Misunderstanding The Function Of The Structure Marker 'Of'

Martin & Doran (2023: 16-7):

A representative description from Halliday with Matthiessen (2014) is provided as Figure 1 below.¹ Note that neither the experiential nor logical tier of analysis provides a specific function label for of.

¹ The experiential label Qualifier on the logical tier, where a Post-Modifier function might be expected, is surprising, as is the absence of a post- α β function below (for of the hills); however, these labelling issues are not directly relevant to the paper and so will be set aside here.

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[1] To be clear, the reason why no function label for of is that does not serve as a functional element in the nominal group. Instead, it marks a relation between nominal groups (the tops and the hills).

[2] Halliday & Matthiessen (2014: 396):

[3] To be clear, the "surprising" use of 'Qualifier' instead of 'Postmodifier' in Halliday & Matthiessen (2014) is simply a typographical error, as a quick glance at the surrounding text makes clear.

[4] To be clear, the Postmodifier is not labelled as a dependent element for reasons explained by Halliday & Matthiessen (2014: 390, 392n):

But the Postmodifier does not itself enter into the logical structure, because it is not construed as a word complex. What the logical analysis does is to bring out the hypotactic basis of premodification in the nominal group…

In the first two editions of IFG, the Postmodifier also was brought into the scope of the logical representation. But this appears to complicate the description without adding further to its explanatory power.