Try to solve my example first. You would need redefine what the directories comprise. It is clear that b cannot contain a and vice versa, but needs to contain a part of a. You can fix it by adding intersections and unions but I don't think this would lead to anything practical.

And alternative would be to use faceted navigation instead of directories.

Your example with photos is a good one. But I still think that search would be much more usefull than tags for text.