Rhythmic Recursion? Human Sensitivity to a Lindenmayer Grammar with Self-similar Structure in a Musical Task

Geambaşu, Andreea; Toron, Laura; Ravignani, Andrea; Levelt, Clara C.

doi:10.1177/2059204320946615

Cited by 6 publications

(10 citation statements)

References 36 publications

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“…We can now introduce the L-system we will focus on for the rest of this paper. Consider the rules of the so-called Fibonacci grammar (Fib henceforth), which has been the focus of much recent AGL research (e.g., Saddy, 2009;Geambaşu et al, 2016Geambaşu et al, , 2020Phillips, 2017;Vender et al, 2019Vender et al, , 2020, and how they should be read if interpreted as NACs (see ( 4) below for a derivation): 0 → 1 (a tree T with a node labelled 0 is well-formed iff every node labelled 0 immediately dominates a node labelled 1 in T) 1 → 01 (a tree T with a node labelled 1 is well-formed iff every node labelled 1 immediately dominates a node labelled 0 and a node labelled 1 in T)…”

Section: Nacs In (Some) Lindenmayer Systemsmentioning

confidence: 99%

From n-grams to trees in Lindenmayer systems

Krivochen¹

2022

Preprint

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In this paper we present two approaches to Lindenmayer systems (L-systems): the procedural (or ‘generative’) approach, which focuses on L-systems as string rewriting systems, and a declarative (or ‘model-theoretic’) approach, where the grammar is a set of local admissibility conditions: in this paper, these conditions will be defined over graphs. We contend that it is possible, for a subset of L-systems and the languages they generate, to map superficial regularities in the distribution of symbols at the string level to local tree admissibility conditions, effectively providing a way to link string languages and tree languages in a novel manner. We will work out how to construct structure assuming only superficial constraints on expressions, and define a set of constraints that well-formed expressions of specific L-languages must satisfy. A significant result is that L-systems which are distinguished by methods focused on derivational properties turn out to satisfy the same model: this has consequences for the use of L-systems as probes for human sensitivity to hierarchical structure in Artificial Grammar Learning (AGL) protocols.

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Section: Nacs In (Some) Lindenmayer Systemsmentioning

confidence: 99%

From n-grams to trees in Lindenmayer systems

Krivochen¹

2022

Preprint

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“…Structural processing in the Fibonacci grammar has already been explored via the classical AGL paradigm (Geambaşu et al, 2016(Geambaşu et al, , 2020. However, these studies have run into the inherent problem of the habituation/discrimination paradigm, as the non-grammatical test strings used did not allow for conclusions about what was actually learned by the participants.…”

Section: A Left Panel)mentioning

confidence: 99%

“…In the present study, we implemented Fibonacci sequences in an SRT task, thus avoiding the need to create non-grammatical Fib-strings (like in Geambaşu et al, 2016Geambaşu et al, , 2020. In contrast to Vender et al (2019Vender et al ( , 2020, dots were presented in the center of the screen, to avoid the interfering congruency factor introduced by the Simon task.…”

Section: A Left Panel)mentioning

confidence: 99%

Finding hierarchical structure in binary sequences : evidence from Lindenmayer grammar learning

Schmid¹,

Saddy²,

Franck³

2022

Preprint

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In this article, we explore the extraction of recursive nested structure in the processing of binary sequences. Our aim was to determine whether the brain learns the higher order regularities of a highly simplified input where only sequential order information marks the hierarchical structure. To this end, we implemented sequence generated by the Fibonacci grammar in a serial reaction time task. This deterministic grammar generates aperiodic but self-similar sequences. The combination of these two properties allowed us to evaluate hierarchical learning while controlling for the use of low-level strategies like detecting recurring patterns. The deterministic aspect of the grammar allowed us to predict precisely which points in the sequence should be subject to anticipation. Results showed that participants’ pattern of anticipation could not be accounted for by “flat” statistical learning processes and was consistent with them anticipating upcoming points based on hierarchical assumptions. We also found that participants were sensitive to the structure constituency, suggesting that they organized the signal into embedded constituents. We hypothesized that the participants built this structure by merging recursively deterministic transitions.

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“…A number of studies that have explored structural processing in the Fibonacci grammar (Fib henceforth) actually failed to provide clear-cut evidence in favor of hierarchical processing [19][20][21]. [19] presented sequences from the Fib grammar consisting of two sounds.…”

Section: Introductionmentioning

confidence: 99%

“…It is thus possible that this made the discrimination too difficult for the participants. [20] reused the same paradigm but controlled the structure of the foils more carefully. Participants were then able to correctly classify grammatical and ungrammatical strings in the test phase.…”

Section: Introductionmentioning

confidence: 99%

Uncovering hierarchical structure through statistical dependency

Schmid¹,

Saddy²,

Franck³

2023

Preprint

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In this paper, we explore the extraction of recursive nested structure in the processing of self-similar binary sequences generated by two Lindenmayer grammars: the Fibonacci grammar and the Skip grammar. In each of these grammars only sequential order information marks the hierarchical structure. Although closely related, these grammars differ from a formal point of view: the Fibonacci grammar is perfectly scale-free and presents an isomorphism between its surface and derivational properties while the Skip grammar, although also self-similar, does not present this isomorphism. Our goal was to explore the influence of these formal differences on the extraction of hierarchical structure by the participants. To this end, we implemented these grammars in a serial reaction time task. The results show that in both the Fibonacci grammar and the Skip grammar, participants elaborated a hierarchical structure from the signal. This suggests the involvement of at least partially similar mechanisms during processing. However, some processing differences remained that cannot be explained by the hypotheses proposed so far regarding the processing of strings generated by L-systems. We hypothesize that these effects would be due to the self-similarity of the signal which would act as a reinforcement of the structure elaborated by the participants.

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Rhythmic Recursion? Human Sensitivity to a Lindenmayer Grammar with Self-similar Structure in a Musical Task

Cited by 6 publications

References 36 publications

From n-grams to trees in Lindenmayer systems

From n-grams to trees in Lindenmayer systems

Finding hierarchical structure in binary sequences : evidence from Lindenmayer grammar learning

Uncovering hierarchical structure through statistical dependency

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