Argumentation is a reasoning model for evaluating arguments. Recently, gradual semantics has received considerable attention in weighted argumentation, which assigns an acceptability degree to each argument as its strength. In this paper, we aim to enhance gradual semantics by non-reciprocally incorporating the notion of rejectability degree. Such a setting offers a bilateral perspective on argument strength, enabling more comprehensive argument evaluations in practical situations. To this end, we first provide a set of principles for our semantics, taking both the acceptability and rejectability degrees into account, and propose three novel semantics conforming to the above principles. These semantics are defined as the limits of iterative sequences that always converge in any given weighted argumentation system, making them preferable for real-world applications.

One of the key expectations of AI product manufacturers for their products is the ability to scale to larger markets, especially across legal systems, with fewer prototypes and lower adaptation costs. This paper focuses on the increasingly dynamic legal compliance challenges faced by designers of AI products in achieving this goal. Based on non-monotonic reasoning, we design an automated reasoning tool to help them better understand the legal implications of their designs in a transnational context and, ultimately, adjust the design of AI products more flexibly. This tool supports the quantitative representation of the strength of legal significance to help designers better understand the reasons for their decisions from their own perspective. To illustrate this functionality, a case study on traffic regulations across the UK, France, and Japan demonstrates the system’s ability to resolve legal conflicts—such as driving-side mandates and speed radar detector prohibitions—through quantitative evaluation.

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.