Learning categorial grammars

In 1967 E. M. Gold published a paper in which the language classes from the Chomsky-hierarchy were analyzed in terms of learnability, in the technical sense of identification in the limit. His results were mostly negative, and perhaps because of this his work had little impact on linguistics. In the early eighties there was renewed interest in the paradigm, mainly because of work by Angluin and Wright. Around the same time, Arikawa and his co-workers refined the paradigm by applying it to so-called Elementary Formal Systems. By making use of this approach Takeshi Shinohara was able to come up with an impressive result; any class of context-sensitive grammars with a bound on its number of rules is learnable. Some linguistically motivated work on learnability also appeared from this point on, most notably Wexler & Culicover 1980 and Kanazawa 1994. The latter investigates the learnability of various classes of categorial grammar, inspired by work by Buszkowski and Penn, and raises some interesting questions. We follow up on this work by exploring complexity issues relevant to learning these classes, answering an open question from Kanazawa 1994, and applying the same kind of approach to obtain (non)learnable classes of Combinatory Categorial Grammars, Tree Adjoining Grammars, Minimalist grammars, Generalized Quantifiers, and some variants of Lambek Grammars. We also discuss work on learning tree languages and its application to learning Dependency Grammars. Our main conclusions are: - formal learning theory is relevant to linguistics, - identification in the limit is feasible for non-trivial classes, - the `Shinohara approach' -i.e., placing a numerical bound on the complexity of a grammar- can lead to a learnable class, but this completely depends on the specific nature of the formalism and the notion of complexity. We give examples of natural classes of commonly used linguistic formalisms that resist this kind of approach, - learning is hard work. Our results indicate that learning even `simple' classes of languages requires a lot of computational effort, - dealing with structure (derivation-, dependency-) languages instead of string languages offers a useful and promising approach to learnabilty in a linguistic contex

Bilingual Education in the United States: An Analysis of the Convergence of Policy, Theory and Research

Bilingual education policy in the United States public school system has a long-standing social and political history plagued by a forty-year debate about its goals and effectiveness. Policy has been informed by theory aimed at identifying best methods to provide English instruction to English Language Learners (ELLs), and research on bilingual education program effectiveness. However, perceptions about language based on cultural and political values have also played a considerable role, and fuel the national debate. On one side of this debate, critics argue bilingual education hinders ELLs’ ability to assimilate and rapidly acquire the dominant language of the US. Proponents of bilingual education, on the other hand, see it as an enrichment program, benefiting both ELLs and native English speakers cognitively and politically within an increasingly globalized context. This study examines the forces (second language acquisition theory in bilingual education, research on program effectiveness, the history of bilingual education policy-making, and the influence of language ideology) comprising bilingual education, with the outcome being twofold. The first is to dispel common misperceptions perpetuated within the debate about bilingual education by unearthing the multiplicities of it through qualitative reviews of each component lending itself to the phenomenon. Second, to illustrate how policy-making is encompassed by language ideologies as evidenced particularly within bilingual education policy shifts over the past forty-years. The reviews in this study are designed to provide policy-makers and educators with a comprehensive account of bilingual education to improve and inform decision making about its future. The findings of these analyses suggest ideologically founded policy have led to legislation lacking alignment with theory and research demonstrating evidence of bilingual education program effectiveness

Vacillatory learning of nearly minimal size grammars

In Gold’s influential language learning paradigm a learning machine converges in the limit to one correct grammar. In an attempt to generalize Gold’s paradigm, Case considered the question whether people might converge to vacillating between up to (some integer) n> 1 distinct, but equivalent, correct grammars. He showed that larger classes of languages can be algorithmically learned (in the limit) by converging to up to n + 1 rather than up to n correct grammars. He also argued that, for “small ” n> 1, it is plausible that people might sometimes converge to vacillating between up to n grammars. The insistence on small n was motivated by the consideration that, for “large ” n, at least one of n grammars would be too large to fit in peoples ’ heads. Of course, even for Gold’s n = 1 case, the single grammar converged to in the limit may be infeasibly large. An interesting complexity restriction to make, then, on the final grammar(s) converged to in the limit is that they all have small size. In this paper we study some of the tradeoffs in learning power involved in making a well-defined version of this restriction. We show and exploit as a tool the desirable property that the learning power under ou

Literary Joint Attention: Social Cognition and the Puzzles of Modernism

The fundamental claim of this project is that the mechanics of social cognition--how we think intersubjectively and process social information--are highly relevant to the study of literature. Specifically, it presents a theory of literary discourse as the emergent product of a network of joint activities and joint attention. Research on joint attention frequently focuses on contexts in which this aspect of social cognition is not fully developed, such as in early childhood, or for autistic people. The study of literature, on the other hand, is continually engaged with circumstances in which joint attention is relevant, highly developed, and complex. Here, linguistics and cognitive science provide the basis for specific and particularizing claims about literature, while literary texts are used to support broader theoretical work about language and the mind. The focus is on modern literature in English and its reception. Many of these texts exploit systematic egocentric biases in social cognition and communication to produce effective ironies and narrative surprises. Further, both detective fiction and experimental Modernist fiction frequently dramatize problems of joint attention that can be traced to the ultimate relation between author, reader, and text. Extended analysis, with special attention to Edgar Allan Poe's "Murders in the Rue Morgue" and Virginia Woolf's To the Lighthouse, demonstrates the importance of this joint attentional trope. In these texts, the external and perceptible serve not only as triggers for the events of a single consciousness, but as a locus for the potential for intersubjective experience, both inside and outside the text. A case study of the publication and reception history of Marianne Moore's "Poetry," finally, demonstrates the utility of a cognitively realistic approach to textual criticism. These literary activities also serve as an important proving ground for the claims of cognitive science, demonstrating complexities of and constraints on shared viewpoint phenomena