transformation rule an axiom-schema or rule of inference. A transformation rule is thus a rule for transforming a (possibly empty) set of wellformed formulas into a formula, where that rule operates only upon syntactic information. It was this conception of an axiom-schema and rule of inference that was one of the keys to creating a genuinely rigorous science of deductive reasoning. In the 1950s, the idea was imported into linguistics, giving rise to the notion of a transformational rule. Such a rule transforms tree structures into tree structures, taking one from the deep structure of a sentence, which determines its semantic interpretation, to the surface structure of that sentence, which determines its phonetic interpretation. See also GRAMMAR , LOGISTIC SYSTE. G.F.S.