In 2001 and 2002, Daowen Qiu has established a new theory of $\mathcal{L}$-valued automata which is based on complete residuated lattices. Moreover, besides the finite automata, several other classes of machines, grammars and languages have been generalized using the ideas introduced by Qiu. This paper generalizes the concept of linear grammars and linear languages in this context, moreover, it presents some operations for $\mathcal{L}$-valued languages and some closure properties for the $\mathcal{L}$-valued linear languages.

中文翻译：

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L值线性语言的闭包性质

2001年和2002年，邱道文建立了一个新的理论 $\mathcal{升}$基于完全剩余格的值自动机。此外，除了有限自动机之外，还有其他几类机器、语法和语言已经使用邱介绍的思想进行了推广。本文在此背景下概括了线性文法和线性语言的概念，此外，它提出了一些操作$\mathcal{升}$-valued 语言和一些闭包属性 $\mathcal{升}$-值线性语言。