Introducing A Few Basic Terms

Martin & Rose (2007: 162):

We can also now introduce a few basic terms for the words that English uses for identifying people and things. Of course words like I, she, it, my, his are pronouns. Words like a and the are known as determiners, since they ‘determine’ whether we can assume an identity or not; ‘a’ is an indefinite determiner, while ‘the’ is a definite determiner. Words like this, that, these, those are known as demonstratives, since they ‘demonstrate’ where to find an identity, ‘near’ with this or ‘far’ with that.

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Halliday & Matthiessen (2014: 75) list the word classes that are assumed by SFL Theory:

see also Halliday & Matthiessen (2014: 365-7).

[1] In SFL Theory, only I, she, it are pronouns; my and his are determiners.

[2] In SFL Theory, a is a non-specific determiner, and serves no referential function, whereas the is a specific determiner of the sub-class demonstrative.

[3] In SFL Theory, this, that, these, those are specific determiners of the sub-class demonstrative.

[4] To be clear, the proximal/distal distinction of deixis marks proximity to speaker, not "where to find an identity" in terms of reference, as demonstrated by the demonstrative reference in:

now tell me, this guy you were talking about…
now tell me, that guy you were talking about… .