Relevance for Stability of Verification Status of a Set of Arguments in Incomplete Argumentation Frameworks (with Proofs)

TL;DR

This paper extends the concept of relevance to the stability of verification status for sets of arguments in incomplete argumentation frameworks, introducing strong relevance and analyzing computational complexity.

Contribution

It introduces the notion of relevance for sets of arguments' stability, proposes strong relevance, and analyzes the complexity of relevance detection under various semantics.

Findings

Relevance detection can be done in polynomial time for most semantics.

Strong relevance is a necessary concept for understanding resolution requirements.

Detecting relevance under grounded semantics remains challenging.

Abstract

The notion of relevance was proposed for stability of justification status of a single argument in incomplete argumentation frameworks (IAFs) in 2024 by Odekerken et al. To extend the notion, we study the relevance for stability of verification status of a set of arguments in this paper, i.e., the uncertainties in an IAF that have to be resolved in some situations so that answering whether a given set of arguments is an extension obtains the same result in every completion of the IAF. Further we propose the notion of strong relevance for describing the necessity of resolution in all situations reaching stability. An analysis of complexity reveals that detecting the (strong) relevance for stability of sets of arguments can be accomplished in P time under the most semantics discussed in the paper. We also discuss the difficulty in finding tractable methods for relevance detection under grounded semantics.