Robustness of inference in quantitative bipolar argumentation

Abstract

We study the robustness of inference in quantitative bipolar argumentation. Viewing argumentation as a dynamic process and inference in terms of the relative (final) strengths of two arguments, we introduce notions of robust inference and robust inconsistency. Robust inference requires that the arguments’ final strength-based ordering is preserved, under potential changes to a given argumentation graph. When an inference change occurs, the notion of robust inconsistency assesses whether the change of inference persists under subsequent changes, thereby capturing whether the change is ‘here to stay’ or merely the result of ephemeral fluctuations. To analyse situations where robust inference is violated, we introduce pockets of robustness—sets of changes that leave the inference robust when applied to the original graph. Based on these pockets, we define robustness violation explanations. These explanations identify the minimal changes made outside some particular pocket that lead to a change of inference. We further show how our explanations give rise to a gradual notion of robustness. We also discuss and evaluate aspects of the implementation of the notions introduced above and finally demonstrate that our approach to robustness of inference can be straightforwardly applied to labelling-based abstract argumentation.