On Some Intuitionistic Modal Logics
On Some Intuitionistic Modal Logics
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论一些直觉模态逻辑
DOI：
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发表时间：
1977
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通讯作者：
H. Ono
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作者：
H. Ono
Fitch [4]，Prior [7]，Bull [1]，[2]，[3]，Prawitz [6]等研究了一些基于弱于经典逻辑的模态逻辑。本文讨论基于直觉命题逻辑的模态逻辑，称之为直觉模态逻辑（简称IML）。设H是以希尔伯特形式表示的直觉主义命题逻辑。H的推理规则是肯定前件和替换规则。IML L0通过添加以下三个公理从H获得，
Some modal logics based on logics weaker than the classical logic have been studied by Fitch [4], Prior [7], Bull [1], [2], [3], Prawitz [6] etc. Here we treat modal logics based on the intuitionistic propositional logic, which call intuitionistic modal logics (abbreviated as IML’s). Let H be the intuitionistic propositional logic formulated in the Hilbertstyle. The rules of inference of H are modus ponens and the rule of substitution. The IML L0 is obtained from H by adding the following three axioms,