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We introduce a computational framework for modeling child language production, focusing on the acquisition of the competence to map meaning onto linguistic form. Our approach uses graphs to formalize meaning and Synchronous Hyperedge Replacement Grammar (SHRG) to formalize the syntax–semantics interface.The setup provides computationally-sound induction algorithms of statistical grammar knowledge. We induce SHRGs solely from semantic graphs, and the resulting interpretable grammars are evaluated by their ability to generate utterances—providing a novel controlled paradigm to simulate child language acquisition.A notable finding is that unsupervised statistical learning (analogous to children’s implicit learning mechanisms) performs as well as the corresponding supervised oracle when a proper symbolic grammar is assumed (reflecting knowledge gained via comprehension).