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When Stable and Preferred Semantics Agree: A Path-Based Approach

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Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 23/10/2026, 04:03:24 UTC.

Briefings

This article investigates when preferred and stable semantics agree in abstract argumentation frameworks using a path-based approach. The authors establish a general criterion for semantic agreement based on attack graph paths and binary relations, generalizing Dung's limited controversiality condition and SCC-symmetry condition. Key findings include a collapse theorem reducing infinite conditions to three distinct ones for the first sequence, and genuinely distinct conditions for the second sequence. The results apply to both finite and infinite frameworks and provide sufficient conditions for stable extensions.

Key points

• The study establishes a general path-based criterion for semantic agreement in abstract argumentation frameworks by analyzing attack graph paths and induced binary relations.
• Dung's limited controversiality condition is recovered as a special case when the path set consists of even paths, while the second sequence yields conditions with no analogous collapse.

Context

The research addresses a fundamental question in abstract argumentation theory regarding the consistency between preferred and stable semantics. Understanding these conditions is crucial for applications in knowledge representation and logical reasoning systems where stable and preferred outcomes must align.

Limitations

The evidence is limited to the arXiv preprint v1, which may not reflect final published results. The study applies to both finite and infinite frameworks, but the paper does not specify computational complexity or practical performance implications for large-scale infinite frameworks.

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