Modal logics differ in what collections of modalities they allow, how the existing modal operators are interpreted, and how the logic is axiomatized. Below is an incomplete list of various interpretations of modal operators studied in the literature:

Possible readings of []A: "it is necessary that A", "A is provable", "I know that A", "everyone knows that A", "I believe that A", "A is obligatory", "A will always be true", "A has always been true", etc.

Possible readings of A>B: "B is interpretable in A", "A logically implies B", etc.