Halliday & Matthiessen (2014: 611, 612):
As we have seen, elaborating, extending and enhancing conjunctions mark relations between semantic domains, i.e. between text segments. These text segments are simultaneously ideational and interpersonal; they construe experience as meaning, e.g. an episode in a narrative or a recount, and they enact roles and relations, e.g. an exchange in a conversation or consultation, or an argument in an exposition. Relations link text segments either in their ideational guise or in their interpersonal guise: they relate either chunks of experience or chunks of interaction. …
Relations between representations of segments of experience are called external relations, and conjunctions marking such relations are called external conjunctions. … Relations linking text segments in their interpersonal guise are called internal relations – internal to the text as a speech event, and conjunctions marking such relations are called internal conjunctions. …
The distinction between external and internal relations was introduced by Halliday & Hasan (1976: Chapter 5) and developed by Martin (e.g. 1992: Chapter 4) in his account of conjunction as a semantic system.
Blogger Comments:
To be clear, Martin (1992) misunderstands Halliday & Hasan's conjunction (evidence here), and the distinction between internal and external relations (evidence here), and rebrands their grammatical system as his discourse semantic system. Relabelling misunderstandings of original work is not developing a theory.