A Note on Rich Incomplete Argumentation Frameworks
  Recently, qualitative uncertainty in abstract argumentation has received much
attention. The first works on this topic introduced uncertainty about the
presence of attacks, then about the presence of arguments, and finally combined
both kinds of uncertainty. This results in the Incomplete Argumentation
Framework (IAFs). But another kind of uncertainty was introduced in the context
of Control Argumentation Frameworks (CAFs): it consists in a conflict relation
with uncertain orientation, i.e. we are sure that there is an attack between
two arguments, but the actual direction of the attack is unknown. Here, we
formally define Rich IAFs, that combine the three different kinds of
uncertainty that were previously introduced in IAFs and CAFs. We show that this
new model, although strictly more expressive than IAFs, does not suffer from a
blow up of computational complexity. Also, the existing computational approach
based on SAT can be easily adapted to the new framework.
