Multidimensional information systems, and specifically what are called OLAP systems, sprang from weaknesses in the Relational (SQL) Databases RDBs developed in the 1980s and 1990s. Specifically, RDBs (optimized for column calculations) were weak at creating partial aggregations and allocations which in relational terms amounted to inter row intra column calculations. Whereas RDBs were table-based, OLAP was array-based. Although some of the basic vanilla summation capabilities of OLAP have been incorporated into current RDBs, array-based architectures remain superior for matrix mathematics.
Though considered a part of Business Intelligence (or Decision support, or Management Information Systems), the logical structuring of hierarchies and multilevel representations researched and implemented across the various OLAP systems is a crucial component of ontologies, knowledge management and therefore of artificial intelligence.
Those interested may wish to consult
♦ OLAP Solutions: Building Multidimensional Information systems 2nd edition
♦ Microsoft OLAP Solutions
♦ OLAP Solutions 1st edition
♦ Patent for multi level hierarchies
♦ FreeThink (user manual and docs), the first software product to support leveled hierarchies, multilevel variables and cell level auditing of multidimensional formulas