Relevance for Stability of Verification Status of a Set of Arguments in Incomplete Argumentation Frameworks (with Proofs)
This work addresses theoretical computational complexity in argumentation frameworks, but it is incremental as it builds on prior research.
The paper extends the notion of relevance to stability for sets of arguments in incomplete argumentation frameworks, proposing strong relevance and analyzing complexity, finding detection is in P time for most semantics but tractable methods are difficult under grounded semantics.
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.