发表机构
School of Philosophy, Zhejiang University（浙江大学哲学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究可计算有限论证框架中基于语义与优先语义的标准判定问题复杂性，明确了有限性对推理复杂性的影响边界。
AI 中文摘要
Dung提出的抽象论证框架（AFs）为人工智能中的非单调推理提供了形式基础。虽然一般无限AFs的判定问题通常处于分析层次的高层（Σ₁¹或Π₁¹），但将框架限制为可计算有限性可将部分复杂性降低至算术层次。本文针对可计算有限AFs中基于语义（grounded semantics）和优先语义（preferred semantics）的标准判定问题：轻信接受（Cred）、怀疑接受（Skep）、扩展存在性（Ex）、唯一性（Uni）及非空存在性（NE），给出了复杂性映射。对于基于语义，已知轻信接受和怀疑接受已为Σ₁⁰完全；本文证明非空存在性也为Σ₁⁰完全，而存在性与唯一性是平凡的，这些分类在有效可计算有限表示的范围内成立。对于优先语义，利用可计算有限分支的计算树，证明Credₚᵣₑբ属于Π₁⁰完全，NEₚᵣₑբ为Σ₂⁰完全；但无法归约全称量词与全局唯一性，导致Skepₚᵣₑբ属于Π₁¹，Uniₚᵣₑբ为Σ₂¹完全。本文结果明确了有限性成功将推理降至算术层次的精确边界，以及二阶量词迫使问题回归分析层次的边界。
英文摘要
Abstract argumentation frameworks (AFs) introduced by Dung provide a formal foundation for non-monotonic reasoning in artificial intelligence. While decision problems for general infinite AFs typically reside at high levels of the analytical hierarchy ($Σ_1^1$ or $Π_1^1$), restricting the framework to be computably finitary reduces some of the complexity to the arithmetical hierarchy. In this paper, we present a complexity mapping of grounded and preferred semantics in computably finitary AFs across standard decision problems: credulous acceptance ($\Cred$), skeptical acceptance ($\Skep$), extension existence ($\Ex$), uniqueness ($\Uni$), and non-empty existence ($\NE$). For grounded semantics, credulous and skeptical acceptance are already known to be $Σ_1^0$-complete. We show that non-empty existence is also $Σ_1^0$-complete, whereas existence and uniqueness are trivial. These classifications are understood within the domain of valid computably finitary representations. For preferred semantics, using a computably finitely branching computation tree, $\Cred_{\pref}$ is shown to be in $Π_1^0$-c and $\NE_{\pref}$ is $Σ_2^0$-c. However, it is insufficient to reduce universal quantification and global uniqueness, leaving $\Skep_{\pref}$ in $Π_1^1$ and $\UniPref$ in $Σ_2^1$-c. Our results show the precise boundary where finitarity succeeds to bring reasoning down to the arithmetical hierarchy and where second-order quantification forces problems back into the analytical hierarchy.
Comments15 pages
