  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 $x\to\neg y$. 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.
