A Formal Theory of Language Development

This paper presents a formal model of language acquisition that, in addition to meeting the traditional learnability condition, makes time-course predictions about child language development. We view language acquisition as a population of human grammars, made available by UG, compete in a selectionist process. Selection is made possible by the variational properties of individual grammars; specifically, their differential compatibility with the primary linguistic data in the environment. We first present developmental facts that are problematic for both a statistical learning approach and traditional learnability models. We then propose a formal model of acquisition in the variational framework, and derive some convergence results. The model receives empirical support from developmental evidence in child language, including the subject drop phenomenon, that a learner is best modeled as a population of grammars in co-existence and competition, rather than a single grammar supplemented by auxiliary assumptions. 1 Learnability and Development A central issue in linguistics and cognitive science is the problem of language acquisition: How does a human child come to acquire her language with such ease, yet without high computational power or favorable learning conditions? As articulated by Chomsky (1965, 1975), the language faculty of the child’s mind/brain undergoes changes in the course of language acquisition, from an initial state S0, the Universal Grammar (UG), to a relatively stable state SL, that of a competent speaker of the language: (1) S0 → S1 → . . . → SL A theory of language acquisition aims to identify and model the process in (1) with sufficient details and clarity. It is evident that any adequate theory must meet the following empirical conditions: (2) a. Learnability: such a theory must accurately characterize the asymptotic properties of the learner in a particular linguistic environment (Gold 1967), under plausible assumptions about the learner’s computational machinery, the nature of the input data, sample size, and so on. b. Developmental compatibility: the learner modeled in such a theory must exhibit behaviors that are analogous to the actual course of language development (Pinker 1979). In this section of the paper, I present developmental facts that are problematic for both statistical learning (e.g. connectionism) and traditional learnability studies, building motivation for the model developed in the rest of the paper. 1.1 Against statistical learning An empiricist approach to language acquisition has (re)gained popularity in computational linguistics and cognitive science; e.g. (Stolcke 1994; Chen 1995; de Marcken 1996; Bates & Elman 1996; Seidenberg 1997).