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We present a new algorithm to model and investigate the learning process of alearner mastering a set of grammatical rules from an inconsistent source. Thecompelling interest of human language acquisition is that the learning succeedsin virtually every case, despite the fact that the input data are formallyinadequate to explain the success of learning. Our model explains how a learnercan successfully learn from or even surpass its imperfect source withoutpossessing any additional biases or constraints about the types of patternsthat exist in the language. We use the data collected by Singleton and Newport(2004) on the performance of a 7-year boy Simon, who mastered the American SignLanguage (ASL) by learning it from his parents, both of whom were imperfectspeakers of ASL. We show that the algorithm possesses a frequency-boostingproperty, whereby the frequency of the most common form of the source isincreased by the learner. We also explain several key features of Simon's ASL.

When Learners Surpass their Sources: Mathematical Modeling of Learning from an Inconsistent Source