n-person game is formalized in numeric argumentation framework to illustrate the rationality of the new theory.