Dvořák, W., Rienstra, T., van der Torre, L., & Woltran, S. (2022). Non-Admissibility in Abstract Argumentation. In F. Toni, S. Polberg, M. Caminada, R. Booth, & H. Kido (Eds.), Computational Models of Argument - Proceedings of COMMA 2022 (pp. 128–139). IOS Press. https://doi.org/10.3233/FAIA220147
In this paper, we give an overview of several recent proposals for non-Admissible non-naive semantics for abstract argumentation frameworks. We highlight the similarities and differences between weak admissibility-based approaches and undecidedness-blocking approaches using examples and principles as well as a study of their computational complexity. We introduce a kind of strengthened undecidedness-blocking semantics combining some of the distinctive behaviours of weak admissibility-based semantics with the lower complexity of undecidedness-blocking approaches. We call it loop semantics, because in our new semantics, an argument can only be undecided if it is part of a loop of undecided arguments. Our paper shows how a principle-based approach and a complexity-based approach can be used in tandem to further develop the foundations of formal argumentation.