On the Complexity of the Grounded Semantics for Infinite Argumentation Frameworks

• URL: http://arxiv.org/abs/2511.22376v1
• Date: Thu, 27 Nov 2025 12:13:30 GMT
• Title: On the Complexity of the Grounded Semantics for Infinite Argumentation Frameworks
• Authors: Uri Andrews, Luca San Mauro,
• Abstract summary: We use methods from mathematical logic, specifically computability and set theory, to analyze the grounded extension.<n>Finding this fixed-point requires transfinite iterations.<n>This shows a marked distinction from the finite case where the grounded extension is-time computable.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Argumentation frameworks, consisting of arguments and an attack relation representing conflicts, are fundamental for formally studying reasoning under conflicting information. We use methods from mathematical logic, specifically computability and set theory, to analyze the grounded extension, a widely-used model of maximally skeptical reasoning, defined as the least fixed-point of a natural defense operator. Without additional constraints, finding this fixed-point requires transfinite iterations. We identify the exact ordinal number corresponding to the length of this iterative process and determine the complexity of deciding grounded acceptance, showing it to be maximally complex. This shows a marked distinction from the finite case where the grounded extension is polynomial-time computable, thus simpler than other reasoning problems explored in formal argumentation.

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