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Nested Ordered Sets and their Use for Data Modelling
Nested Ordered Sets and their Use for Data Modelling
Alexandr Savinov
Dept. of Computer Science III, University of Bonn,
Roemerstr. 164, 53117 Bonn, Germany
Institute of Mathematics and Computer Science, Academy of Sciences of Moldova
str. Academiei 5, 2028 Chisinau, Moldova
savinov@iai.uni-bonn.de
/savinov
Abstract. In this paper we present a new approach to data modelling, called the concept-oriented
model (CoM), and describe its main features and characteristics including data semantics and
operations. The distinguishing feature of this model is that it is based on the formalism of nested
ordered sets where any element participates in two structures simultaneously: hierarchical (nested)
and multi-dimensional (ordered). An element of the model is postulated to consist of two parts, called
identity and entity, and the whole approach can be naturally broken into two branches: identity
modelling and entity modelling. We also propose a new query language with the main construct,
called concept, defined as a pair of two classes: identity class and entity class. We describe how its
operations of projection, de-projection and product can be used to solve typical data modelling tasks.
Keywords: data modelling, concept-oriented model, nested ordered sets, dimension, logical
navigation, multi-dimensional analysis.
1 Introduction2
2 Nested Ordered Sets 2
3 Data Semantics and Operations 6
3.1 Canonical Representation 6
3.2 Operations7
4 Concept-Oriented Query Language 8
4.1 Concept and Concept Schema 8
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