The functional correlates of grammatical constructions can be given heuristically as (i) “the discourse context within which the grammatical construction is used”. They can also be given as the more cognitive-sounding (ii) “the communicative intent of the speaker using the construction”. This paper suggests that the cognitive-sounding definition (ii) above needs to be specified more precisely in cognitive terms, bringing it in line with more up-to-date work in cognitive neuro-science. More specifically, it suggests that in using grammar, speakers create mental models of the knowledge (epistemic) and intention (deontic) states of their interlocutors, in a way already implicit in H. P. Grice’s work. These models are created rapidly, on-line, automatically and with high specificity of the ever-shifting communicative context. The traditional pragmatic notions of “communicative context” (i) and “communicative intent” (ii) may thus be expressed more precisely in terms of so-called “Theories of Mind”, i.e. the mental models socially-cooperative organisms build of the presumed mental states of their cooperating interlocutors.