How subsentential can premisses be?

This is yet a different sub-thread from "Subsentential Grice", but it dwells on A. Hall´s remarks about subpropositional (logical) forms hardly having the power to feature explicitly or not as premisses in one´s piece of reasoning.

But then -- who said they should?

Most theorists agree on the inferential basis of most communication. Yet, this does not mean that the "model" entertained by a given expression should be isomorphic with a full propositional premise in one´s piece of reasoning. Or not.