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My understanding is that, while natural languages aren't completely context-free, you can get a good approximation of a specification of English in Backus-Naur form, in that if you look at a given sentence, you can usually parse it into a tree described by the context-free grammar the BNF entails. On the other hand, I haven't been able to find any sample specifications for dependency tree grammars. Are there any specifications of dependency grammars for English? To be honest, I'm not sure what such a specification would even look like, but I'm defining it as something, like a BNF, which can be easily used to produce sentences which are (mostly) syntactically correct given a list of word-POS pairs.

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