Mathematical Representation
Returning to the more general mathematical notion of a grammar, an important feature of all transformational grammars is that they are more powerful than context-free grammars. This idea was formalized by Chomsky in the Chomsky hierarchy. Chomsky argued that it is impossible to describe the structure of natural languages using context-free grammars. His general position regarding the non-context-freeness of natural language has held up since then, although his specific examples regarding the inadequacy of CFGs in terms of their weak generative capacity were later disproven.
Read more about this topic: Transformational Grammar
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“The circumstances of human society are too complicated to be submitted to the rigour of mathematical calculation.”
—Marquis De Custine (1790–1857)