Validation of a probabilistic model of language acquisition in children
Kenneth Jerold Straus · 2008
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.