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Abstract. A Conceptual Information System consists of a database together with conceptual hierarchies. The management system TOSCANA visualizes arbitrary combinations of conceptual hierarchies by nested line diagrams and allows an on-line interaction with
On-Line Analytical Processing with Conceptual Information SystemsGerd StummeTechnische Universitat Darmstadt, Fachbereich Mathematik Schlo gartenstr. 7, D{64289 Darmstadt, stumme@mathematik.tu-darmstadt.de
Abstract. A Conceptual Information System consists of a database to-
gether with conceptual hierarchies. The management system TOSCANA visualizes arbitrary combinations of conceptual hierarchies by nested line diagrams and allows an on-line interaction with a database to analyze data conceptually. The paper describes the conception of Conceptual Information Systems and discusses the use of their visualization techniques for On-Line Analytical Processing (OLAP).
1 IntroductionA Conceptual Information System consists of a (relational) database together with conceptual hierarchies. These hierarchies, called conceptual scales, are used to support navigation through the data. An important factor for the success of Conceptual Information Systems is the visualization of conceptual scales by line diagrams. By combining conceptual scales in nested line diagrams, a large variety of perspectives can be generated interactively, in which relationships and dependencies can be investigated. The management system TOSCANA allows an on-line interaction with a database to analyze and explore data conceptually. On-Line Analytical Processing (OLAP) relies on the metaphor of a (high-dimensional) cube containing the data. For dimensions which are not structured hierarchically, the cube metaphor provides a good intuitive understanding of multidimensional data. But an essential feature of OLAP dimensions is that they are ordered hierarchally: days roll up into months, months into quarters and years, products into product groups and product lines. Often they are trees (simple hierarchies ), but they may be any arbitrary partially ordered set (multiple hierarchy ). In this setting, the cube metaphor which re ects the mathematical construction of a direct product of linear vector spaces is not the most natural way, since the hierarchies have to be forced into a at linear form. Instead of listing the hierarchies on (one-dimensional) axes, we suggest to visualize them by line diagrams. By using nested line diagrams, arbitrary dimensions can be combined for ad hoc analysis.
2 Conceptual Information SystemsConceptual Information Systems are based on the mathematical theory of Formal Concept Analysis. The aim of Formal Concept Analysis (cf. 11], 2]) is a mathematical formalization of the concept`concept'. It re ects the philosophical understanding of concepts as units of thought consisting of two parts: the extension containing all