Nested Ordered Sets and their Use for Data Modelling

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.

[1]  Alexandr Savinov,et al.  Hierarchical Multidimensional Modelling in the Concept-Oriented Data Model , 2005, CLA.

[2]  Ronald Fagin,et al.  A simplied universal relation assumption and its properties , 1982, TODS.

[3]  Brian A. Davey,et al.  An Introduction to Lattices and Order , 1989 .

[4]  Riccardo Torlone.  Conceptual Multidimensional Models , 2003, Multidimensional Databases.

[5]  Carlo Zaniolo,et al.  Database relations with null values , 1982, J. Comput. Syst. Sci..

[6]  Sunita Sarawagi,et al.  Modeling multidimensional databases , 1997, Proceedings 13th International Conference on Data Engineering.

[7]  Alexandr A. Savinov,et al.  An Approach to Programming Based on Concepts , 2007, ArXiv.

[8]  Alexandr A. Savinov,et al.  Concept-Oriented Programming , 2008, ArXiv.

[9]  William Kent.  Consequences of assuming a universal relation , 1981, TODS.

[10]  Esteban Zimányi,et al.  Hierarchies in a multidimensional model: From conceptual modeling to logical representation , 2006, Data Knowl. Eng..

[11]  Alexandr Savinov,et al.  Logical Navigation in the Concept-Oriented Data Model , 2005 .

[12]  Bernhard Ganter,et al.  Formal Concept Analysis: Mathematical Foundations , 1998 .

[13]  David W. Shipman.  The functional data model and the data language DAPLEX , 1979, SIGMOD '79.

[14]  Alexandr A. Savinov,et al.  Two-Level Concept-Oriented Data Model , 2007, ArXiv.

[15]  Larry Kerschberg,et al.  Guest Editor Introduction: Functional Approach to Intelligent Information Systems , 2004, Journal of Intelligent Information Systems.

[16]  Peter Buneman,et al.  Using Powerdomains to Generalize Relational Databases , 1991, Theor. Comput. Sci..

[17]  Alexandr A. Savinov.  Query by Constraint Propagation in the Concept-Oriented Data Model , 2006, Comput. Sci. J. Moldova.

[18]  Laks V. S. Lakshmanan,et al.  A Foundation for Multi-dimensional Databases , 1997, VLDB.

[19]  David Maier,et al.  On the foundations of the universal relation model , 1984, TODS.

[20]  A Min Tjoa,et al.  An Object Oriented Multidimensional Data Model for OLAP , 2000, Web-Age Information Management.

[21]  Alexandr Savinov,et al.  Concept as a Generalization of Class and Principles of the Concept-Oriented Programming , 2005, Comput. Sci. J. Moldova.

[22]  Alexandr A. Savinov,et al.  Concepts and Concept-Oriented Programming , 2008, J. Object Technol..

[23]  Rudolf Wille,et al.  Formal Concept Analysis as Applied Lattice Theory , 2006, CLA.

[24]  Alexandr A. Savinov,et al.  Grouping and aggregation in the concept-oriented data model , 2006, SAC.

[25]  Chang Li,et al.  A data model for supporting on-line analytical processing , 1996, CIKM '96.