Halliday & Matthiessen (1999: 605):
This category corresponds to Hjelmslev's (1943) concept of a "connotative semiotic": a higher-level system that has language as its plane of expression. These include theories: every theoretical construction, scientific, philosophical, aesthetic, and so on, is a higher-level semiotic realised in language. They also include the codified aspects of social institutions such as the law, the financial system, constitutions and codes of practice.
Martin interprets both genre and ideology in this light, as social activity structures and ideological formations that are realised in language (e.g. 1985, 1992; for a critique of Martin's view, see Hasan, 1995).
From a semantic point of view, such systems constitute contexts for language;
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Importantly, Hjelmslev's (1943) concept of a "connotative semiotic" includes both a content plane and an expression plane, not just a content plane. That is, in SFL terms, the connotative semiotic is both context and language, not just context.