从直觉主义到布劳尔的模态逻辑

Q2 Arts and Humanities Bulletin of the Section of Logic Pub Date : 2020-10-08 DOI:10.18778/0138-0680.2020.22

Zofia Kostrzycka

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引用次数: 0

摘要

我们试图将直觉命题逻辑INT转化为布劳沃的模态逻辑KTB。我们的翻译是基于布劳沃公理p背后的直觉→☐◊p其主要思想是将直觉蕴涵解释为模态严格蕴涵，而变量和其他肯定句则保持原样。所提出的翻译保留了Rieger Nishimura格的片段，该格是INT中一元公式的Lindenbaum代数。不幸的是，INT没有通过这种映射嵌入到KTB中。

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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From Intuitionism to Brouwer's Modal Logic

We try to translate the intuitionistic propositional logic INT into Brouwer's modal logic KTB. Our translation is motivated by intuitions behind Brouwer's axiom p →☐◊p The main idea is to interpret intuitionistic implication as modal strict implication, whereas variables and other positive sentences remain as they are. The proposed translation preserves fragments of the Rieger-Nishimura lattice which is the Lindenbaum algebra of monadic formulas in INT. Unfortunately, INT is not embedded by this mapping into KTB.

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