Properties of Boolean functions

Studies of Boolean functions

Family is a hard property. The image shows a family with eight members.

Twin is a soft property. E.g. the twin of the tautology is always the NOR of all arguments.

Properties of Boolean functions are maps that assign values to Boolean functions.
The codomain is often a set of non-negative integers, Boolean values or Boolean functions. It may also be a tuple.
Usually the codomain is smaller than the domain. (But there are some permutations.)

Soft properties are dependent on arity.
For them the domain is always just the set of $2^{2^{n}}$ Boolean functions with arity $n$.

Hard properties are rarer, and probably more useful.
For them the domain can be the infinite set of all Boolean functions. (Typically the codomain will also be infinite, unless the values are Boolean.)