The Logical Structure Of The Verbal Group

Matthiessen (1995: 640-1):

In contrast, in verbal groups, the Head is not the main experiential function, the Event, but rather the Finite, i.e., the function that relates to the now of the communicative exchange — the interpersonal reference point created in the speech interaction. Consequently, expansion within the verbal group of the Head does not start as a construal of the event; rather, it construes a (stepwise) move away from the interpersonal reference point of the Finite to the experiential Event through time and/or modality.

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[1] Again, this misrepresents Halliday's analysis of the logical structure of the verbal group. As previously explained, the logical structure realises the system of TENSE, so the elements of logical structure are realisations of tense, not individual words. The Head is not the Finite, but the realisation of primary tense. Halliday & Matthiessen (2014: 398-9):

However, the structural labelling of the words that make up the verbal group is of limited value, not only because the meaning can be fully represented in terms of grammatical features (of tense, voice, polarity and modality), but also because it is the logical structure that embodies the single most important semantic feature of the English verb, its recursive tense system, and the elements of the logical structure are not the individual words but certain rather more complex elements. …

The logical structure of the verbal group realises the system of tense. … Thus tense in English is a recursive system. The primary tense is that functioning as Head, shown as α. This is the Deictic tense: past, present or future relative to the speech event. The modifying elements, at β and beyond, are secondary tenses; they express past, present or future relative to the time selected in the previous tense. Realisations are shown in Table 6-12.

[2] Again, this misrepresents Halliday's analysis of the logical structure of the verbal group. As previously explained, the Finite and the Event are not elements of logical structure, so the expansion of the verbal group can not be 'a stepwise move from the Finite to the Event'.