Partha Niyogi
University of Chicago
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.
Reception to follow in 1413 Marie Mount Hall.