Bayesian validation of grammar productions for the language of thought
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 bui...
Guardado en:
| Publicado: |
2018
|
|---|---|
| Materias: | |
| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_19326203_v13_n7_p_Romano http://hdl.handle.net/20.500.12110/paper_19326203_v13_n7_p_Romano |
| Aporte de: |
| id |
paper:paper_19326203_v13_n7_p_Romano |
|---|---|
| record_format |
dspace |
| spelling |
paper:paper_19326203_v13_n7_p_Romano2023-06-08T16:30:49Z Bayesian validation of grammar productions for the language of thought 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 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. 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_19326203_v13_n7_p_Romano http://hdl.handle.net/20.500.12110/paper_19326203_v13_n7_p_Romano |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
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 |
| spellingShingle |
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 Bayesian validation of grammar productions for the language of thought |
| topic_facet |
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 |
| description |
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. |
| 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://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_19326203_v13_n7_p_Romano http://hdl.handle.net/20.500.12110/paper_19326203_v13_n7_p_Romano |
| _version_ |
1768542759910637568 |