In a perfect world, in my opinion is that they are incompatibles, and the equality operation should return False in both cases.

But equality is a very complicated concept.

I guess if the values are incomparable != preserves PEM

But Boolean algebra is a lattice, with two+ binary operators were two of those are meet and join with a shared absorbing property.

X == not not X being PEM, we lose that in NP vs co-NP and in vector clocks etc…

But that is just my view.