Identifying the Class of Maxi-Consistent Operators in Argumentation
  Dung's abstract argumentation theory can be seen as a general framework for
non-monotonic reasoning. An important question is then: what is the class of
logics that can be subsumed as instantiations of this theory? The goal of this
paper is to identify and study the large class of logic-based instantiations of
Dung's theory which correspond to the maxi-consistent operator, i.e. to the
function which returns maximal consistent subsets of an inconsistent knowledge
base. In other words, we study the class of instantiations where very extension
of the argumentation system corresponds to exactly one maximal consistent
subset of the knowledge base. We show that an attack relation belonging to this
class must be conflict-dependent, must not be valid, must not be
conflict-complete, must not be symmetric etc. Then, we show that some attack
relations serve as lower or upper bounds of the class (e.g. if an attack
relation contains canonical undercut then it is not a member of this class). By
using our results, we show for all existing attack relations whether or not
they belong to this class. We also define new attack relations which are
members of this class. Finally, we interpret our results and discuss more
general questions, like: what is the added value of argumentation in such a
setting? We believe that this work is a first step towards achieving our
long-term goal, which is to better understand the role of argumentation and,
particularly, the expressivity of logic-based instantiations of Dung-style
argumentation frameworks.
