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What are currently used computational models/frameworks of language acquisition?

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Computational models of early learning in children on CogSci.SE

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I'll break up my response into categories.

Literature Reviews / Surveys: An OK survey of various models in psycholinguistics, cognitive science, and computer science is "Computational Models of Language Acquisition" by Shuly Wintner. Cambridge has a good paper on the Categorial Grammar Learner (CGL) model, which is "Computational models for first language acquisition" by Paula J. Buttery.

They build on previous models (such as the Triggering Learning Algorithm of Gibson and Wexler and the Structural Triggers Learner of Fodor and Sakas) and improve CGL.

Books: A decent book, always "Computational Models of Language Acquisition", has been written on the subject by Wintner which covers several accepted models, and a recent similar book (same title as the other one) has been published on the topic by Charles Yang (but I have never read the most recent work, so I cannot vet for its quality, but it appears to be good).

A Google search for 'computational models of language acquisition' will reveal many more results, but these are some that I've found helpful.

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