Gradual Semantics for Weighted Higher-Order Argumentation Frameworks

Abstract

This paper investigates complex argumentation settings, called weighted higher-order argumentation frameworks (wHO-AFs), where both arguments and attacks carry initial weights and may be subject to attacks from arguments. It focuses on developing gradual semantics capable of rationally evaluating these elements by assigning each argument and attack a numerical value, representing their respective degrees of acceptance and seriousness.

The contributions of the paper are five-fold: i) It identifies key technical challenges for semantics in wHO-AFs, such as handling the distinction between arguments and attacks, and determining how their values should be combined. To address these challenges, the paper introduces a set of guiding principles that capture various semantic strategies. ii) It introduces a broad family of semantics that treat arguments and attacks uniformly, evaluating them in the same way. This family encompasses both semantics inspired by extension-based approaches and those that are purely gradual. iii) It defines a second extensive family of semantics that differentiate between arguments and attacks. This includes instances where a single function evaluates both types of elements, as well as hybrid variants that apply distinct evaluation functions to arguments and attacks. iv) It offers a formal analysis and comprehensive comparison of the resulting diverse semantics. v) It presents an empirical evaluation of these semantics. The results are promising as they show that the values of all elements can be computed in fewer than 20 iterations, even for large frameworks, while maintaining very low runtime. The paper ultimately delivers a catalogue of semantics, each offering distinct formal properties and behaviors, contributing a flexible toolkit for reasoning in rich argumentative contexts.