Halliday & Matthiessen (1999: 596n):
Alongside this cognitivist approach, there is a material one embodied in formal approaches to semantics, where the ‘aboutness’ of linguistic expressions is taken as central and these expressions are interpreted in terms of models of possible worlds. However, in this respect there is a formal-cognitive alliance: meaning is interpreted not as something in its own right but as something outside language, either a mental construct (concepts, ideas etc) or a material one (referents in the real world or a formal model of a possible world).