Argument Ranking with Categoriser Function
  Recently, ranking-based semantics is proposed to rank-order arguments from
the most acceptable to the weakest one(s), which provides a graded assessment
to arguments. In general, the ranking on arguments is derived from the strength
values of the arguments. Categoriser function is a common approach that assigns
a strength value to a tree of arguments. When it encounters an argument system
with cycles, then the categoriser strength is the solution of the non-linear
equations. However, there is no detail about the existence and uniqueness of
the solution, and how to find the solution (if exists). In this paper, we will
cope with these issues via fixed point technique. In addition, we define the
categoriser-based ranking semantics in light of categoriser strength, and
investigate some general properties of it. Finally, the semantics is shown to
satisfy some of the axioms that a ranking-based semantics should satisfy.
