The emergence of quantifiers

Human natural languages use quantifiers as ways to designate the number of objects of a set. They include numerals, such as ``three'', or circumscriptions, such as ``a few''. The latter are not only underdetermined but also context dependent. We provide a cultural-evolution explanation for the emergence of such quantifiers, focusing in particular on the role of environmental constraints on strategy choices. Through a series of situated interaction experiments, we show how a community of robotic agents can self-organize a quantification system. Different perceptions of the scene make underdetermined quantifiers useful and environments in which the distribution of objects exhibits some degree of predictability creates favorable conditions for context-dependent quantifiers.