SCC-recursiveness in infinite argumentation (extended version)
This work addresses a foundational problem in AI for modeling reasoning in unbounded domains, though it is incremental as it builds on existing SCC-recursive principles.
The paper tackled the failure of SCC-recursive semantics to generalize to infinite argumentation frameworks by proposing two extension approaches, showing that directionality fails in general but some semantics satisfy it in finitary frameworks.
Argumentation frameworks (AFs) are a foundational tool in artificial intelligence for modeling structured reasoning and conflict. SCC-recursiveness is a well-known design principle in which the evaluation of arguments is decomposed according to the strongly connected components (SCCs) of the attack graph, proceeding recursively from "higher" to "lower" components. While SCC-recursive semantics such as \cft and \stgt have proven effective for finite AFs, Baumann and Spanring showed the failure of SCC-recursive semantics to generalize reliably to infinite AFs due to issues with well-foundedness. We propose two approaches to extending SCC-recursiveness to the infinite setting. We systematically evaluate these semantics using Baroni and Giacomin's established criteria, showing in particular that directionality fails in general. We then examine these semantics' behavior in finitary frameworks, where we find some of our semantics satisfy directionality. These results advance the theory of infinite argumentation and lay the groundwork for reasoning systems capable of handling unbounded or evolving domains.