Quantifiers satisfying semantic universals have shorter minimal description length

Iris van de Pol, Paul Lodder, Leendert van Maanen, Shane Steinert-Threlkeld, Jakub Szymanik

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Despite wide variation among natural languages, there are linguistic properties thought to be universal to all or nearly all languages. Here, we consider universals at the semantic level, in the domain of quantifiers, which are given by the properties of monotonicity, quantity, and conservativity, and we investigate whether these universals might be explained by differences in complexity. First, we use a minimal pair methodology and compare the complexities of individual quantifiers using approximate Kolmogorov complexity. Second, we use a simple yet expressive grammar to generate a large collection of quantifiers and we investigate their complexities at an aggregate level in terms of both their minimal description lengths and their approximate Kolmogorov complexities. For minimal description length we find that quantifiers satisfying semantic universals are simpler: they have a shorter minimal description length. For approximate Kolmogorov complexity we find that monotone quantifiers have a lower Kolmogorov complexity than non-monotone quantifiers and for quantity and conservativity we find that approximate Kolmogorov complexity does not scale robustly. These results suggest that the simplicity of quantifier meanings, in terms of their minimal description length, partially explains the presence of semantic universals in the domain of quantifiers.
Original languageEnglish
Article number105150
Pages (from-to)1-29
JournalCognition
Volume232
DOIs
Publication statusPublished - Mar 2023

Bibliographical note

Funding Information:
We thank three anonymous reviewers for their useful feedback. We thank Fausto Carcassi, Nima Motamed, the CoSaQ research group, and the Meaning, Logic, and Cognition seminar at the Institute for Logic, Language and Computation, the Computational Cognitive Science group at the Donders Centre for Cognition, Thomas Icard, Michael Hahn, Steven Piantadosi, and the CoCoLab and CoLaLa research groups at Stanford University and UC Berkeley, respectively, for interesting discussions and useful feedback. Iris van de Pol was supported by Gravitation Grant 024.001.006 of the Language in Interaction Consortium from the Netherlands Organization for Scientific Research. Jakub Szymanik received funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007–2013) / ERC Grant Agreement n. STG 716230 CoSaQ. The computational work was carried out on the Dutch national e-infrastructure with the support of SURF Cooperative.

Funding Information:
We thank three anonymous reviewers for their useful feedback. We thank Fausto Carcassi, Nima Motamed, the CoSaQ research group, and the Meaning, Logic, and Cognition seminar at the Institute for Logic, Language and Computation, the Computational Cognitive Science group at the Donders Centre for Cognition, Thomas Icard, Michael Hahn, Steven Piantadosi, and the CoCoLab and CoLaLa research groups at Stanford University and UC Berkeley, respectively, for interesting discussions and useful feedback. Iris van de Pol was supported by Gravitation Grant 024.001.006 of the Language in Interaction Consortium from the Netherlands Organization for Scientific Research . Jakub Szymanik received funding from the European Research Council under the European Union's Seventh Framework Programme ( FP/2007–2013 ) / ERC Grant Agreement n. STG 716230 CoSaQ . The computational work was carried out on the Dutch national e-infrastructure with the support of SURF Cooperative.

Publisher Copyright:
© 2022 The Author(s)

Keywords

  • Semantic universals
  • Generalized quantifiers
  • Logical grammar
  • Complexity
  • Minimal description length

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