Quantifiers satisfying semantic universals have shorter minimal description length.

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.