A labelling semantics for weighted argumentation frameworks

Argumentation Theory provides tools for both modelling and reasoning with controversial information and is a methodology that is go- ing to be proposed 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: Ac- ceptable, rejected and undecidable (instead of classical Dung two sets IN and OUT partitions). This kind of semantics have been studied only for classical AFs, whilst the more powerful weighted and preference-based framework has been not studied yet. In this paper, we define a novel labelling semantics for Weighted Argumentation Frameworks, extending and generalising the crisp one.