I think this kind of thing is great, but it runs into some of the same considerations that make probabilistic graphical models hard. If I have two variables de

I think this kind of thing is great, but it runs into some of the same considerations that make probabilistic graphical models hard. If I have two variables defined as x = [0,1]; y = [0,1]; z = x - y; Then we see that z should be the interval [-1,1]. But for a similar problem, a = [0,1]; b = a - a; x = a; y = a; z = x - y; b should clearly be the interval [0,0]. z is computed the same way as the first example, as the difference between two [0,1] intervals. But this time we want it to be [0,0]. That means we want to keep around some notion similar to the joint distribution of x and y. That makes arithmetic immensely harder than simple rules. Not to say it's not worth it, just that it's hard.