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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“It is by a mathematical point only that we are wise, as the sailor or the fugitive slave keeps the polestar in his eye; but that is sufficient guidance for all our life. We may not arrive at our port within a calculable period, but we would preserve the true course.”
—Henry David Thoreau (1817–1862)