Revisiting Vacuous Reduct Semantics for Abstract Argumentation (Extended Version)
Lydia Blümel, Matthias Thimm
TL;DR
This work revisits vacuous reduct semantics for abstract argumentation by systematically combining a base extension-based semantics $\sigma$ with a vacuity condition $\tau$ to form $vac_\sigma(\tau)$. It catalogs 17 novel vacuous reduct semantics and 31 correspondences across instantiations, providing a general principle-based framework to assess how standard properties carry over to these weakened or strengthened formulations. The authors derive criteria for principle inheritance (e.g., conflict-freeness, reinstatement, directionality, existence) from the base and vacuity components and give a detailed analysis for the undisputed semantics, revealing which principles are preserved or violated by various vacuous reducts. The results illuminate the landscape of weak and refined semantics in abstract argumentation, offering a foundation for applying vacuous reduct ideas to related formalisms and structured argumentation, and suggest directions for future work on connections to jelia23 and beyond.
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.