In a complete analysis of a sentence, all lexically substantial items have a discourse function role (topic, focus, background, etc.) based on the utterance context. Since the discourse function constituents does not always overlap with the f-structure constituency, information should be projected from the c-structure into a distinct i(nformation)-structure, which can be accessed by the s(emantic)-structure. This is shown in (16).
(16)
The mapping between i-structure and s-structure serves a dual role. First, it allows the semantics access to discourse function information as needed. Second, the fact that all lexical items with PRED values are assigned a discourse function role can be checked here; that is, any item with a semantic predicate must have a corresponding i-structure role. This effectively ensures completeness of the i-structure.
Consider the mismatches occuring between the f-structure and i-structure. There are phrases which are constituents in f-structure, but not in i-structure. A classic example of this is the English cleft. In English clefts, the clefted material must contain the focus of the cleft, but need not be focused in its entirety (see Jackendoff 1972 for detailed discussion of these and similar examples).
(17)
[Q:] Was it the ex-convict with the red SHIRT that he was warned to look out for?
[A:] No, it was an ex-convict with a red [TIE] 
that he
was warned to look out for. (Jackendoff 1972:232)
In (17) the entire NP `an ex-convict with a red tie' is clefted and forms an f-structure constituent. Only the head noun `tie' of the adjunct modifier of the clefted NP is focused; the remainder of the NP is presupposed and hence background material. As seen by the partial f- and i-structures in (18), there is a mismatch between f- and i-structure constituency. By having distinct projections for these two types of information, such mismatches can be captured by the LFG architecture.
(18) F-structure
I-structure
