  A novel method to infer logical relationships between sets is presented.
These sets can be any collection of elements, for example astronomical catalogs
of celestial objects. The method does not require the contents of the sets to
be known explicitly. It combines incomplete knowledge about the relationships
between sets to infer a priori unknown relationships. Relationships between
sets are represented by sets of Boolean hypercubes. This leads to deductive
reasoning by application of logical operators to these sets of hypercubes. A
pseudocode for an efficient implementation is described.
  The method is used in the Astro-WISE information system to infer
relationships between catalogs of astronomical objects. These catalogs can be
very large and, more importantly, their contents do not have to be available at
all times. Science products are stored in Astro-WISE with references to other
science products from which they are derived, or their dependencies. This
creates full data lineage that links every science product all the way back to
the raw data. Catalogs are created in a way that maximizes knowledge about
their relationship with their dependencies. The presented algorithm is used to
determine which objects a catalog represents by leveraging this information.
