On Equivalence Relations Between Interpreted Languages, with an Application to Modal and First-Order Language

I examine notions of equivalence between logics (understood as languages interpreted model-theoretically) and develop two new ones that invoke not only the algebraic but also the string-theoretic structure of the underlying language. As an application, I show how to construe modal operator languages as what might be called typographical notational variants of bona fide first-order languages.