Dual and Axiomatic Systems for Constructive S4, a Formally Verified Equivalence

Q3 Computer Science

Electronic Notes in Theoretical Computer Science Pub Date : 2020-03-01 DOI:10.1016/j.entcs.2020.02.005

Lourdes del Carmen González Huesca , Favio E. Miranda-Perea , P. Selene Linares-Arévalo

引用次数: 1

Abstract

We present a proof of the equivalence between two deductive systems for the constructive modal logic S4. On one side, an axiomatic characterization inspired by Hakli and Negri's Hilbert-style system of derivations from assumptions for modal logic K. On the other side, the judgmental reconstruction given by Pfenning and Davies by means of a so-called dual natural deduction approach that makes a distinction between valid, true and possible formulas. Both systems and the proof of their equivalence are formally verified using the Coq proof assistant.

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构式S4的对偶和公理化系统，一个正式验证的等价

给出了构式模态逻辑S4的两个演绎系统的等价证明。一方面，受Hakli和Negri的hilbert式模态逻辑k的假设推导系统启发的公理化表征;另一方面，p芬宁和戴维斯通过所谓的对偶自然演绎方法给出了判断重构，该方法区分了有效、真和可能的公式。使用Coq证明助手对两个系统及其等价性的证明进行了形式化验证。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Electronic Notes in Theoretical Computer Science Computer Science-Computer Science (all)

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