Complexity and learnability in the explanation of semantic universals of quantifiers

Despite wide variation among natural languages, there are linguistic properties universal to all (or nearly all) languages. An important challenge is to explain why these linguistic universals hold. One explanation employs a learnability argument: semantic universals hold because expressions that satisfy them are easier to learn than those that do not. In an exploratory study we investigate the relation between learnability and complexity and whether the presence of semantic universals for quantifiers can also be explained by differences in complexity. We develop a novel application of (approximate) Kolmogorov complexity to measure fine-grained distinctions in complexity between different quantifiers. Our results indicate that the monotonicity universal can be explained by complexity while the conservativity universal cannot. For quantity we did not find a robust result. We also found that learnability and complexity pattern together in the monotonicity and conservativity cases that we consider, while that pattern is less robust in the quantity cases.