Martin (1992: 331):
All the discourse structures introduced to this point have been covariate ones, with the exception of the multivariate interpretation of the exchange introduced in Chapter 2. But even there the multivariate approach presented only a partial picture; covariate tracking and challenging structures had to be developed to fill out the picture. Lexical relations are also covariate structures — message parts depend semantically on each other, and depending message parts are themselves depended on.
[1] In SFL theory, units have internal structure. In discourse semantics, on the other hand, the units participant, message and message part form structures. This inconsistency is necessary because, as previously explained, these discourse semantic structures are not actually structures. The discourse semantic unit move, on the other hand — inconsistent with the other discourse semantic units — is presented as a unit with internal structure and one which realises elements of structure at a higher rank, exchange. See previous post here.
[2] The multivariate interpretation of the exchange confused multivariate structures (of a rank) with constituency (rank hierarchy). See previous post here.
[3] In SFL theory, dependency is a relation of the logical metafunction. In this chapter on experiential meaning, it is applied to lexical cohesion (textual metafunction), modality (interpersonal metafunction), and only some logico-semantic relations — extension and enhancement, but not elaboration or projection.
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