Rejection in Abstract Argumentation: Harder Than Acceptance?
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916362900733952 |
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| author | Fichte, Johannes K. Hecher, Markus Mahmood, Yasir Meier, Arne |
| author_facet | Fichte, Johannes K. Hecher, Markus Mahmood, Yasir Meier, Arne |
| contents | Abstract argumentation is a popular toolkit for modeling, evaluating, and comparing arguments. Relationships between arguments are specified in argumentation frameworks (AFs), and conditions are placed on sets (extensions) of arguments that allow AFs to be evaluated. For more expressiveness, AFs are augmented with \emph{acceptance conditions} on directly interacting arguments or a constraint on the admissible sets of arguments, resulting in dialectic frameworks or constrained argumentation frameworks. In this paper, we consider flexible conditions for \emph{rejecting} an argument from an extension, which we call rejection conditions (RCs). On the technical level, we associate each argument with a specific logic program. We analyze the resulting complexity, including the structural parameter treewidth. Rejection AFs are highly expressive, giving rise to natural problems on higher levels of the polynomial hierarchy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_10683 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rejection in Abstract Argumentation: Harder Than Acceptance? Fichte, Johannes K. Hecher, Markus Mahmood, Yasir Meier, Arne Artificial Intelligence Computational Complexity Logic in Computer Science Abstract argumentation is a popular toolkit for modeling, evaluating, and comparing arguments. Relationships between arguments are specified in argumentation frameworks (AFs), and conditions are placed on sets (extensions) of arguments that allow AFs to be evaluated. For more expressiveness, AFs are augmented with \emph{acceptance conditions} on directly interacting arguments or a constraint on the admissible sets of arguments, resulting in dialectic frameworks or constrained argumentation frameworks. In this paper, we consider flexible conditions for \emph{rejecting} an argument from an extension, which we call rejection conditions (RCs). On the technical level, we associate each argument with a specific logic program. We analyze the resulting complexity, including the structural parameter treewidth. Rejection AFs are highly expressive, giving rise to natural problems on higher levels of the polynomial hierarchy. |
| title | Rejection in Abstract Argumentation: Harder Than Acceptance? |
| topic | Artificial Intelligence Computational Complexity Logic in Computer Science |
| url | https://arxiv.org/abs/2408.10683 |