Exact analytical-hierarchy completeness of skeptical acceptance under preferred semantics

Determine the exact completeness level within the analytical hierarchy of the skeptical acceptance problem for preferred semantics in computably finitary argumentation frameworks.

Background

The paper establishes that skeptical acceptance under preferred semantics for computably finitary argumentation frameworks belongs to the class $\Pi^1_1$. However, membership in this class does not determine whether the problem is $\Pi^1_1$-complete or belongs to a lower level of the analytical hierarchy. The authors explicitly leave this exact classification unresolved.