The Attack as Intuitionistic Negation

We translate the argumentation networks cal A=(S, R) into a theory D of intuitionistic logic, retaining S as the domain and using intuitionistic negation to model the attack R in cal A: the attack xRy is translated to x→neg y. The intuitionistic models of D characterise the complete extensions of cal A. The reduction of argumentation networks to intuitionistic logic yields, in addition to a representation theorem, some additional benefits: it allows us to give semantics to higher level attacks, where an attack "xRy" can itself attack another attack "uRv"; one can make higher level meta-statements W on (S, R) and such meta-statements can attack and be attacked in the domain.