Set Contribution Functions for Quantitative Bipolar Argumentation and their Principles

Abstract: We present functions that quantify the contribution of a set of arguments in quantitative bipolar argumentation graphs to (the final strength of) an argument of interest, a so-called topic. Our set contribution functions are generalizations of existing functions that quantify the contribution of a single contributing argument to a topic. Accordingly, we generalize existing contribution function principles for set contribution functions and provide a corresponding principle-based analysis. We introduce new principles specific to set-based functions that focus on properties pertaining to the interaction of arguments within a set. Finally, we sketch how the principles play out across different set contribution functions given a recommendation system application scenario.