In this paper, we deal with a relationship among the law of excluded middle, the double negation elimination and the independence of premiss rule (\(\mathrm {IPR}\)) for (many-sorted) intuitionistic predicate logic. After giving a general machinery, we give, as corollaries, several examples of extensions of \(\mathbf {HA}\) and \(\mathbf {HA}^\omega \) which are closed under \(\mathrm {IPR}\) but do not derive the independence of premiss axiom.

中文翻译：

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论前提公理与规则的独立性

在本文中，我们处理了（多种）直觉谓词逻辑的排除中间定律，双重否定消除和前提规则（\（\ mathrm {IPR} \））的独立性之间的关系。在给出一般机制之后，我们给出\（\ mathbf {HA} \）和\（\ mathbf {HA} ^ \ omega \）扩展名的几个示例，这些扩展名在\（\ mathrm {IPR}下关闭\），但不能得出前提公理的独立性。