After having another look around, I might have found something that comes close to what I'm looking for: simple temporal problems (STPs), which define intervals that restrict the values of the temporal distance between two events. Found them here:

http://rakaposhi.eas.asu.edu/cse574/tcn-meiri-dechter-aij.pdf

Article Discovering metric temporal constraint networks on temporal databases

@Stan: I agree that it is probably very difficult to generalize them to more dimensions in an abstract way. Fortunately, that's not what I'm looking for, I still want to keep to one dimension, but add numeric constraints to the relationships.

I do not know

There could be, but it is unlikely that there is worked-out one having a broad consensus because, IMO, the problem becomes rapidly too specific. Allen's algebra regards 1D intervals which might become circular or eliptical discs in 2D, spheres or ellipsoids in 3D, etc, and metric & congruence considerations would vary in subtle but important ways. I have posed myself similar questions while working on certain 2D-NMR spectroscopy tasks, for example, and eventually I have worked out my own application rules for that particular app, finding it hard to think of an abstraction that a pure mathematicion might care about. There is too much freedom in creating algebras to suggest many universally useful ones. Beyong a few "template" cases, one needs to invert the problem and focus on what the specific application needs. The templates (like Allen's) are important simply because they pave the way and open the eyes.

At least, that is how I perceive it.

After having another look around, I might have found something that comes close to what I'm looking for: simple temporal problems (STPs), which define intervals that restrict the values of the temporal distance between two events. Found them here:

http://rakaposhi.eas.asu.edu/cse574/tcn-meiri-dechter-aij.pdf

Article Discovering metric temporal constraint networks on temporal databases

@Stan: I agree that it is probably very difficult to generalize them to more dimensions in an abstract way. Fortunately, that's not what I'm looking for, I still want to keep to one dimension, but add numeric constraints to the relationships.