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Abstract:

Probabilistic proposals of Language of Thoughts (LoTs) can explain learning across different domains as statistical inference over a compositionally structured hypothesis space. While frameworks may differ on how a LoT may be implemented computationally, they all share the property that they are built from a set of atomic symbols and rules by which these symbols can be combined. In this work we propose an extra validation step for the set of atomic productions defined by the experimenter. It starts by expanding the defined LoT grammar for the cognitive domain with a broader set of arbitrary productions and then uses Bayesian inference to prune the productions from the experimental data. The result allows the researcher to validate that the resulting grammar still matches the intuitive grammar chosen for the domain. We then test this method in the language of geometry, a specific LoT model for geometrical sequence learning. Finally, despite the fact of the geometrical LoT not being a universal (i.e. Turing-complete) language, we show an empirical relation between a sequence’s probability and its complexity consistent with the theoretical relationship for universal languages described by Levin’s Coding Theorem. © 2018 Romano et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Registro:

Documento: Artículo
Título:Bayesian validation of grammar productions for the language of thought
Autor:Romano, S.; Salles, A.; Amalric, M.; Dehaene, S.; Sigman, M.; Figueira, S.
Filiación:Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Computación, Buenos Aires, Argentina
CONICET-Universidad de Buenos Aires, Instituto de Investigación en Ciencias de la Computación (ICC), Buenos Aires, Argentina
CONICET-Universidad de Buenos Aires, Instituto de Cálculo (IC), Buenos Aires, Argentina
Cognitive Neuroimaging Unit, CEA DSV/I2BM, INSERM, Université Paris-Sud, Université Paris-Saclay, NeuroSpin center, Gif/Yvette, 91191, France
CONICET-Universidad Torcuato Di Tella., Laboratorio de Neurociencia, Buenos Aires, C1428BIJ, Argentina
Palabras clave:article; geometry; grammar; human; human experiment; language; probability; scientist; sequence learning; theoretical study; thinking; validation process; Bayes theorem; cognition; linguistics; probability learning; theoretical model; Bayes Theorem; Cognition; Humans; Linguistics; Models, Theoretical; Probability Learning; Thinking
Año:2018
Volumen:13
Número:7
DOI: http://dx.doi.org/10.1371/journal.pone.0200420
Título revista:PLoS ONE
Título revista abreviado:PLoS ONE
ISSN:19326203
CODEN:POLNC
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_19326203_v13_n7_p_Romano

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Citas:

---------- APA ----------
Romano, S., Salles, A., Amalric, M., Dehaene, S., Sigman, M. & Figueira, S. (2018) . Bayesian validation of grammar productions for the language of thought. PLoS ONE, 13(7).
http://dx.doi.org/10.1371/journal.pone.0200420
---------- CHICAGO ----------
Romano, S., Salles, A., Amalric, M., Dehaene, S., Sigman, M., Figueira, S. "Bayesian validation of grammar productions for the language of thought" . PLoS ONE 13, no. 7 (2018).
http://dx.doi.org/10.1371/journal.pone.0200420
---------- MLA ----------
Romano, S., Salles, A., Amalric, M., Dehaene, S., Sigman, M., Figueira, S. "Bayesian validation of grammar productions for the language of thought" . PLoS ONE, vol. 13, no. 7, 2018.
http://dx.doi.org/10.1371/journal.pone.0200420
---------- VANCOUVER ----------
Romano, S., Salles, A., Amalric, M., Dehaene, S., Sigman, M., Figueira, S. Bayesian validation of grammar productions for the language of thought. PLoS ONE. 2018;13(7).
http://dx.doi.org/10.1371/journal.pone.0200420