Full Idea
There are two approaches to an 'interpretation' of a logic: the first method assigns objects to names, and then defines connectives and quantifiers, focusing on truth; the second assigns objects to variables, then variables to names, using satisfaction.
Gist of Idea
Interpretation by assigning objects to names, or assigning them to variables first
Source
report of David Bostock (Intermediate Logic [1997], 3.4) by PG - Db (lexicon)
Book Reference
Bostock,David: 'Intermediate Logic' [OUP 1997], p.82
A Reaction
[a summary of nine elusive pages in Bostock] He says he prefers the first method, but the second method is more popular because it handles open formulas, by treating free variables as if they were names.