Hierarchical structure in language and action: A formal comparison.

Abstract

Since the cognitive revolution, language and action have been compared as cognitive systems, with crossdomain 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.

Continuous Theta-Burst Stimulation on the Left Posterior Inferior Frontal Gyrus Perturbs Complex Syntactic Processing Stability in Mandarin Chinese

“…However, our results might shed limited light on the debate regarding the role of LpIFG in syntax and domain-general hierarchical processing. It is plausible to hypothesize that non-linguistic domains like music and behavior share cognitive and neural resources with syntax, given the similarity of their hierarchical systems to those in linguistic domains ( Coopmans et al, 2023 ; Fitch & Martins, 2014 ; Fujita, 2014 ; Pulvermüller & Fadiga, 2010 ; Stout & Chaminade, 2009 ). Nevertheless, neuroimaging studies suggest only a limited overlap between linguistic and non-linguistic hierarchical processing in the LpIFG ( Fazio et al, 2009 ; Friederici, 2020 ; Roy et al, 2013 ; Thibault et al, 2021 ).…”

Pragmatic grammar in genus homo

“…Moreover, it is also argued that the late Acheulean techniques (< 800k years ago) imply hierarchical steps and nested part-whole structures (Stout, 2011;Stout et al, 2008). More recently it has been argued, however, that action grammar is sequential in nature and shows weak compositionality (Coopmans et al, 2023).…”

Evolutionary Tinkering Enriches the Hierarchical and Nested Structures in Amino Acid Sequences

“…Shannon entropy has found extensive applications in biology and biochemistry, such as identifying genetic motifs [7], analyzing the evolution of genes [8], and describing the complexity of chemical molecules [9]. Nevertheless, this type of approach overlooks the internal hierarchical and nested relationships in a sequence that are found to be very important at the protein domain level [2,10,11] or even in language [12].…”