The derivation problem of summary data

Given a statistical database consisting of two summary tables based on a common but not identical classification criterion (e.g., two geographical partitionings of a country) there are additional summary tables that are derivable in the sense that they are uniquely (i.e., with no uncertainty) determined by the tables given. Derivable tables encompass not only, of course, “less detailed” tables (that is, aggregated data) but also “more detailed” tables (that is, disaggregated data). Tables of the second type can be explicitly constructed by using a “procedure of data refinement” based on the graph representation of the correspondences between the categories of the two classification systems given in some cases, that is, when such a graph representation meets the acyclicity condition, the underlying database is “equivalent” to a single table (called representative table) and then a necessary and sufficient condition for a table to be derivable can be stated.