The GMD Data Model for Multidimensional Information: Preliminary Report

In this short paper we introduce a novel data model for multidimensional information, GMD, generalising the MD data model first proposed in [Cabibbo and Torlone, 1998]. The aim of this work is not to propose yet another data model, but to find the most general formalism encompassing all the proposals for a logical data model in the data warehouse field, as for example summarised in [Vassiliadis and Sellis, 1999]. Our proposal is compatible with all these proposals, making therefore possible a formal comparison of the different expressivities of the models in the literature. In this first proposal we concentrate only on the logical model, disregarding a possible algebra built on top of the basic types; this will be the necessary next step of our research. Still, we believe that the GMD data model is already very useful in its current form, since it provides a very precise and, we believe, very elegant and uniform way to model multidimensional information. For example, interestingly enough, GMD reduces as expected to the standard relational model for dimensionless information; and obviously the star and the snowflake schemas (together with their variants) can be encoded as GMD schemas. It turns out that most of the proposals in the literature make many hidden assumptions which may harm the understanding of the advantages or disadvantages of the proposal itself. An embedding in our model would make all these assumptions explicit. We hope that a discussion will arise at the workshop about the possible limits of the current status of GMD, in order to have better versions of it in the future. In this short paper we do not present how the most famous data models can be embedded into GMD; please note that we prove that for each schema in some data model its translated GMD schema imposes the same constraints on the data warehouse. So far, we have considered, among others, the logical data models introduced in [Agrawal et al., 1997; Cabibbo and Torlone, 1998; Franconi and Sattler, 1999; Golfarelli et al., 1998; Gray et al., 1996; Gyssens and Lakshmanan, 1997; Tsois et al., 2001; Vassiliadis, 1998; Vassiliadis and Skiadopoulos, 2000]. In the following, we introduce the formal syntax and semantics of the GMD data model, together with worked out examples.