Fawcett (2010: 254):
In the Cardiff Grammar the realisation operation that generates this relationship is "Expound an element by an item". Its notation is simply:h < mountain.Surprisingly, the equivalent operation in the Sydney Grammar is termed "Lexify". It is surprising because the traditional distinction between "grammatical" and "lexical" items has always been reflected in Halliday's work (e.g., what he does and does not cover in his system networks) so that it is odd to find the term "lexify" being used as the name of the operation that inserts all types of items, irrespective of where they come on the continuum from the most "lexical" to the most "grammatical". But the example in Halliday 1993:4505) shows that it really is intended to generate grammatical as well as lexical items.
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Surprisingly, this is misleading because, surprisingly, it is untrue, since, surprisingly, 'lexify' is not the SFL equivalent of Fawcett's 'expound an element by an item'.
In SFL Theory, unlike the Cardiff Grammar, the elements of a structure at group rank are realised by the units of a syntagm at word rank, and there is no realisation statement for such a relation, since it is the formal constituents of groups, (grammatical) words, that are assigned structural functions at group rank. Halliday & Matthiessen (2014: 364):
In the Cardiff Grammar, on the other hand, an element of group structure is expounded (realised) by an item, which as previously observed, is a confusion of lexical item, grammatical word, and its graphological/phonological expression, surprisingly.
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