Hierarchies in Multidimensional Databases

Hierarchies play a fundamental role in knowledge representation and reasoning. They have been considered as the structures created by abstraction processes. According to Smith and Smith (1977), an abstraction process is an instinctively known human activity, and abstraction processes and their properties are generally used for multilevel object representation in information systems. An abstraction can be understood as a selection of a set of attributes, objects, or actions from a much larger set of attributes, objects, or actions according to certain criteria. Repeating this selection several times, that is, continuing to choose from each subset of objects, another subset of objects with even more abstract properties, we create other levels of (semantic) details of objects. The complete structure created by the abstraction process is a hierarchy and the type of hierarchy depends on the operation used for the abstraction process and the relations. As for the relations, the best known in the literature are classification, generalization, association (or grouping), and aggregation. Their main characteristics are briefly listed in the following.