Convergent Semantics for Weighted Bipolar Argumentation

Establishing convergent semantics for weighted argumentation graph is a fundamental and long-standing issue. Particularly, it is challenging to develop convergent semantics for weighted bipolar argumentation graph (wBAG), which include both support and attack relations on weighted arguments. Existing semantics in the literature are not general enough in the sense that they only apply to acyclic graphs or special cyclic cases. In this paper, we provide a general and elegant solution to this issue by adopting the so-called bilateral gradual semantics, so that the strength of arguments can be defined as the limits of iterative functions that always converge for any wBAG including cyclic ones. A preliminary experimental analysis shows that our semantics appear quite efficient in calculating argument strength. Overall, this paper offers a solid and promising foundation for weighted bipolar argumentation in theoretical and practical aspects.