Modalized modal sentence
A \(A\) 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 \(p\).
- Modal logic
The logic of boxes and bots.