Using Matrix Exponentials for Abstract Argumentation

We investigate the relationship between semantics for formal argumentation and measures from social networking theory. In particular, we consider using matrix exponentials, which are measures used for link prediction and recommendation in social networks, as a way to measure acceptability of arguments in abstract argumentation frameworks. We reformulate the approach of matrix exponentials to adhere for the fact that, compared to the social network setting, edges in argumentation frameworks have a negative connotation, arguments linked by edges should not be accepted together, and empirically evaluate this approach on benchmark graphs from ICCMA’15. Moreover, matrix exponentials can also be used for prediction in so-called signed social networks, which have both positive and negative edges denoting friend and foe relationships. As these networks bear a close resemblance to bipolar argumentation frameworks, we extend our framework and investigate the applicability of matrix exponentials from signed networks to be used in bipolar argumentation frameworks as well. Finally, we evaluate postulates for ranking-based argumentation semantics for our approach.