A Labelling Semantics and Strong Admissibility for Weighted Argumentation Frameworks

Abstract

Abstract Argumentation Theory provides tools for both modelling and reasoning with controversial information and is a methodology that is often used as a way to give explanations to results provided using machine learning techniques. In this context, labelling-based semantics for Abstract Argumentation Frameworks (AFs) allow for establishing the acceptability of sets of arguments, dividing them into three partitions: in, out and undecidable (instead of classical Dung acceptable and not acceptable sets). This kind of semantics have been studied only for classical AFs, while the more powerful weighted and preference-based frameworks have not been studied yet. In this paper, we define a novel labelling semantics for Weighted Argumentation Frameworks (WAFs), extending and generalizing the crisp one, and we provide some insights towards a definition of strong admissibility for WAFs.