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P2 Dualized Simple Type Theory

对偶化简单类型理论
LMCS vol.Volume 12, Issue 32017匹配度 1/10 · 该论文属于纯类型论与证明论研究,讨论双直觉主义简单类型论及其规范化,不涉及LLM/Agent、静态分析、浮点程序分析或贝叶斯程序分析,与用户研究画像的核心方向几乎没有交集。引用 3 inbox
Harley Eades III, Aaron Stump, Ryan McCleeary
dblp: 2026-09-10crossref: 2026-09-10arxiv: 2026-09-10

AI 速览

一句话:提出带完美直觉主义对偶性的简单类型论 DTT,对应单侧极化序列演算,并证明强规范化与类型保持。

论文提出一种新的双直觉主义类型理论——对偶化类型理论(DTT)。DTT 是具有完美直觉主义对偶性的简单类型理论,对应单侧极化序列演算。其逻辑基础是新的命题双直觉主义逻辑 DIL,该逻辑建立在 Pinto 与 Uustalu 的 L 之上,通过删除若干可容许推理规则并采用带极性的对偶化语法来简化推理系统,同时保持一致性与完备性。作者证明 DTT 强规范化与类型保持,并给出 DIL 一致性的直接证明;完备性则通过归约到 L 来证明。

问题
如何构造一个具有完美直觉主义对偶性且证明论性质良好的简单类型理论及相应双直觉主义逻辑。
方法
基于 Pinto 与 Uustalu 的 L,采用极性和对偶化语法简化双直觉主义逻辑 DIL,并由此定义对应单侧极化序列演算的 DTT。
评估
形式化证明 DTT 的强规范化与类型保持,直接证明 DIL 一致性,并通过归约到 L 证明其完备性。
原文摘要(Abstract)

We propose a new bi-intuitionistic type theory called Dualized Type Theory (DTT). It is a simple type theory with perfect intuitionistic duality, and corresponds to a single-sided polarized sequent calculus. We prove DTT strongly normalizing, and prove type preservation. DTT is based on a new propositional bi-intuitionistic logic called Dualized Intuitionistic Logic (DIL) that builds on Pinto and Uustalu's logic L. DIL is a simplification of L by removing several admissible inference rules while maintaining consistency and completeness. Furthermore, DIL is defined using a dualized syntax by labeling formulas and logical connectives with polarities thus reducing the number of inference rules needed to define the logic. We give a direct proof of consistency, but prove completeness by reduction to L.

链接与引用

DOI 原文 · arXiv · PDF(开放获取) · DBLP

BibTeX
@article{EadesSM16,
  title = {Dualized Simple Type Theory},
  author = {Harley Eades III and Aaron Stump and Ryan McCleeary},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 12, Issue 3},
  year = {2017},
  doi = {10.2168/lmcs-12(3:2)2016}
}