Abstract
Language relies on a division of labor between stored units and structure building operations which combine the stored units into larger structures. This division of labor leads to a tradeoff: more structure-building means less need to store while more storage means less need to compute structure. We develop a hierarchical Bayesian model called fragment grammar to explore the optimum balance between structure-building and reuse. The model is developed in the context of stochastic functional programming (SFP), and in particular, using a probabilistic variant of Lisp known as the Church programming language. We show how to formalize several probabilistic models of language structure using Church, and how fragment grammar generalizes one of them---adaptor grammars. We conclude with experimental data with adults and preliminary evaluations of the model on natural language corpus data.
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