Advisor(s)

Samuel Gutmann

Contributor(s)

John N. Frampton, Mikhail B. Malioutov, Charles D. Yang

Date of Award

2008

Date Accepted

4-2008

Degree Grantor

Northeastern University

Degree Level

Ph.D.

Degree Name

Doctor of Philosophy

Department or Academic Unit

College of Arts and Sciences. Department of Mathematics.

Keywords

language learning, children, native language

Subject Categories

Language awareness in children, Language acquisition--Mathematical models, Children--Knowledge and learning--Mathematical models

Disciplines

Mathematics

Abstract

Charles D. Yang has developed a mathematical model of how a child learns his first language. This model, based on Noam Chomsky's Principles and Parameters theory of Universal Grammar, represents the actual process of a child learning the parameter settings for the grammar of his native language. The process is one of ""natural selection"" wherein the correct settings (for his native language) gradually ""prevail"" and the incorrect ones ""die out"". Mathematically, this is expressed as probabilities associated with each of the possible settings, probabilities which give the likelihood that the child will use a particular parameter setting when he parses (makes grammatical sense of ) the next sentence he encounters or constructs. This dissertation proves that the probabilities for the native language settings all converge to 1, which means that, eventually, the child only uses his native grammar to parse sentences. Put more precisely, for each parameter ?i there is a sequence of random variables {Xn,i }, and, for each n, Xn,i is the probability that the child chooses the native language setting of ?i for parsing the 'next' (the nth ) sentence. We prove that, for each i, {Xn,i } converges to 1, almost surely. Thus, this dissertation lends support to Yang's mathematical model.

Document Type

Dissertation

Rights Holder

Kenneth Jerold Straus


View Full Text

Click button above to open, or right-click to save.

Included in

Mathematics Commons

Share

COinS