Some Of The Problems With The Four General Types Of Logical Relations

Martin & Rose (2007: 116-7):

Both systems use the same four general types of logical relations: adding units together, comparing them as similar or different, sequencing them in time, or relating them causally — as cause and effect, or evidence and conclusion. These four general types are known as addition, comparison, time and consequence. The units they relate range from simple clauses, to more complex sentences, to text phases, to stages of a genre.

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[1] To be clear, the original source of the authors' theorising is Halliday & Hasan (1976: 226-73), where the four categories of conjunction are

• additive
• adversative
• causal
• temporal.

However, Halliday (1985) reworked the system of conjunction in terms of the three most general types of expansion:

• elaboration
• extension
• enhancement.

Importantly, these three general categories are manifested throughout the grammar.  Halliday & Matthiessen (2014: 669):

Let us now present a systematic and comprehensive summary of the different grammatical environments in which elaboration, extension and enhancement are manifested: see Table 10-3. As the table shows, the environments of manifestation can be differentiated in terms of (i) metafunction – textual (CONJUNCTION), logical (INTERDEPENDENCY; MODIFICATION) and experiential (CIRCUMSTANTIATION; PROCESS TYPE: relational), and (ii) rank – clause and group/phrase. (The table could, in fact, be extended downwards along the rank scale to take account of patterns below the rank of group/phrase within the logical metafunction: word and morpheme complexes also embody interdependency relations that combine with expansion.) 

Moreover, it is this multiple manifestation that makes possible grammatical metaphor and the expansion of the semantic system, as Halliday & Matthiessen (1999: 294-5) explain:

The whole metaphorical elaboration [of the semantic system] is made possible by a fractal pattern that runs through the whole system. We have suggested that the metaphorical elaboration is a token–value relation; but in order for it to be a token–value relation within the semantic system, it has to be natural in the sense that the token and the value domains have to be similar enough to allow for the token to stand for the value. The principle behind this similarity is the fractal pattern of projection/expansion … 

That is, while grammatical metaphor constitutes a move from one “phenomenal domain” to another … this move is made possible because fractal types engender continuity across these domains: the metaphorical move from one phenomenal domain to another takes place within the one and the same transphenomenal domain.

It can be seen that these later insights and the explanatory advantages they provide are lost in the authors' rebranding of the original Halliday & Hasan (1976) model.  It can also be seen that the major category of elaboration is entirely absent from the authors' model, since the model only includes one type of extension (addition) and three types of enhancement (comparison, time and consequence).

[2] To be clear, in SFL theory, these correspond to cause: reason and cause: result. The relation between evidence and conclusion is not necessarily causal.

[3] Importantly, in confusing Halliday's cohesive conjunction with Halliday's clause complexing, the authors have omitted the major logico-semantic relation of projection from "their" model.  This is because their source, cohesive conjunction, is the textual deployment of expansion relations only.  This omission means that clause complexes involving mental or verbal projection are not accounted for at the level of discourse semantics.  This is a major weakness in the model, not least because it provides neither congruent nor metaphorical relations between the strata of discourse semantics and lexicogrammar for this major type of logico-semantic relation.

[4] To be clear, Martin & Rose model genre as context instead of language, but nevertheless claim that these relations at the level of language (discourse semantics) obtain between units of context (generic stages).  This demonstrates most clearly that the authors do not understand the SFL hierarchy of stratification or the notion of symbolic abstraction by which it is organised.

It can be noted at this point that Martin's model of genre arises, in part, from his misunderstanding of Hasan's Generic Structure Potential (Halliday & Hasan 1989 [1985]: 64), which models potential semantic structures, varying according to genre, as modelling potential genre structures.