The point of departure of this paper is the hypothesis that there is a general format common to all representations in the human cognitive system. There is evidence from cognitive psychology that this might be frames in the sense of Barsalou's. The aim of the paper is an exploration of the consequences of this assumption for natural language. Does natural language provide evidence in favor of Barsalou frames being the general format of representations in human cognition? The paper discusses two levels of representation of linguistic gestures: syntactic structure and meaning. The first part deals with syntactic structure and compositional meaning. It is argued that specific universal uniqueness constraints on the syntactic and semantic structure of complex linguistic gestures provide positive evidence for the assumption. The second part investigates lexical semantics, in particular the emergence of abstract attribute vocabulary. Observations in this field, too, corroborate the hypothesis.