generative grammar

In theoretical linguistics, generative grammar refers to a proof-theoretic framework for the study of syntax partially inspired by formal grammar theory and popularized by Noam Chomsky, and more specifically to particular instantiations of this general framework, that is, grammatical frameworks adopting as a core assumption that the domain of a grammatical theory is to predict the precise set of sentences which would be considered "grammatical" in a given natural language while simultaneously predicting any other sentence's grammatical failings (and as such are able to "generate" the languages's grammar).
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