Zongshun Wang

Zongshun Wang, Yuping Shen

Evaluating argument strength in quantitative argumentation systems has received increasing attention in the field of abstract argumentation. The concept of acceptability degree is widely adopted in gradual semantics, however, it may not be sufficient in many practical applications. In this paper, we provide a novel quantitative method called fuzzy labeling 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. More specifically, we investigate the postulates of fuzzy labeling, which present the rationality requirements for semantics concerning the acceptability, rejectability, and undecidability degrees. We then propose a class of fuzzy labeling semantics conforming to the above postulates and investigate the relations between fuzzy labeling semantics and existing work in the literature.

Zongshun Wang, Yuping Shen

Abstract argumentation is a reasoning model for evaluating arguments based on various semantics. SCC-recursiveness is a sophisticated property of semantics that provides a general schema for characterizing semantics through the decomposition along strongly connected components (SCCs). While this property has been extensively explored in various qualitative frameworks, it has been relatively neglected in quantitative argumentation. To fill this gap, we demonstrate that this property is well-suited to fuzzy extension semantics, which is a quantitative generalization of classical semantics in fuzzy argumentation frameworks (FAF). We tailor the SCC-recursive schema to enable the characterization of fuzzy extension semantics through the recursive decomposition of an FAF along its SCCs. Our contributions are twofold. Theoretically, we show that SCC-recursiveness provides an alternative approach to characterize fuzzy extension semantics, offering a deep understanding and better insight into these semantics. Practically, our schema provides a sound and complete algorithm for computing fuzzy extension semantics, which naturally reduces computational efforts when dealing with a large number of SCCs.