SCC-recursiveness in infinite argumentation (extended version)

2025-07-09

AI Summary

This paper addresses the failure of SCC-recursive semantics (e.g., CF2, STGT) on infinite argumentation frameworks (AFs) due to the absence of well-foundedness. We propose two novel constructions of SCC-recursive semantics extendable to infinite AFs, based on SCC decomposition of the attack graph and top-down recursive definition. We systematically analyze the breakdown of key properties—particularly directionality—in the infinite setting, and restore their validity within the finitary subclass. Theoretical evaluation adheres to Baroni and Giacomin’s semantic postulates, demonstrating that the proposed semantics achieve both rationality and expressive power. Notably, certain new semantics satisfy directionality on finitary AFs—the first SCC-recursive semantics to do so—thereby enabling a sound generalization of SCC-recursion to infinite argumentation. This work establishes a new paradigm for semantic modeling of infinite reasoning systems.

Technology Category

• Knowledge Representation and Reasoning: Argumentation
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Multiagent Systems: Agreement, Argumentation & Negotiation

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

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.

Problem

• Extending SCC-recursiveness to infinite argumentation frameworks
• Evaluating semantics using Baroni and Giacomin's criteria
• Ensuring directionality in finitary argumentation frameworks

Innovation

• Extends SCC-recursiveness to infinite argumentation frameworks
• Evaluates semantics using Baroni and Giacomin's criteria
• Satisfies directionality in finitary frameworks