You could start solving this problem by distinguishing lexicogrammatical from discourse semantic functions. The term Deictic denotes a function in a function structure at group rank... +Thing;+Deictic. It is realised at word rank by various classes of items.Halliday starts his definition of Deictic functions of ‘the’ below on LG criteria, as specific, determinativeBut then he switches to DS criteria to distinguish its function more delicately, from the functions of demonstrative and possessive determiners (as discussed with Bea on sysfling 9-10 September).It’s not wrong, but doesn't make the switch explicit. In fact these delicate distinctions couple features from DS identification and LG deixis systems. Here’s parts of both...
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[1] As previously explained, this is misleading, because it is untrue. See:
David Rose Misconstruing Discourse Semantic Systems As More Delicate Grammatical Systems
David Rose Misunderstanding Delicacy And Instantiation
[2] To be clear, as demonstrated here, Martin's (1992) discourse semantic system of identification is a rebranding of Halliday & Hasan's (1976) lexicogrammatical system of reference, which, among other things, confuses cohesive reference with nominal group determination. Rose here repeats that confusion in juxtaposing a reference system with a nominal group determination system as if reference and nominal group determination were the same function.
