On the Efficient Implementation of Social Abstract Argumentation

In this paper we present a novel iterative algorithm – the Iterative Successive Substitution (ISS) – to efficiently approximate the models of debates structured according to Social Abstract Argumentation [10]. Classical iterative algorithms such as the Iterative Newton-Raphson (INR) and the Iterative Fixed-point (IFP) don’t always converge and, when they do, usually take too long to be effective. We analytically prove convergence of ISS, and empirically show that, even when INR and IFP converge, ISS always outperforms them, often by several orders of magnitude. The ISS is able to approximate the models of complex debates with thousands of arguments in well under a second, often in under one tenth of a second, making it comfortably suitable for its purpose. Additionally, we present a small modification to ISS that, with a negligible overhead, takes advantage of the topological structure of certain debates to significantly increase convergence times.