Complexity of Grounded Semantics and Preferred Semantics in Finitary Argumentation Frameworks
Abstract argumentation frameworks (AFs) introduced by Dung provide a formal foundation for non-monotonic reasoning in artificial intelligence. While decision problems for general infinite AFs typically reside at high levels of the analytical hierarchy ($Σ_1^1$ or $Π_1^1$), restricting the framework to be computably finitary reduces some of the complexity to the arithmetical hierarchy. In this paper, we present a complexity mapping of grounded and preferred semantics in computably finitary AFs across standard decision problems: credulous acceptance ($\Cred$), skeptical acceptance ($\Skep$), extension existence ($\Ex$), uniqueness ($\Uni$), and non-empty existence ($\NE$). For grounded sema...
| Authors | Jinfan Xu, Jieting Luo |
|---|---|
| Primary category | cs.AI |
| Published | 8 October 2026 |
| Last updated at source | 8 October 2026 |
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