|Date:||2018, May 16|
|Author:||Mossakowski, Till and Neuhaus, Fabian|
|Title:||Modular Semantics and Characteristics for Bipolar Weighted Argumentation Graphs|
This work addresses the semantics of weighted argumentation graphs that are bipolar, i.e. contain both attacks and supports for arguments. We build on previous work by Amgoud, Ben-Naim et. al. We study the various characteristics of acceptability semantics that have been introduced in these works. We provide a simplified and mathematically elegant formulation of these characteristics. The formulation is modular because it cleanly separates aggregation of attacking and supporting arguments (for a given argument a) from the computation of their influence on a’s initial weight. We discuss various semantics for bipolar argumentation graphs in the light of these characteristics. We also show divergence of Euler-based semantics for certain cyclic graphs, and provide the first semantics for bipolar weighted graphs that converges for all graphs.
Open problem for one of our proofs:
Let D\subseteq R be a connected set of reals, e.g. D=[0,1] or D=R. Given a continuous (perhaps also: differentiable) function iota: R \times D -> D that is strictly increasing in both arguments and that satisfies iota(0,y) = y, can we find different a,b in [0,1] and k in N such that iota(k(b-a),a) = iota(k(a-b),b) ?