Revisiting Vacuous Reduct Semantics for Abstract Argumentation (Extended Version)
This work addresses foundational issues in formal argumentation theory, offering incremental refinements to existing semantics for researchers in computational logic and AI.
The paper tackles the problem of refining abstract argumentation semantics by introducing vacuous reduct semantics, which filters extensions based on a vacuity condition, and provides a systematic analysis of principle satisfaction for these semantics, including criteria for inheritance from base and vacuity conditions.
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.