%0 Journal Article %1 Dimopoulos2024-rf %A Dimopoulos, Yannis %A Dvorak, Wolfgang %A König, Matthias %A Rapberger, Anna %A Ulbricht, Markus %A Woltran, Stefan %D 2024 %I Association for the Advancement of Artificial Intelligence (AAAI) %J Proc. Conf. AAAI Artif. Intell. %K topic_knowledge %N 9 %P 10493--10500 %T Redefining ABA+ semantics via abstract set-to-set attacks %V 38 %X Assumption-based argumentation (ABA) is a powerful defeasible reasoning formalism which is based on the interplay of assumptions, their contraries, and inference rules. ABA with preferences (ABA+) generalizes the basic model by allowing qualitative comparison between assumptions. The integration of preferences however comes with a cost. In ABA+, the evaluation under two central and well-established semantics---grounded and complete semantics---is not guaranteed to yield an outcome. Moreover, while ABA frameworks without preferences allow for a graph-based representation in Dung-style frameworks, an according instantiation for general ABA+ frameworks has not been established so far. In this work, we tackle both issues: First, we develop a novel abstract argumentation formalism based on set-to-set attacks. We show that our so-called Hyper Argumentation Frameworks (HYPAFs) capture ABA+. Second, we propose relaxed variants of complete and grounded semantics for HYPAFs that yield an extension for all frameworks by design, while still faithfully generalizing the established semantics of Dung-style Argumentation Frameworks. We exploit the newly established correspondence between ABA+ and HYPAFs to obtain variants for grounded and complete ABA+ semantics that are guaranteed to yield an outcome. Finally, we discuss basic properties and provide a complexity analysis. Along the way, we settle the computational complexity of several ABA+ semantics.

@article{Dimopoulos2024-rf, abstract = {Assumption-based argumentation (ABA) is a powerful defeasible reasoning formalism which is based on the interplay of assumptions, their contraries, and inference rules. ABA with preferences (ABA+) generalizes the basic model by allowing qualitative comparison between assumptions. The integration of preferences however comes with a cost. In ABA+, the evaluation under two central and well-established semantics---grounded and complete semantics---is not guaranteed to yield an outcome. Moreover, while ABA frameworks without preferences allow for a graph-based representation in Dung-style frameworks, an according instantiation for general ABA+ frameworks has not been established so far. In this work, we tackle both issues: First, we develop a novel abstract argumentation formalism based on set-to-set attacks. We show that our so-called Hyper Argumentation Frameworks (HYPAFs) capture ABA+. Second, we propose relaxed variants of complete and grounded semantics for HYPAFs that yield an extension for all frameworks by design, while still faithfully generalizing the established semantics of Dung-style Argumentation Frameworks. We exploit the newly established correspondence between ABA+ and HYPAFs to obtain variants for grounded and complete ABA+ semantics that are guaranteed to yield an outcome. Finally, we discuss basic properties and provide a complexity analysis. Along the way, we settle the computational complexity of several ABA+ semantics.}, added-at = {2024-09-10T10:41:24.000+0200}, author = {Dimopoulos, Yannis and Dvorak, Wolfgang and K{\"o}nig, Matthias and Rapberger, Anna and Ulbricht, Markus and Woltran, Stefan}, biburl = {https://puma.scadsai.uni-leipzig.de/bibtex/2042fb2e110605f57d399b0a072245f7a/scadsfct}, interhash = {e6a4afac42db6aeffd1af2f41815974a}, intrahash = {042fb2e110605f57d399b0a072245f7a}, journal = {Proc. Conf. AAAI Artif. Intell.}, keywords = {topic_knowledge}, month = mar, number = 9, pages = {10493--10500}, publisher = {Association for the Advancement of Artificial Intelligence (AAAI)}, timestamp = {2024-11-22T15:46:10.000+0100}, title = {Redefining {ABA+} semantics via abstract set-to-set attacks}, volume = 38, year = 2024 }