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Quantifiers satisfying semantic universals have shorter minimal description length.

Iris van de Pol1, Paul Lodder1, Leendert van Maanen2

  • 1Institute for Logic, Language and Computation, University of Amsterdam, the Netherlands.

Cognition
|December 23, 2022
PubMed
Summary

Semantic universals in quantifiers, like monotonicity, may stem from their simplicity. This study found that quantifiers with these universal properties have shorter minimal description lengths, suggesting simplicity explains their prevalence.

Keywords:
ComplexityGeneralized quantifiersLogical grammarMinimal description lengthSemantic universals

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Area of Science:

  • Linguistics
  • Computational Linguistics
  • Cognitive Science

Background:

  • Natural languages exhibit universal properties despite significant variation.
  • Semantic universals, such as monotonicity, quantity, and conservativity in quantifiers, are hypothesized but require explanation.
  • Investigating the role of complexity in explaining these semantic universals is crucial for understanding language structure.

Purpose of the Study:

  • To determine if differences in complexity explain semantic universals in quantifiers.
  • To analyze the complexity of individual quantifiers and large quantifier sets.
  • To correlate quantifier properties with measures of complexity.

Main Methods:

  • Minimal pair methodology to compare individual quantifier complexities using approximate Kolmogorov complexity.
  • Generation of a large quantifier collection using a simple grammar.
  • Aggregate complexity analysis using minimal description length and approximate Kolmogorov complexity.

Main Results:

  • Quantifiers satisfying semantic universals exhibit simpler meanings, indicated by shorter minimal description lengths.
  • Monotone quantifiers demonstrate lower approximate Kolmogorov complexity compared to non-monotone quantifiers.
  • Approximate Kolmogorov complexity did not robustly scale for quantity and conservativity properties.

Conclusions:

  • The simplicity of quantifier meanings, particularly their minimal description length, offers a partial explanation for semantic universals.
  • Complexity, specifically minimal description length, is a significant factor in the prevalence of certain linguistic universals.
  • Further research is needed to robustly explain quantity and conservativity universals through complexity measures.