Argumentation Frameworks with Justified Attacks

After Dung's semina lpaper on argumentation frameworks, the relation of attack between arguments has occupied pride of place in formal argumentation theory. Yet, very little attention has been devoted to modelling argumentation about attack relations. Argumentation of this kind is encountered in many situations, especially when arguers discuss there levance of each other's arguments.To model it, we introduce argumentation frameworks with justified attacks, where an attack succeeds only if one of its justification arguments are accepted. The main technical result is are presentation theorem, showing how to translate argumentation framework swith justified attacks into standard argumentation frameworks with dummy arguments whose combinatorial properties encode the support-function of attack justifications.