In the Boole Library in Ireland (which has entrances on different floors) they use an algebraic (affine) system. There is a floor designated "Q" and then other floors are labelled relatively, "Q+2", "Q-1", etc.

A possible interpretation....

Using the insight from the top comment that "it all depends on whether u're counting the items themselves (1-based) or the spaces btwn them," the American way of numbering floors is based on counting actual floors (ie, the things you stand on) -- and the one at earth level is one floor. If you go up a flight of stairs, there is second floor to stand on, and so on.

For buildings that go underground, the "-" sign can now act as a signifier of being underground, and the counting works as normal. If you take the stairs down one level, you are on the first underground floor, -1.

Of course, you want to interpret it like a y-axis number line, where 0 is the earth, 1 is "1 floor unit" above the earth, -1 is "1 floor unit" below the earth, etc. This is the "space between" model.

Elegance aside, both can be viewed as logically consistent depending on your lense.

When my badge doesn't scan at work, that is great art

At the University of Arizona (or at least in most of the buildings there), the lowest floor of the building is always 1, even if it’s a basement. So the ground floor is often 2. Maddening.

In the '80s the ground floor of the EE building (Steele) at Caltech was labeled ⏚. Anyone here happen to know if it is still labeled that way?