I think a subpartition of S can be thought of as a partial function on S, or equivalently, a variable on S that has the possible value “Null”/”undefined”.
That’s right. A partial function can be thought of as a subset (of its domain) and a total function on that subset. And a (total) function can be thought of as a partition (of its domain): the parts are the inverse images of each point in the function’s image.
I think a subpartition of S can be thought of as a partial function on S, or equivalently, a variable on S that has the possible value “Null”/”undefined”.
That’s right. A partial function can be thought of as a subset (of its domain) and a total function on that subset. And a (total) function can be thought of as a partition (of its domain): the parts are the inverse images of each point in the function’s image.