Underplaying The Scope Of Logical Relations

Martin (1992: 162-3):

The following clauses in particular do not make use of clause complex resources to encode causal or temporal relations:

That's because it's a low dog.

That is so the judge can get the hind movement of your dog.

After that he usually tells you…

He proceeds to do that with every dog.

… The point is that while examples such as these make use of resources other than the clause complex to mark logical relations between part of a text, there is a sense in which the alternative realisations are all variations on the same theme — namely that of relating one part of a text to another in terms of the natural logic of time, cause, comparison and addition.  So not only does the clause complex need to be supplemented as far as a consideration of logical relations is concerned, but it needs to be abstracted from as well so that a more general treatment can be pursued, taking the clause complex into account as just one of its manifestations.  It is for this reason of course that logical relations will be interpreted from the perspective of discourse semantics, rather than that of lexicogrammar here.

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[1] This vastly underplays the place of logical relations in SFL theory.  The logico-semantic relations that obtain between clauses in clause complexes are those of expansion and projection.

Firstly, these are called transphenomenal categories because they 'operate across the various categories of phenomena' (Halliday & Matthiessen 1999: 223).  For example,  as well as obtaining between rank units in complexes, they are also manifested in relational clause types (Halliday & Matthiessen 2004: 210-48) and circumstance types (Halliday & Matthiessen 2004: 262-3).

Secondly, they are called fractal types because they recur at various levels in the system.  Halliday & Matthiessen (1999: 223):

… they are principles of construing our experience of the world that generate identical patterns of semantic organisation which are of variable magnitude and which occur in variable semantic environments. Such patterns therefore constitute fractal types.

Thirdly, they are thus "meta" to the organisation of ideational meaning, and provide an additional level of agnation in the system. Halliday & Matthiessen (1999: 223-4): 

… the fractal types constitute an additional order of agnation that is projected onto the ideational system as a whole. We can refer to this as fractal agnation. Because of this, a qualifying sequence and a figure of circumstantial being, such as cause, are agnate; they are both manifestations of the fractal type of enhancement.

Fourthly, as fractal types, they provide the major means of creating new meaning in the system.  Halliday & Matthiessen (1999: 224): 

The fractal types of projection and expansion are also a primary resource by which the semantic system creates new meanings. […] The ideation base thus itself embodies, auto-genetically, the principles on which it is organised and enabled to develop further, such that the primary systems of ideational meaning then serve as a grid within which more delicate categories are construed.

Fifthly, it is these fractal types that make grammatical metaphor possible. Halliday & Matthiessen (1999: 225):

Thus our concept of “construing experience through meaning” refers to the construal in human consciousness of an ideational system in which such [transphenomenal] motifs play a crucial part. Expansion and projection are, as we put it earlier, fractal principles; they generate organisation within many environments in the ideation base, at different strata and at different ranks within one stratum. These environments are thus related to one another through the local manifestations of these different motifs; and this opens up the system’s potential for alternative construals of experience … . What this means is, that whatever is construed can also be reconstrued, giving yet another dimension to the topology of semantic space.

Halliday & Matthiessen (1999: 294-5): 

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.

Sixthly, it is these fractal types, especially elaboration, that makes the "importation" of experience into the system possible.  Halliday & Matthiessen (1999: 224):

Here we have foregrounded especially the motif of elaborating, with particular reference to its manifestation in the identifying and ascriptive figures of being. We have tried to show how elaboration makes it possible to “import” extra-linguistic experience into the meaning base by actively construing it (as in ‘that [thing there] is a circle’); and also to “transport” meanings internally from one region of the ideation base in order to construe new meanings in another (as in ‘balance means you hold it in your fingers and it does not go’). The extension of meaning in delicacy — not merely generalising across different types but construing such types into dimensional and open-ended taxonomies — is a function of the elaborating potential, exploiting the basic dimensions of the system itself.

[2]  A consideration of logico-semantic relations as transphenomenal fractal types that provide an additional organisation of ideational meaning undermines the stated justification for a 'discourse semantics of logical relations'.