Graduate School of Human and Environmental Studies, Kyoto University, Kyoto, Japan; Department of Humanities, Kanazawa Seiryo University, Kanazawa, Japan.
Lyon Neuroscience Research Center (CRNL), (INSERM/CNRS/University of Lyon), Bron, France; Araya Inc., Tokyo, Japan; Advanced Comprehensive Research Organization, Teikyo University, Tokyo, Japan.
Cogn Psychol. 2023 Nov;146:101606. doi: 10.1016/j.cogpsych.2023.101606. Epub 2023 Sep 23.
Mathematical expressions consist of recursive combinations of numbers, variables, and operators. According to theoretical linguists, the syntactic mechanisms of natural language also provide a basis for mathematics. To date, however, no theoretically rigorous investigation has been conducted to support such arguments. Therefore, this study uses a methodology based on theoretical linguistics to analyze the syntactic properties of mathematical expressions. Through a review of recent behavioral and neuroimaging studies on mathematical syntax, we report several inconsistencies with theoretical linguistics, such as the use of ternary structures. To address these, we propose that a syntactic category called Applicative plays a central role in analyzing mathematical expressions with seemingly ternary structures by combining binary structures. Besides basic arithmetic expressions, we also examine algebraic equations and complex expressions such as integral and differential calculi. This study is the first attempt at building a comprehensive framework for analyzing the syntactic structures of mathematical expressions.
数学表达式由数字、变量和运算符的递归组合构成。根据理论语言学家的说法，自然语言的句法机制也为数学提供了基础。然而，迄今为止，还没有进行理论上严格的调查来支持这些论点。因此，本研究使用基于理论语言学的方法来分析数学表达式的句法属性。通过对最近关于数学语法的行为和神经影像学研究的回顾，我们报告了与理论语言学的几个不一致之处，例如三元结构的使用。为了解决这些问题，我们提出，通过组合二元结构，一种称为应用的句法范畴在分析具有看似三元结构的数学表达式方面起着核心作用。除了基本的算术表达式外，我们还检查了代数方程和复杂表达式，如积分和微分演算。本研究首次尝试构建一个全面的框架来分析数学表达式的句法结构。
