Revisiting Vacuous Reduct Semantics for Abstract Argumentation (Extended Version)

Lydia Blümel, Matthias Thimm
8/26/2024
cs.AI

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Abstract

We consider the notion of a vacuous reduct semantics for abstract argumentation frameworks, which, given two abstract argumentation semantics σ and τ, refines σ (base condition) by accepting only those σ-extensions that have no non-empty τ-extension in their reduct (vacuity condition). We give a systematic overview on vacuous reduct semantics resulting from combining different admissibility-based and conflict-free semantics and present a principle-based analysis of vacuous reduct semantics in general. We provide criteria for the inheritance of principle satisfaction by a vacuous reduct semantics from its base and vacuity condition for established as well as recently introduced principles in the context of weak argumentation semantics. We also conduct a principle-based analysis for the special case of undisputed semantics.

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Cite this paper

@article{blmel2024revisiting,
  title  = {Revisiting Vacuous Reduct Semantics for Abstract Argumentation (Extended Version)},
  author = {Lydia Blümel and Matthias Thimm},
  year   = {2024},
  eprint = {2408.14069},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2408.14069v1}
}

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