Fuzzy labelling semantics for quantitative argumentation

Abstract Abstract argumentation is a well-studied model for evaluating arguments. Recently, evaluating argument strength in quantitative argumentation has received increasing attention, in which arguments are evaluated through acceptability degree. However, argument strength solely defined on acceptability degree appears not sufficient in practical applications. In this paper, we provide a novel quantitative method called fuzzy labelling for fuzzy argumentation systems, in which a triple of acceptability, rejectability and undecidability degrees is used to evaluate argument strength. Such a setting sheds new light on defining argument strength and provides a deeper understanding of the status of arguments. Specifically, we investigate the postulates of fuzzy labelling, which present the rationality requirements for semantics concerning the acceptability, rejectability and undecidability degrees. We then propose a class of fuzzy labelling semantics conforming to the above postulates and investigate the properties. Finally, we demonstrate that fuzzy labelling semantics can be considered both a conservative generalization of classical labelling semantics and a labelling version of fuzzy extension semantics.