在锁和钥匙下:一个多模态逻辑的证明系统

The Bulletin of Symbolic Logic Pub Date : 2022-11-11 DOI:10.1017/bsl.2023.14

G. A. Kavvos, Daniel Gratzer

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摘要

摘要在前人关于模态Martin-Löf类型理论的基础上，提出了一个多模态和多模态逻辑的证明体系。模态、模态和它们之间的含义的规范是作为模态理论给出的，即一个小的2类。将逻辑扩展到λ演算，建立Curry-Howard对应关系。

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UNDER LOCK AND KEY: A PROOF SYSTEM FOR A MULTIMODAL LOGIC

Abstract We present a proof system for a multimode and multimodal logic, which is based on our previous work on modal Martin-Löf type theory. The specification of modes, modalities, and implications between them is given as a mode theory, i.e., a small 2-category. The logic is extended to a lambda calculus, establishing a Curry–Howard correspondence.

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The Bulletin of Symbolic Logic

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