SCC-recursiveness in infinite argumentation (extended version)

TL;DR

This paper explores extending SCC-recursive semantics from finite to infinite argumentation frameworks, analyzing their properties and limitations, and identifying conditions under which they behave well.

Contribution

It introduces two methods for extending SCC-recursive semantics to infinite AFs and evaluates their properties using established criteria.

Findings

Directionality fails in general for infinite AFs

Some semantics satisfy directionality in finitary frameworks

The results advance the theory of infinite argumentation

Abstract

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.