Modalized modal sentence

A modal sentence \(A\) is said to be modalized in \(p\) if every occurrence of \(p\) happens within the scope of a \(\square\).

As an example, \(\square p \wedge q\) is modalized in \(p\), but not in \(q\).

If \(A\) does not contain \(p\), then it is trivially modalized in \(p\).

A sentence which is modalized in every sentence letter is said to be fully modalized.

Being modalized in \(p\) is a sufficient condition for having a fixed point on \(p\).