Quantifiers satisfying semantic universals have shorter minimal description length

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.

Keywords: Complexity; Generalized quantifiers; Logical grammar; Minimal description length; Semantic universals.