Indeed, if Michael Halliday and Christian Matthiessen had formed a clear view of the way in which the choices described in their Construing Experience through Meaning determine the choices in the major system networks of the lexicogrammar, they would surely have said so in that book. I have looked hard for a section that makes this connection, but I have yet to find it. This suggests that the model proposed there is simply one possible, half-complete hypothesis that needs to be subject to the normal process in science of development, testing, evaluation, revision (or rejection), retesting, re-evaluation, and so on.
(1) Here are some of the quotes that Robin Fawcett was unable to find.
Halliday & Matthiessen (1999: 375):
More specifically, inter-stratal realisation is specified by means of inter-stratal preselection: contextual features are realised by preselection within the semantic system, semantic features are realised by preselection within the lexicogrammatical system, and lexicogrammatical features are realised by preselection within the phonological/graphological system.
Halliday & Matthiessen (1999: 378):
The realisational relationship between semantics and lexicogrammar is one of preselection: semantic features … are realised in lexicogrammar by means of prespecification of lexicogrammatical information, most centrally preselection of lexicogrammatical features.
(2) Regarding the notion that strata "determine" one another, note that higher stratal choices do not cause lower stratal choices.
Halliday & Matthiessen (1999: 25):
In any stratal system (i.e. any system where there are two strata such that one is the realisation of the other) there is no temporal or causal ordering between the strata. … the relationship is an intensive one, not a causal circumstantial one.
(3) On realisation as an analogue of cause:effect in classical physics:
Halliday & Matthiessen (1999: 510):
… we do not yet fully understand the nature of the relationship that is the semiotic analogue of the “cause : effect” of classical physics: this is the problem of realisation.
Having had his claim falsified, Fawcett subsequently re-interpreted his original question (extending it) in an attempt to obscure the falsification. This is a subtype of the logical fallacy known as the 'red herring':
The red herring is as much a debate tactic as it is a logical fallacy. It is a fallacy of distraction, and is committed when a listener attempts to divert an arguer from his argument by introducing another topic.