Halliday & Matthiessen (1999: 26):
Thus when we move from the lexicogrammar into the semantics, as we are doing here, we are not simply relabelling everything in a new terminological guise. We shall stress the fundamental relationship between (say) clause complex in the grammar and sequence in the semantics, precisely because the two originate as one: a theory of the logical relationships between processes.
Halliday & Matthiessen (1999: 604)
But in modelling the semantic system we face a choice: namely, how far “above” the grammar we should try to push it. Since the decision has to be made with reference to the grammar, this is equivalent to asking how abstract the theoretical constructs are going to be. We have chosen to locate ourselves at a low point on the scale of abstraction, keeping the semantics and the grammar always within hailing distance. There were various reasons for this. First, we wanted to show the grammar at work in construing experience; since we are proposing this as an alternative to cognitive theories, with an “ideation base” rather than a “knowledge base”, we need to posit categories such that their construal in the lexicogrammar is explicit. Secondly, we wanted to present the grammar as “natural”, not arbitrary; this is an essential aspect of the evolution of language from a primary semiotic such as that of human infants. Thirdly, we wanted to explain the vast expansion of the meaning potential that takes place through grammatical metaphor; this depends on the initial congruence between grammatical and semantic categories.
But in any case, it is not really possible to produce a more abstract model of semantics until the less abstract model has been developed first. One has to be able to renew connection with the grammar.