Halliday & Matthiessen (1999: 422):
In modelling meaning, formal semantics models it as both extensional and intensional: extensional meaning is cast in terms of sets of entities in a model of some world, and intensional meaning is the relation between a linguistic expression and its extension in any possible world. Formal semantics has thus been concerned with how semantic representations can be related to some extra-linguistic world model. Dowty et al (1981: 5) emphasise the relationship between language and the world in their introductory characterisation of truth conditional semantics:"... truth conditional semantics, in contrast to other approaches mentioned [including Katz & Fodor, Jackendoff, and generative semantics, MAKH & CM], is based squarely on the assumption that the proper business of semantics is to specify how language connects with the world — in other words, to explicate the inherent "aboutness" of language."This is, of course, an ideational orientation: the focus here is on representational meaning only. One central method has been to build models of the world in set theoretic terms, and to relate these to linguistic expressions — the model theoretic approach.