The computational nature of language learning and evolution

Abstract

Computational and mathematical studies of language acquisition (learnability theory) has focused on the idealized interaction between parent and child in a homogeneous linguistic setting. One assumes there is a target grammar (parent) and one asks whether the learning algorithm (child) will acquire it in the limit.

In reality, however, the linguistic community is heterogeneous, there is no target grammar, and since learning lifetimes are finite, there is no limit. To make contact with this reality, models of language acquisition will need to be situated in a population setting where the natural variability of linguistic populations may be characterized. This new setting allows one to seamlessly consider learning by individuals over developmental time and evolution by populations over generational time. By considering an ensemble of language learners, one can derive various dynamical systems that show how the population might evolve under those assumptions. We will consider several such dynamical systems and see how they might shed light on questions such as dialect formation, language evolution, convergence on shared languages and so on. Along the way, the mathematical framework will be elaborated and connections to other disciplines will be emphasized.