Language Learning Problems in the Principles and Parameters Framework
This chapter considers a learning problem in which the hypothesis class is a class of parameterized grammars. After a brief introduction to the “principles and parameters” framework of modern linguistic theory, we consider a specific learning problem previously analyzed in a seminal work by Gibson and Wexler (1994). With our informational-complexity point of view developed in this book, we reanalyze their learning problem. This puts particular emphasis on the sample complexity of learning, in contrast to previous research in the inductive inference, or Gold frameworks (see Osherson and Weinstein, 1986). We show how to formally characterize this problem in particular, and a class of learning problems in finite parameter spaces in general, as a Markov structure. Important new language learning results follow directly: we explicitly compute sample complexity bounds under different distributional assumptions, learning regimes, and grammatical parameterizations. Briefly, we may view this as a precise way to model the “poverty of stimulus” children face in language acquisition. Our reanalysis alters several conclusions made by Gibson and Wexler. We therefore consider this chapter as a useful application of learning-theoretic notions to natural languages, and their acquisition. Finally, we describe several directions for further research.