  In this paper, we provide a comprehensive rigorous modeling for
multidimensional spaces with hierarchically structured dimensions in several
layers of abstractions and data cubes that live in such spaces. We model cube
queries and their semantics and define typical OLAP operators like Selections,
Roll-Up, Drill-Down, etc. The model serves as the basis to offer the main
contribution of this paper which includes theorems and algorithms for being
able to associate data cube queries via comparative operations that are
evaluated only on the syntax of the queries involved. Specifically, these
operations include: (a) foundational containment, referring to the coverage of
common parts of the most detailed level of aggregation of the multidimensional
space, (b/c) same-level containment and intersection, referring to the
inclusion/existence of common parts of the multidimensional space in two query
results of the same aggregation levels, (d) query distance, referring to being
able to assess the similarity of two queries in the same multidimensional
space, and, (e) cube usability, i.e., the possibility of computing a new cube
from a previous one, defined at a different level of abstraction.
