Not[expr] can be input in StandardForm and InputForm as ¬expr. The character can be entered as Esc ! Esc, Esc not Esc or \[Not]. »
Not gives symbolic results when necessary, applying various simplification rules to them.
If you are using Mathematica with a text-based front end, then you cannot use the notation !expr for Not[expr] if it appears at the very beginning of a line. In this case, !expr is interpreted as a shell escape. »