Abstract: In formal argumentation theory,the proof theory of argumentation semantics sloves the problem of how to determine the status of justification of an argument in a given argumentation semantic,which always needs a corresponding argument game model.Argument game happens the process of argument interactions between a proponent and an opponent,and they both object and defense their arguments by giving attacking arguments,only if the proponent wins an argument game,its initial argument could obtain explicit status of justification.This paper defined a kind of gradual argumentation semantic,namely BRD-argumentation semantic,which is different from Dung’s abstract argumentation semantic,embeding a circular semantic for calculating the strengthes and degrees of justification of arguments into a structured argumentation framework ASPIC+.For sake of giving the proof theory of this semantic,this paper constructed a corresponding argument game model.

Key words: Structured argumentation framework,Gradual argumentation semantics,Argument game