David Corfield subsentential inferentialism

Precisely.

[The] performances Brandom dubs “assertions” have … no recognizable subsentential semantic structure, but are internally simple, un-structured semantic “blobs”. Accordingly, Brandom owes us a theory, couched in normative pragmatic terms, of subsentential expressions – names and predicates – and their meaning, and of how speakers may combine and recombine names and predicates in ever-new ways so as to produce and understand ever-new assertions and declarative sentences. Loeffler (2017, p.85) (h/t Gavin)

Also McCullagh.

Since a proposition is a kind of type, this concerns all the type formation rules. E.g., we may have a proposition reached finally by proposition truncation from a type that itself derived from a complex type formation process, using many rules.