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Continuous Dynamical Systems for Weighted Bipolar Argumentation

Last modified: 2018-09-24

#### Abstract

Weighted bipolar argumentation frameworks determine the strength of arguments based on an initial weight and the strength of their attackers and supporters. These frameworks can be applied to model and solve problems that arise in areas like social media analysis and decision support. Approaches for computing strength values often assume an acyclic argumentation graph and successively set arguments’ strength based on the strength of their parents. A natural idea for cyclic graphs is to update strength values simultaneously rather than successively. Continuous dynamical systems seem well-suited for this approach because they can feature better convergence behaviour than their discrete counterparts. We investigate such a system here. For acyclic graphs, our model is guaranteed to converge and solutions can be computed as efficiently as for successive update procedures. We currently cannot prove very general guarantees for cyclic frameworks, but give empirical evidence that our model converges quickly even in complex cyclic graphs with thousands of nodes and ten thousands of edges. We also explain how potential oscillations can be detected visually. Our model’s axiomatic properties complement existing approaches. We also give sufficient conditions under which successive update procedures can be transformed to well-defined dynamical systems with similar guarantees easily.

#### Keywords

bipolar argumentation; weighted argumentation; continuous dynamical systems

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