  Gradual semantics with abstract argumentation provide each argument with a
score reflecting its acceptability, i.e. how "much" it is attacked by other
arguments. Many different gradual semantics have been proposed in the
literature, each following different principles and producing different
argument rankings. A sub-class of such semantics, the so-called weighted
semantics, takes, in addition to the graph structure, an initial set of weights
over the arguments as input, with these weights affecting the resultant
argument ranking. In this work, we consider the inverse problem over such
weighted semantics. That is, given an argumentation framework and a desired
argument ranking, we ask whether there exist initial weights such that a
particular semantics produces the given ranking. The contribution of this paper
are: (1) an algorithm to answer this problem, (2) a characterisation of the
properties that a gradual semantics must satisfy for the algorithm to operate,
and (3) an empirical evaluation of the proposed algorithm.
