Statistical analysis of corpora provides an approach to quantitatively investigate natural languages. This approach has revealed that several power laws consistently emerge across different corpora and languages, suggesting the universal principles underlying languages. Particularly, the power-law decay of correlation has been interpreted as evidence for underlying hierarchical structures in syntax, semantics, and discourse. This perspective has also been extended to child languages and animal signals. However, the argument supporting this interpretation has not been empirically tested. To address this problem, this study examines the validity of the argument for syntactic structures. Specifically, we test whether the statistical properties of parse trees align with the implicit assumptions in the argument. Using English corpora, we analyze the mutual information, deviations from probabilistic context-free grammars (PCFGs), and other properties in parse trees, as well as in the PCFG that approximates these trees. Our results indicate that the assumptions do not hold for syntactic structures and that it is difficult to apply the proposed argument to child languages and animal signals, highlighting the need to reconsider the relationship between the power law and hierarchical structures.

本研究针对自然语言中的层级结构与幂律之间的关系进行了实证检验，指出现有观点缺乏实证支持，特别是在句法结构方面的假设并不成立。研究结果表明，难以将这一观点应用于儿童语言和动物信号，从而促使我们重新思考幂律与层级结构的相关性。

重新审视幂律与层级结构之间的关系