The Complexity of Ranking Hypotheses in Optimality Theory

Given a constraint set with k constraints in the framework of Optimality Theory (OT), what is its capacity as a classification scheme for linguistic data? One useful measure of this capacity is the size of the largest data set of which each subset is consistent with a different grammar hypothesis. This measure is known as the Vapnik-Chervonenkis dimension (VCD) and is a standard complexity measure for concept classes in computational learnability theory. In this work, I use the three-valued logic of Elementary Ranking Conditions to show that the VCD of Optimality Theory with k constraints is k-1. Analysis of OT in terms of the VCD establishes that the complexity of OT is a well-behaved function of k and that the ‘hardness’ of learning in OT is linear in k for a variety of frameworks that employ probabilistic definitions of learnability.

The neural basis of cognitive development: A constructivist manifesto

How do minds emerge from developing brains? According to “neural constructivism,” the representational features of cortex are built from the dynamic interaction between neural growth mechanisms and environmentally derived neural activity. Contrary to popular selectionist models that emphasize regressive mechanisms, the neurobiological evidence suggests that this growth is a progressive increase in the representational properties of cortex. The interaction between the environment and neural growth results in a flexible type of learning: “constructive learning” minimizes the need for prespecification in accordance with recent neurobiological evidence that the developing cerebral cortex is largely free of domain-specific structure. Instead, the representational properties of cortex are built by the nature of the problem domain confronting it. This uniquely powerful and general learning strategy undermines the central assumption of classical learnability theory, that the learning properties of a system can be deduced from a fixed computational architecture. Neural constructivism suggests that the evolutionary emergence of neocortex in mammals is a progression toward more flexible representational structures, in contrast to the popular view of cortical evolution as an increase in innate, specialized circuits. Human cortical postnatal development is also more extensive and protracted than generally supposed, suggesting that cortex has evolved so as to maximize the capacity of environmental structure to shape its structure and function through constructive learning.

The learnability of the alphabetic principle: Children's initial hypotheses about how print represents spoken language

ABSTRACTThis research examines the hypotheses about how print represents the speech that preliterate children select when they receive input compatible with several such hypotheses. In Experiment 1, preschoolers were taught to readhatandhatsandbookandbooks. Then, in generalization tests, they were probed for what they had learned about the letters. All of the children were able to transfer to other plurals (e.g., to decide thatbikessaid “bikes” rather than “bike,” and thatdogsaid “dog” and not “dogs”), but only those who knew the sound of the letter s prior to the experiment were able to decide, for example, thatbussaid “bus” and not “bug.” The failure to detect the phonemic value of s on the part of alphabetically naive children was replicated in Experiments 2, 3, and 4, which instituted a variety of controls. In Experiment 5, it was found that, although preschoolers who had been taught to read pairs of words distinguished by the comparative affixer(such assmall/smaller) were able to generalize to other comparatives (e.g.,mean/meaner), they could not generalize to pairs whereerhad no morphemic value (e.g.,corn/corner). A similar failure by alphabetically naive children to detect the syllabic, as compared with the morphemic, status of the superlative affixestwas found in Experiment 6. Overall, the results indicate that most preliterate children fail to select phonologically based hypotheses, even when these are available in the input. Instead, they focus on morphophonology and/or semantic aspects of words' referents. The research is couched in terms of the Learnability Theory (LT) (Gold, 1967), which provides a convenient framework for considering a series of interrelated questions about the acquisition of literacy. In particular, it is argued that if the data available to the child includes the pronunciation of written words, the alphabetic principle may be unlearnable, given the hypothesis selection procedures identified in these experiments.

Learnability and the Acquistion of Extraction in Relative Clauses andWh-Questions

Learnability theory is an investigation of the cognitive principles that determine developmental stages and eventual success in language acquistion. The focus of this study is on the learning principles within learnability theory that account for developmental stages in adult second language acquisition. Three learning principles, cumulative development, continuity, and conservatism, predict a complex sequence of development in the acquisition of relative clauses andwh-questions in English. They predict an early no-prep stage, gradual development through two additional stages of greater embeddedness of the extracted noun, stranded before nonstranded prepositional structures, and the likelihood of resumption at early stages. These predictions are confirmed by data from previous studies and are further investigated in this study by means of elicited production data collected from 35 Japanese learners of English and 17 native speakers of English. The data show the expected stages of development and confirm the relevance of learning principles to a comprehensive theory of learnability in second language acquisition (SLA).