C. I. Lewis’ systems were the first axiomatisations of modal logics. However some of those systems are non-normal modal logics, since they do not admit a full rule of necessitation, but only a restricted version thereof. We provide G3-style labelled sequent calculi for Lewis’ non-normal propositional systems. The calculi enjoy good structural properties, namely admissibility of structural rules and admissibility of cut. Furthermore they allow for straightforward proofs of admissibility of the restricted versions of the necessitation rule. We establish completeness of the calculi and we discuss also related systems.

中文翻译：

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刘易斯非正规命题模态逻辑的标记序列演算

CI Lewis 的系统是模态逻辑的第一个公理化。然而，其中一些系统是非正规模态逻辑，因为它们不承认完整的必然性规则，而只承认其受限制的版本。我们为 Lewis 的非正规命题系统提供 G3 风格的标记序列演算。微积分具有良好的结构特性，即结构规则的可容许性和切割的可容许性。此外，它们允许直接证明必要规则的限制版本的可接受性。我们建立了微积分的完整性，我们还讨论了相关的系统。