Rediscovering Argumentation Principles Utilizing Collective Attacks

TL;DR

This paper extends principle-based analysis to Collective Attack Argumentation Frameworks (SETAFs), introduces new concepts like reduct and modularization, and demonstrates their utility in incremental extension computation and tractability results.

Contribution

It provides a comprehensive overview of principles for SETAF semantics, introduces the reduct and modularization principles, and explores their applications in computation and complexity analysis.

Findings

Investigation of principles reveals additional challenges in SETAFs.

Introduction of the reduct concept aids in modular analysis of SETAFs.

New tractability results for verifying preferred extensions in SETAFs.

Abstract

Argumentation Frameworks (AFs) are a key formalism in AI research. Their semantics have been investigated in terms of principles, which define characteristic properties in order to deliver guidance for analysing established and developing new semantics. Because of the simple structure of AFs, many desired properties hold almost trivially, at the same time hiding interesting concepts behind syntactic notions. We extend the principle-based approach to Argumentation Frameworks with Collective Attacks (SETAFs) and provide a comprehensive overview of common principles for their semantics. Our analysis shows that investigating principles based on decomposing the given SETAF (e.g. directionality or SCC-recursiveness) poses additional challenges in comparison to usual AFs. We introduce the notion of the reduct as well as the modularization principle for SETAFs which will prove beneficial for this kind of investigation. We then demonstrate how our findings can be utilized for incremental computation of extensions and give a novel parameterized tractability result for verifying preferred extensions.