Bayesian validation of grammar productions for the language of thought

Probabilistic proposals of Language of Thoughts (LoTs) can explain learning across differ- ent 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 b...

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Autores principales: Romano, Sergio, Salles, Alejo, Amalric, Marie, Deahene, Stanislas, Sigman, Mariano, Figueira, Santiago
Formato: Documento de trabajo publishedVersion
Lenguaje:Inglés
Publicado: 2018
Materias:
Gramática
Lenguaje
Teoría de la información
Simetría
Aprendizaje
Lenguajes de programación
Sintaxis
Grammar
Language
Information theory
Symmetry
Learning
Programming languages
Syntax
Acceso en línea:https://doi.org/10.1371/journal.pone.0200420
https://repositorio.utdt.edu/handle/20.500.13098/11219
Aporte de:
Repositorio Digital Universidad Torcuato Di Tella de Universidad Torcuato Di Tella
id I57-R16320.500.13098-11219
record_format dspace
institution Universidad Torcuato Di Tella
institution_str I-57
repository_str R-163
collection Repositorio Digital Universidad Torcuato Di Tella
language Inglés
orig_language_str_mv eng
topic Gramática
Lenguaje
Teoría de la información
Simetría
Aprendizaje
Lenguajes de programación
Sintaxis
Grammar
Language
Information theory
Symmetry
Learning
Programming languages
Syntax
spellingShingle Gramática
Lenguaje
Teoría de la información
Simetría
Aprendizaje
Lenguajes de programación
Sintaxis
Grammar
Language
Information theory
Symmetry
Learning
Programming languages
Syntax
Romano, Sergio
Salles, Alejo
Amalric, Marie
Deahene, Stanislas
Sigman, Mariano
Figueira, Santiago
Bayesian validation of grammar productions for the language of thought
description Probabilistic proposals of Language of Thoughts (LoTs) can explain learning across differ- ent 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 cho- sen 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 uni- versal languages described by Levin’s Coding Theorem.
format Documento de trabajo
publishedVersion
author Romano, Sergio
Salles, Alejo
Amalric, Marie
Deahene, Stanislas
Sigman, Mariano
Figueira, Santiago
author_facet Romano, Sergio
Salles, Alejo
Amalric, Marie
Deahene, Stanislas
Sigman, Mariano
Figueira, Santiago
author_sort Romano, Sergio
title Bayesian validation of grammar productions for the language of thought
title_short Bayesian validation of grammar productions for the language of thought
title_full Bayesian validation of grammar productions for the language of thought
title_fullStr Bayesian validation of grammar productions for the language of thought
title_full_unstemmed Bayesian validation of grammar productions for the language of thought
title_sort bayesian validation of grammar productions for the language of thought
publishDate 2018
url https://doi.org/10.1371/journal.pone.0200420
https://repositorio.utdt.edu/handle/20.500.13098/11219
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