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Open AccessArticle

Criticality in Pareto Optimal Grammars?

by 1,* and 2,3,4,*
1
Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus UIB, 07122 Palma de Mallorca, Spain
2
ICREA-Complex Systems Lab, Universitat Pompeu Fabra (GRIB), Dr Aiguader 80, 08003 Barcelona, Spain
3
Institut de Biologia Evolutiva, CSIC-UPF, Pg Maritim de la Barceloneta 37, 08003 Barcelona, Spain
4
Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
*
Authors to whom correspondence should be addressed.
Entropy 2020, 22(2), 165; https://doi.org/10.3390/e22020165
Received: 31 December 2019 / Revised: 26 January 2020 / Accepted: 27 January 2020 / Published: 31 January 2020
(This article belongs to the Special Issue Information Theory and Language)
What are relevant levels of description when investigating human language? How are these levels connected to each other? Does one description yield smoothly into the next one such that different models lie naturally along a hierarchy containing each other? Or, instead, are there sharp transitions between one description and the next, such that to gain a little bit accuracy it is necessary to change our framework radically? Do different levels describe the same linguistic aspects with increasing (or decreasing) accuracy? Historically, answers to these questions were guided by intuition and resulted in subfields of study, from phonetics to syntax and semantics. Need for research at each level is acknowledged, but seldom are these different aspects brought together (with notable exceptions). Here, we propose a methodology to inspect empirical corpora systematically, and to extract from them, blindly, relevant phenomenological scales and interactions between them. Our methodology is rigorously grounded in information theory, multi-objective optimization, and statistical physics. Salient levels of linguistic description are readily interpretable in terms of energies, entropies, phase transitions, or criticality. Our results suggest a critical point in the description of human language, indicating that several complementary models are simultaneously necessary (and unavoidable) to describe it. View Full-Text
Keywords: syntax; Pareto-optimality; bottleneck method; phase transitions; statistical mechanics syntax; Pareto-optimality; bottleneck method; phase transitions; statistical mechanics
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MDPI and ACS Style

Seoane, L.F; Solé, R. Criticality in Pareto Optimal Grammars? Entropy 2020, 22, 165. https://doi.org/10.3390/e22020165

AMA Style

Seoane LF, Solé R. Criticality in Pareto Optimal Grammars? Entropy. 2020; 22(2):165. https://doi.org/10.3390/e22020165

Chicago/Turabian Style

Seoane, Luís F; Solé, Ricard. 2020. "Criticality in Pareto Optimal Grammars?" Entropy 22, no. 2: 165. https://doi.org/10.3390/e22020165

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