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Does there exist a complete axiomatization of the class of evidential argumentation frameworks that are coherent under transfinite chains of attack and support relations?

Related: Suslin Hypothesis, Zermelo-Fraenkel axioms and independence results, Dung's fundamental lemma on admissible argumentation semantics

The problem asks whether one can write down a finite or recursively enumerable set of axioms that exactly captures when an evidential argumentation framework remains logically coherent as chains of supporting and attacking arguments grow without bound into transfinite ordinal lengths. Current frameworks handle finite chains well, but when arguments depend on other arguments that themselves depend on further arguments in a potentially infinite regress, it is unclear whether any fixed logical calculus can decide membership in the class of coherent frameworks. This connects directly to questions about well-foundedness in set-theoretic trees and the combinatorics of Suslin-type structures, since an infinitely branching argumentation tree with specific coherence conditions mirrors the structural requirements studied in Suslin forest theory.

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