Since the cognitive revolution, language and action have been compared as cognitive systems, with cross-domain convergent views recently gaining renewed interest in biology, neuroscience, and cognitive science. Language and action are both combinatorial systems whose mode of combination has been argued to be hierarchical, combining elements into constituents of increasingly larger size. This structural similarity has led to the suggestion that they rely on shared cognitive and neural resources. In this article, we compare the conceptual and formal properties of hierarchy in language and action using set theory. We show that the strong compositionality of language requires a particular formalism, a magma, to describe the algebraic structure corresponding to the set of hierarchical structures underlying sentences. When this formalism is applied to actions, it appears to be both too strong and too weak. To overcome these limitations, which are related to the weak compositionality and sequential nature of action structures, we formalize the algebraic structure corresponding to the set of actions as a trace monoid. We aim to capture the different system properties of language and action in terms of the distinction between hierarchical sets and hierarchical sequences and discuss the implications for the way both systems could be represented in the brain. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

中文翻译：

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语言和动作的层次结构：正式比较。

自认知革命以来，语言和行为一直被视为认知系统，跨领域的趋同观点最近重新引起了生物学、神经科学和认知科学的兴趣。语言和动作都是组合系统，其组合模式被认为是分层的，将元素组合成尺寸越来越大的成分。这种结构上的相似性导致人们认为它们依赖于共享的认知和神经资源。在本文中，我们使用集合论比较了语言和动作中层次结构的概念和形式属性。我们表明，语言的强组合性需要一种特定的形式主义，即岩浆，来描述与句子底层的层次结构集相对应的代数结构。当这种形式主义运用到行动中时，它显得既太强又太弱。为了克服这些与动作结构的弱组合性和顺序性有关的限制，我们将与动作集相对应的代数结构形式化为迹幺半群。我们的目标是根据层次集和层次序列之间的区别来捕获语言和动作的不同系统属性，并讨论这两个系统在大脑中表示方式的含义。（PsycInfo 数据库记录 (c) 2023 APA，保留所有权利）。我们将对应于动作集的代数结构形式化为迹幺半群。我们的目标是根据层次集和层次序列之间的区别来捕获语言和动作的不同系统属性，并讨论这两个系统在大脑中表示方式的含义。（PsycInfo 数据库记录 (c) 2023 APA，保留所有权利）。我们将对应于动作集的代数结构形式化为迹幺半群。我们的目标是根据层次集和层次序列之间的区别来捕获语言和动作的不同系统属性，并讨论这两个系统在大脑中表示方式的含义。（PsycInfo 数据库记录 (c) 2023 APA，保留所有权利）。