This paper explores proof-theoretic aspects of hybrid type-logical grammars , a logic combining Lambek grammars with lambda grammars. We prove some basic properties of the calculus, such as normalisation and the subformula property and also present both a sequent and a proof net calculus for hybrid type-logical grammars. In addition to clarifying the logical foundations of hybrid type-logical grammars, the current study opens the way to variants and extensions of the original system, including but not limited to a non-associative version and a multimodal version incorporating structural rules and unary modes.

中文翻译：

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混合类型逻辑文法的逻辑基础

本文探讨了混合类型逻辑文法的证明理论方面，这是一种将 Lambek 文法与 lambda 文法相结合的逻辑。我们证明了微积分的一些基本属性，例如归一化和子公式属性，并且还提供了混合类型逻辑文法的连续和证明网络演算。除了阐明混合类型逻辑语法的逻辑基础之外，当前的研究为原始系统的变体和扩展开辟了道路，包括但不限于非关联版本和包含结构规则和一元模式的多模态版本。