Martin & Rose (2007: 17):
Conjunction looks at inter-connections between activities — reformulating them, adding to them, sequencing them, explaining them and so on. These are also ideational types of meanings, but of the subtype logical’. Logical meanings are used to form temporal, causal and other kinds of connectivity.
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The system of conjunction (& continuity) — aptly glossed as 'the logic of English Text' — is Martin's (1992) logical system on his stratum of discourse semantics. As demonstrated at considerable length here, it is a confusion of the non-structural system of conjunction (textual metafunction) and the structural system of expansion relations between clauses (logical metafunction).
The most general expansion categories, elaboration, extension and enhancement, do not feature in the model, and instead, more delicate categories are used, but repeatedly misapplied. Because it is an attempted rebranding of Halliday's cohesive conjunction, the logical relation of projection does not figure at all in Martin's logical discourse system.
Martin's model makes much of the distinction of internal vs external conjunction, as a way of differentiating it from Halliday's model — but without understanding the distinction. In SFL, external conjunction is an expansion relation between processes, whereas internal conjunction is a relation between propositions, that is, the relation is 'internal to the speech event'. As Martin's chapter develops, the distinction generally comes to mean the distinction between cohesive conjunction (misconstrued as internal) and the logical expansion of clauses (misconstrued as external), though not consistently.
A serious consequence of creating a model of logical discourse semantics that is inconsistent with the model of logical grammar is that ideational metaphor can no longer be systematically (or coherently!) explored, since there is no longer any basis for the distinction between congruent and incongruent realisations of the discourse system in the lexicogrammar.