Full Idea
We can distinguish between narrower and broader kinds of logical necessity. There are, for example, the logical necessities of propostional logic, those of first-order logic, and so on. Maybe they are necessities expressed using logical vocabulary.
Gist of Idea
Maybe each type of logic has its own necessity, gradually becoming broader
Source
Bob Hale (Necessary Beings [2013], 04.5)
Book Reference
Hale,Bob: 'Necessary Beings' [OUP 2013], p.114
A Reaction
Hale goes on to prefer a view that embraces conceptual necessities. I think in philosophy we should designate the necessities according to their sources. This might clarify a currently rather confused situation. First-order includes propositional logic.