Implementing Permutations in the Brain and SVO Frequencies of Languages

The subject-verb-object (SVO) word order prevalent in English is shared by about $42\%$ of world languages. Another $45\%$ of all languages follow the SOV order, $9\%$ the VSO order, and fewer languages use the three remaining permutations. None of the many extant explanations of this phenomenon take into account the difficulty of implementing these permutations in the brain. We propose a plausible model of sentence generation inspired by the recently proposed Assembly Calculus framework of brain function. Our model results in a natural explanation of the uneven frequencies. Estimating the parameters of this model yields predictions of the relative difficulty of dis-inhibiting one brain area from another. Our model is based on the standard syntax tree, a simple binary tree with three leaves. Each leaf corresponds to one of the three parts of a basic sentence. The leaves can be activated through lock and unlock operations and the sequence of activation of the leaves implements a specific word order. More generally, we also formulate and algorithmically solve the problems of implementing a permutation of the leaves of any binary tree, and of selecting the permutation that is easiest to implement on a given binary tree.

英语中普遍存在的主题 - 动物对象（SVO）单词顺序约为$ 42 \％的世界语言。所有语言中的另外$ 45 \％$遵循SOV订单，$ 9 \％$ the VSO订单，更少的语言使用剩余的三个排列。对这种现象的许多现有解释都没有考虑到在大脑中实施这些排列的困难。我们提出了一个由最近提出的脑功能组合框架启发的句子生成模型。我们的模型可以自然地解释不均匀的频率。估计该模型的参数可以预测抑制另一个大脑区域的相对难度。我们的模型基于标准语法树，这是一个带有三片叶子的简单二进制树。每个叶子对应于基本句子的三个部分之一。可以通过锁和解锁操作来激活叶子，叶子的激活顺序实现了特定的单词顺序。更一般而言，我们还制定和算法解决了实现任何二进制树叶子置换的问题，并选择最容易实现在给定二进制树上的排列。