In mathematical logic, formation rules are rules for describing well-formed words over the alphabet of a formal language. These rules only address the location and manipulation of the strings of the language. It does not describe anything else about a language, such as its semantics (i.e. what the strings mean). (See also formal grammar).
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Formation rule in the context of Transformational grammar
In linguistics, transformational grammar (TG) or transformational-generative grammar (TGG) was the earliest model of grammar proposed within the research tradition of generative grammar. Like current generative theories, it treated grammar as a system of formal rules that generate all and only grammatical sentences of a given language. What was distinctive about transformational grammar was that it posited transformation rules that mapped a sentence's deep structure to its pronounced form. For example, in many variants of transformational grammar, the English active voice sentence "Emma saw Daisy" and its passive counterpart "Daisy was seen by Emma" share a common deep structure generated by phrase structure rules, differing only in that the latter's structure is modified by a passivization transformation rule.
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