In addition to the experiential, interpersonal and textual metafunctions just considered, Halliday has in addition proposed a fourth metafunction, the logical. Systemically the logical metafunction comprises recursive systems (such as TENSE, PROJECTION and AGENCY in English; see Halliday 1985a), which tend to be associated across languages with experiential meaning. Structurally logical meaning is realised as another kind of particulate structure — but this time as part/part rather than part/whole. … These complementary perspectives are outlined in Fig. 1.9.
The relationship between the metafunctions, realisation principles and types of structural [sic] is summarised in Table 1.3.
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[1] To be clear, in SFL Theory, recursive systems are realised by the iterative structures of the logical metafunction. Of the systems cited by Martin, the system of TENSE is realised by an iterative logical structure, and the system of PROJECTION is one system within the recursive systems of the clause complex and verbal group complex; see Halliday & Matthiessen (2014: 410, 438, 589). The system of AGENCY, on the other hand, is not a recursive system, and is not realised by an iterative structure; Halliday & Matthiessen (2014: 355):
The 'open-endedness' of ergative structure, whereby agency can be added in analytical causative constructions (Halliday & Matthiessen 2014: 352) is effected by the recursive system that is realised by the iterative structure of the verbal group complex. Halliday & Matthiessen 2014: 579-80):
[2] To be clear, this confuses formal constituency (nominal group consisting of words) with function structure (the relations between functional elements). In both experiential and logical structures of the nominal group, the structure is the relation between the functions of the constituents (parts). Halliday & Matthiessen (2014: 85) characterise the experiential as segmental, and the logical as iterative:
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