Sketch Data Models, Relational Schema and Data Specifications

Abstract When different mathematical models are used for software analysis and development it is important to understand their relationships. When the models are truly mathematical, and when the aspects of reality that they seek to model are common, it may be possible to express their relationships in precise mathematical terms. This paper studies three mathematical models: The sketch data model, the relational data model, and the data specifications of Piessens and Steegmans, and determines their relationships mathematically and in detail. The constructions presented here answer reasonably long-standing theoretical questions, and offer techniques that promise to be practically useful in integrating data models.

[1]  Michael Johnson,et al.  On category theory as a (meta) ontology for information systems research , 2001, FOIS.

[2]  Michael Johnson,et al.  View updates in a semantic data modelling paradigm , 2001, Proceedings 12th Australasian Database Conference. ADC 2001.

[3]  Zinovy Diskin,et al.  Algebraic Graph-Based Approach to Management of Multidatabase Systems , 1995, NGITS.

[4]  Arthur H. M. ter Hofstede,et al.  A Category Theory Approach to Conceptual Data Modeling , 1996, RAIRO Theor. Informatics Appl..

[5]  C. J. Date.  An Introduction to Database Systems , 1975 .

[6]  Wesley Phoa,et al.  Categorical Models of Relational Databases I: Fibrational Formulation, Schema Integration , 1994, TACS.

[7]  Dan A. Simovici,et al.  A categorical approach to database semantics , 1994, Mathematical Structures in Computer Science.

[8]  Frank Piessens,et al.  Categorical data-specifications , 1995 .

[9]  Michael Barr,et al.  Category theory for computing science , 1995, Prentice Hall International Series in Computer Science.

[10]  Christopher N. G. Dampney,et al.  An illustrated mathematical foundation for ERA , 1992 .

[11]  Frank Piessens,et al.  Selective Attribute Elimination for Categorial Data Specifications , 1997, AMAST.

[12]  Christopher N. G. Dampney,et al.  Half-Duplex Interoperations for Cooperating Information Systems , 2001 .

[13]  Michael Johnson,et al.  Enterprise Information Systems: Specifying the Links among Project Data Models Using Category Theory , 2001, ICEIS.

[14]  Michael Johnson,et al.  Database Interoperability Through State Based Logical Data Independence , 2003 .

[15]  Marc Gyssens,et al.  CGOOD, a Categorical Graph-Oriented Object Data Model , 1996, Theor. Comput. Sci..

[16]  Michael Johnson,et al.  Engineering legacy information systems for internet based interoperation , 2001, Proceedings IEEE International Conference on Software Maintenance. ICSM 2001.

[17]  H. J. Pels,et al.  An introduction to database systems, sixth edition , 1997 .

[18]  Michael Johnson,et al.  On the Value of Commutative Diagrams in Information Modelling , 1993, AMAST.

[19]  Michael Johnson,et al.  View Updatability Based on the Models of a Formal Specification , 2001, FME.