In this work we define formal grammars in terms of free monoidal categories, along with a functor from the category of formal grammars to the category of automata. Generalising from the Booleans to arbitrary semirings, we extend our construction to weighted formal grammars and weighted automata. This allows us to link the categorical viewpoint on natural language to the standard machine learning notion of probabilistic language model.

中文翻译：

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增量单形语法

在这项工作中，我们根据自由幺半群范畴定义形式文法，以及从形式文法范畴到自动机范畴的函子。从布尔值推广到任意半环，我们将构造扩展到加权形式文法和加权自动机。这使我们能够将自然语言的分类观点与概率语言模型的标准机器学习概念联系起来。