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 \(p\).