Logic Alphabet for more than Two Variables

Question

Is it possible to generalise Zellweger’s logic alphabet for more than two Boolean variables?

Can it be done by only using the 16 binary connectives?

Thanks.

Answer 1

Well, when the number of Boolean variables is $n=3$, since the number of connectives is $2^{2^n}=(2^{2^2})^{n-1}$, we can use infix notation like $pxqyr$, where $p$, $q$, $r$ are Boolean variables and $x$, $y$ are among the 16 symbols. The interpretation is that if $p$ is true then the value is $qxr$, otherwise $qyr$.

In general $2^{2^n}$ is probably too big for any compact notation to be possible.