Final answer:
The system that converts deep structure to surface structure in a language is called transformational grammar, part of Noam Chomsky's generative grammar theory. It involves transforming an abstract syntactical representation into the actual form used in spoken and written language.
Step-by-step explanation:
The system for converting a deep structure into a surface structure in a language is called transformational grammar. This concept is a part of the theory of generative grammar, primarily developed by Noam Chomsky. In this framework, the deep structure represents the abstract syntactical relationships of a sentence, which are then transformed into the surface structure, the actual spoken or written output we recognize in everyday communication. These transformations include various grammatical processes such as moving constituents, adding or deleting elements, and changing the form of words to produce sentences that conform to the rules of syntax in a given language.