Modalized modal sentence

by Jaime Sevilla Molina Jul 27 2016 updated Jul 27 2016

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$~$.