Bilateral Gradual Semantics for Weighted Argumentation

The Abstract 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.