Convexity and Monotonicity in Language Coordination: Simulating the Emergence of Semantic Universals in Populations of Cognitive Agents

Natural languages vary in their quantity expressions, but the variation seems to be constrained by general properties, so-called universals. Their explanations have been sought among constraints of human cognition, communication, complexity, and pragmatics. In this article, we apply a state-of-the-art language coordination model to the semantic domain of quantities to examine whether two quantity universals—monotonicity and convexity—arise as a result of coordination. Assuming precise number perception by the agents, we evolve communicatively usable quantity terminologies in two separate conditions: a numeric-based condition in which agents communicate about a number of objects and a quotient-based condition in which agents communicate about the proportions. We find out that both universals take off in all conditions but only convexity almost entirely dominates the emergent languages. Additionally, we examine whether the perceptual constraints of the agents can contribute to the further development of universals. We compare the degrees of convexity and monotonicity of languages evolving in populations of agents with precise and approximate number sense. The results suggest that approximate number sense significantly reinforces monotonicity and leads to further enhancement of convexity. Last but not least, we show that the properties of the evolved quantifiers match certain invariance properties from generalized quantifier theory.