Fuzzy Labeling Semantics for Quantitative Argumentation

The topic of evaluating argument strength in various quantitative argumentation systems has received increasing attention in the field of abstract argumentation. However, the existing gradual semantics on argument strength considers acceptability degree alone, which may be not sufficient to evaluate arguments in practical scenarios. To adopt a richer characterization for argument strength in real-world applications, we provide a novel quantitative method called fuzzy labeling for fuzzy argumentation systems. For fuzzy labeling, the argument strength is represented as a triple consisting of acceptability, rejectability, and undecidability degree. With a richer scale, it sheds new light on argument strength and gives us a deeper understanding into status of arguments. For the purpose of evaluating arguments, we provide a new way to establish gradual semantics by fuzzy labeling, which is crucial in the evaluation process. We first investigate the rationality postulates of fuzzy labeling, which are important for explaining the rationality of new semantics taking into account the acceptability, rejectability and undecidability degree together. We then propose a set of fuzzy labeling semantics and prove some important properties which are crucial for comparing, understanding and applying semantics.