We introduce proper display calculi for basic monotonic modal logic, the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative, and enjoy cut elimination and subformula property. Our proposal applies the multi-type methodology in the design of proper display calculi, starting from a semantic analysis which motivates syntactic translations from single-type non-normal modal logics to multi-type normal poly-modal logics.

中文翻译：

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非正规模态逻辑和条件逻辑：语义分析和证明论

我们为基本单调模态逻辑、条件逻辑 CK 和它们的许多公理扩展引入了适当的显示演算。这些演算是健全的、完整的、保守的，并享有削减消除和子公式的性质。我们的建议将多类型方法应用于适当显示演算的设计，从语义分析开始，该分析促使句法从单类型非正规模态逻辑转换为多类型正规多模态逻辑。