This paper introduces a natural deduction calculus for intuitionistic logic of belief \(\mathsf {IEL}^{-}\) which is easily turned into a modal \(\lambda \)-calculus giving a computational semantics for deductions in \(\mathsf {IEL}^{-}\). By using that interpretation, it is also proved that \(\mathsf {IEL}^{-}\) has good proof-theoretic properties. The correspondence between deductions and typed terms is then extended to a categorical semantics for identity of proofs in \(\mathsf {IEL}^{-}\) showing the general structure of such a modality for belief in an intuitionistic framework.

中文翻译：

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直觉主义信仰的库里-霍华德-兰贝克通信

本文介绍了一种用于信念的直觉逻辑 \(\mathsf {IEL}^{-}\)的自然演绎演算，它很容易转化为模态 \(\lambda \) -演算，为\(\ mathsf {IEL}^{-}\)。通过使用这种解释，还证明了\(\mathsf {IEL}^{-}\)具有良好的证明理论性质。然后将演绎和类型术语之间的对应关系扩展到\(\mathsf {IEL}^{-}\)中证明同一性的分类语义，显示了这种直觉框架中信念的模态的一般结构。