Higher-Order Argumentation Frameworks: Principles and Gradual Semantics

The paper investigates how to evaluate elements in complex argumentation frameworks, where both arguments and attacks are weighted and might be attacked by arguments. We propose the first gradual semantics that assign a numerical value to every argument and attack. The value represents the acceptance (seriousness) degree of an argument (attack). We start by highlighting various technical challenges facing semantics in such complex settings, including how to deal with attacks vs arguments, and how to combine their values. We present principles that describe different strategies offered to semantics to meet such challenges. Then, we introduce various semantics per strategy. For instance, some semantics evaluate attacks and arguments in the same way while others, called hybrid, treat them differently. Finally, the principles are used to compare the plethora of novel semantics. The final result is a catalogue of semantics with different formal guarantees and behaviours.