The idea behind the !(x y) = !x ?y rule

[bvssvni]

Another option was !(x y) = !x !y, but was discarded due to similarity with !(x, y) = (!x, !y).

The only alternative to !(x y) = !x ?y is !(x y) = !x ?!y.

Under the !(x y) = !x ?!y rule in Closed Joker Calculus,
Seshatic Joker Seshatism becomes Seshatism:

not(not(Seshatic Joker Seshatism))
not(not(Seshatic) Joker not(Joker Seshatism))    by !(x y) = !x ?!y
not(Platonic Joker Joker Platonism)    by !1 = 0 and !?1 = ?0
not(Platonic Platonism)    by ??x = x
not(Platonism)    by 0 0 = 0
Seshatism    by !0 = 1

This would mean 1 ?1 = 1, which is too similar to 1 1 = 1.

The !(x y) = !x ?y was chosen due to novelty.