Let us use to denote those such that

Obviously the following is true:

There must be a better notation than — we are open to suggestions. Any?

I think is just the set of places where the partial differential of with respect to is 

See Tables A9 and A10 in my article on Differential Logic and Dynamic Systems.

For example, look at which is just the logical conjunction

In this case,

This means that crossing the boundary of will change the value of exactly in those places where is true.

The See a Number, Make a Set principle leads to the following observation, that an arbitrary set of cells in a venn diagram or an arbitrary set of vertices in a -cube is described by a proposition or a boolean function as its fiber of so the above types of differential operators take us from propositions to propositions, in other words, they stay within the same general datatype.