Not

is a monadic scalar function that returns the logical negation of a Boolean argument—that is, 0 if the argument is 1 and 1 if it is 0. In some languages, such as J, it is extended so that Not  is equivalent to   while in others, such as K, it is extended so that Not   is equivalent to.

Examples
Attempting to negate a non-Boolean argument usually results in a DOMAIN ERROR. In some languages it may instead subtract the argument from one.

Properties
Not is the only Boolean function of a single argument which depends on that argument (it is not constant) and is not trivial (the same as Identity). Not is its own Inverse.

History
A Programming Language negates arrays using an overbar symbol like $$\overline{p}$$, matching a convention sometimes used in mathematics. In APL\360 the current symbol  was chosen, also due to its use in mathematics. Mathematical usage has arguably diverged from APL in this respect, as the negation of a variable $$p$$ is now more often written $$\neg p$$ when a prefix operator is desired.

The arithmetic extension     was introduced to the array langauge family by J. For arguments in the interval $$[0,1]$$ this extension may be seen as a probabilistic interpretation of negation.

Lessons

 * APL Cultivation

Documentation

 * Dyalog
 * APLX
 * J Dictionary, NuVoc