Revisiting Vacuous Reduct Semantics for Abstract Argumentation (Extended Version)

TL;DR

This paper explores vacuous reduct semantics in abstract argumentation, analyzing how different semantics interact and establishing criteria for principle inheritance and vacuity conditions.

Contribution

It provides a systematic overview and principle-based analysis of vacuous reduct semantics derived from various argumentation semantics.

Findings

Criteria for inheritance of principles in vacuous reduct semantics

Vacuity conditions for established and new principles

Analysis of vacuous reduct semantics in the context of weak argumentation semantics

Abstract

We consider the notion of a vacuous reduct semantics for abstract argumentation frameworks, which, given two abstract argumentation semantics {\sigma} and {\tau}, refines {\sigma} (base condition) by accepting only those {\sigma}-extensions that have no non-empty {\tau}-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.