AI 中文总结
该研究提出了基于闭包、可比性与联合可容许性的统一框架，用于从多结构理论构造典范解释，区分非确定性类型并给出对应确定化机制，还可应用于LLM辅助推理以分析幻觉问题。
AI 中文摘要
我们开发了一个形式框架，用于从多个结构理论中构造典范解释。结构理论是一个三元组 T = (Σ, A, I)，由签名、公理和推理策略组成，其可容许解释族收集了所有全局一致的结构结论赋值。我们区分三个层面的典范化：闭包稳定化（针对单个种子的收敛）、全局完备化（与种子无关的收敛）以及确定化（唯一的可容许解释）。非确定性被分为认知多元性（E型）和结构多元性（S型），其中细化的S型强子类的特征是缺乏公共上界。两种典范化机制应运而生：基于算子的完备化和基于选择器的构造。我们给出了这些机制存在的充分结构条件，并证明在满足附加可靠性条件的正非收缩规则下，纯基于推理的完备化可归约为饱和闭包算子。对于E型理论，闭包稳定化是可实现的，而完全确定化依赖于仍未解决的全局合流性质；对于S型强理论，确定化可通过典范选择实现。我们进一步表明，多层典范化通过分阶段算子形成结构上非交换的系统，并提供了一个条件分类定理，将理论内在机制归约为闭包或选择。该框架也适用于大语言模型（LLM）辅助推理，其中幻觉可被视为无依据的典范化。
英文摘要
We develop a formal framework for constructing canonical interpretations from plural structure theories. A structure theory is a triple T = (Σ, A, I) consisting of a signature, axioms, and an inference policy, whose admissible interpretation family collects all globally consistent assignments of structural conclusions. We distinguish three levels of canonicalization: closure stabilization (per-seed convergence), global completion (seed-independent convergence), and determinization (a unique admissible interpretation). Non-determinism is classified into epistemic plurality (Type E) and structural plurality (Type S), with a refined Type S-strong subclass characterized by the absence of common upper bounds. Two canonicalization mechanisms arise: operator-based completion and selector-based construction. We provide sufficient structural conditions under which these mechanisms exist, and show that pure inference-based completion reduces to a saturated closure operator under positive, non-retractive rules with an additional soundness condition. For Type E theories, closure stabilization is established, while full determinization depends on a global confluence property that remains open. For Type S-strong theories, determinization is achieved via canonical selection. We further show that multi-level canonicalization forms a structurally non-commutative system via staged operators, and provide a conditional classification theorem reducing theory-intrinsic mechanisms to closure or selection. The framework also applies to LLM-assisted reasoning, where hallucination can be viewed as unsupported canonicalization.
CommentsFormal framework paper on canonicalization and determinization in structure theories; version v2.16.4; 29 pages
