Restrictiveness and Phonological Grammar and Lexicon Learning

1 Introduction A central problem of language learnability is the learning of restrictive grammars, grammars that generate all the observed forms but as few others as possible. Given only positive evidence, there are many grammars consistent with the observed data, and the learner must select the most restrictive grammar among these. If the learner mistakenly adopts a broader grammar, no positive evidence will contradict this decision since the broader grammar is consistent with all the positive evidence plus additional data. This is known as the subset problem a well-known solution to the restrictiveness problem is a ranking bias, a preference for a particular relative ranking between certain constraint types. Ranking biases have been successfully implemented in algorithms that focus on the learning of a language-particular ranking given the correct underlying forms point out, however, when the full problem of learning rankings and underlying forms is considered, ranking biases are not sufficient to identify restrictive combinations of grammars and lexicons due to the interdependence of grammar and lexicon learning. This paper presents an alternative solution to the restrictiveness problem: Maximum Likelihood Learning of Lexicons and Grammars (MLG; Jarosz 2006). MLG subsumes the effects of ranking biases and naturally extends to the full phonological learning problem, identifying restrictive grammar and lexicon combinations. Rather than using ranking biases to define the relative restrictiveness of multiple analyses of the same data, MLG relies on the likelihood, or probability, that each grammar and lexicon combination assigns to the data. The likelihood provides an explicit measure of how well the grammar and lexicon explain the data, an objective function that may be maximized using a well-known statistical learning algorithm. The paper is organized as follows. Section 2 briefly overviews the use of ranking biases in OT learning. Section 3 introduces MLG, discusses its ability to identity restrictive grammar and lexicon combinations, and explains how the principles of MLG are implemented in the simulations presented in this paper. Section 4 discusses a series of simulations illustrating MLG's capacity to learn restrictive grammar and lexicon combinations. In Section 4.1, simulations illustrate MLG's capacity to derive the effects of the three ranking biases. Sections 4.2 and 4.3 discuss a system with grammar-lexicon interaction for which