The Inverse Problem for Argumentation Gradual Semantics
This work addresses a specific computational challenge in formal argumentation, providing a tool for reverse-engineering weights in weighted semantics, which is incremental as it builds on existing semantics.
The paper tackles the inverse problem for weighted gradual semantics in argumentation, developing an algorithm to determine if initial weights exist to produce a desired argument ranking, and characterizes necessary semantic properties while empirically evaluating the algorithm.
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.