用几何不变量分析语言循环，探索语言前的思维结构。
Linguistic Loops and Geometric Invariants as a Way to Pre-Verbal Thought?
- 引入语言环与语义缺陷概念，基于李群理论建模语言结构
- 发现语言环中可计算的几何不变量，刻画其内在属性
- 为语言前思维提供数学表征，适合认知科学与形式语言研究者
本文提出语言变换、语言环和语义缺陷的概念。通过运用李群理论与几何方法，定义了能够捕捉整个语言环结构特性的不变量。该成果开辟了新研究方向，将李理论与高维几何工具应用于语言学研究。更引人注目的是，本研究暗示了对元语言或语言前思维的数学刻画，即那些先于语言产生的认知结构。
原文摘要 · Abstract (English)
In this work we introduce the concepts of linguistic transformation, linguistic loop and semantic deficit. By exploiting Lie group theoretical and geometric techniques, we define invariants that capture the structural properties of a whole linguistic loop. This result introduces new line of research, employing tools from Lie theory and higher-dimensional geometry within language studies. But, even more intriguingly, our study hints to a mathematical characterization of the meta-linguistic or pre-verbal thought, namely of those cognitive structures that precede the language.
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