Modular Semantics and Characteristics for Bipolar Weighted Argumentation Graphs
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This paper 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. Based on the modular framework, we prove general convergence and divergence theorems. We show that all semantics converge for all acyclic graphs and that no sum-based semantics can converge for all graphs. In particular, we show divergence of Euler-based semantics for certain cyclic graphs. We also provide the first semantics for bipolar weighted graphs that converges for all graphs.
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