David Rose replied to Robert Spence's analysis of two lexically dense relational clauses on the sys-func and sysfling lists on 4 April 2017 at 13:09:
… I am also intrigued by the roles of interpreting lexical items in the grammatical analysis. For example, the first clause is interpreted as receptive circumstantial identifying, subclassified as Cause:purpose, from synonymy of ‘purpose’ with the lexical item ‘aim’ and the embedded clause ‘to (do)’ …
The primary clauses are attributive, in which each 'experimental method’ is classified as 'an isothermal process’ or 'an isochoric process’. That seems to be the function of the non-specific Deictic “an”, to indicate a class of items. …
What’s particularly intriguing to me is the extent of assumptions of lexical meanings and lexical relations in grammatical analysis. This is most apparent in Halliday’s discussion of relational processes in IFG, which I found baffling until I started recognising the lexical assumptions implicit in his categories. Has anyone else experienced this?
 These false claims proceed from a misunderstanding of the theoretical dimension of delicacy (but see also point  below). The subtypes of process are located intermediate between the most general systems and the most delicate systems that specify individual lexical items.
 This misunderstands the reasoning behind the grammatical analysis of the clause (shown here). The clause construes a relation of identity between an embedded clause complex of cause: purpose (to investigate the properties of air…) and a nominal group of cause: purpose (the aim of this experiment); see Halliday & Matthiessen (2014: 500ff) on 'nouns of expansion'.
 The two 'primary' clauses are embedded and identifying, not attributive (as detailed here). Each identifies (encodes) one experimental method. The nominal groups with the non-specific Deictic an function as Identifier Token, not Attribute.