PriMera Scientific Engineering (ISSN: 2834-2550)

Research Article

Volume 9 Issue 3

(Elementary) Mathematical Data Models of the Relational and Entity-Relationship Ones

Christian Mancas*

September 02, 2026

DOI : 10.56831/PSEN-09-290

Abstract

This paper presents (Elementary) Mathematical Data Models of the Relational and the Entity-Relationship Data Models. The first one was obtained starting with a Relational Data Model of itself shown in our Conceptual Data Modeling and Database Design book (Volume 1: The Shortest Advisable Path) and then applying several forward and reverse engineering algorithms between these two data models, as well as the Entity-Relationship one. The second one was obtained directly from the Entity-Relationship Data Model of itself also shown in our book.

Keywords: Conceptual Data Modeling; Relational Data Model; Entity-Relationship Data Model; E-R diagram cycle analysis; (Elementary) Mathematical Data Model; Relational and Entity-Relationship Database Management Systems design

References

  1. Codd EF. “A relational model for large shared data banks”. CACM 13.6 (1970): 377-387.
  2. Abiteboul S, Hull R and Vianu V. “Foundations of Databases”. Addison-Wesley, Reading, MA (1995).
  3. Mancas C. “Conceptual Data Modeling and Database Design: A Completely Algorithmic Approach. Volume 1: The Shortest Advisable Path”. Apple Academic Press, Waretown, NJ (2015).
  4. IBM Corp. “IBM Db2” (2026).
  5. Oracle Corp. “Oracle® AI Database” (2026).
  6. Microsoft Corp. “Microsoft SQL Server 2025” (2026).
  7. Chen PP. “The entity-relationship model. Toward a unified view of data”. ACM TODS 1.1 (1976): 9-36.
  8. Thalheim B. “Entity-Relationship Modeling: Foundations of Database Technology”. Springer-Verlag, Berlin, Germany (2000).
  9. Mancas C. “The (Elementary) Mathematical Data Model revisited”. PriMera Scientific Engineering 5.4 (2024): 78-91.
  10. Date CJ and Darwen H. “Foundation for future database systems: The third manifesto; a detailed study of the impact of type theory on the relational model of data, including a comprehensive model of type inheritance (2 ed.)”. Addison-Wesley, Reading, MA (2000).
  11. Mancas C and Mancas DC. “MatBase Algorithm for Translating Entity-Relationship Data Models into (Elementary) Mathematical Data Model Schemes”. PriMera Scientific Engineering 7.6 (2025): 04-11.
  12. Mancas C and Mocanu A. “Matbase DFS Detecting and Classifying E-RD Cycles Algorithm”. J. Comp. Sci. Appl. Inform. Technol 2.4 (2017): 1-14.
  13. Mancas C. “MatBase E-RD Cycles Associated Non-Relational Constraints Discovery Assistance Algorithm”. Intelligent Computing. CompCom 2019. Advances in Intelligent Systems and Computing 997 (2019).
  14. Mancas C. “Algorithms for Key Discovery Assistance”. BIR 2016, Lecture Notes in Business Information Processing 261 (2016): 322-338.
  15. Mancas C. “MatBase Constraint Sets Coherence and Minimality Enforcement Algorithms”. Proc. 22nd ADBIS Conf. on Advances in DB and Inf. Syst., LNCS, Springer, Cham, Switzerland 11019 (2018): 263-277.
  16. Mancas C. and Dragomir S. “On the Equivalence Between Entity-Relationship and Functional Data Modeling”. In: Hamza M. (ed.). Proc. 7th IASTED Int. Conf. on Soft. Eng. and App. (SEA 2003) (2003): 335-340.
  17. Kerschberg L. and Pacheco JES. “A Functional Data Base Model”. Monographs in Computer Science and Computer Applications No. 2/76 (1976).
  18. Shipman DW. “The Functional Data Model and the Data Language DAPLEX”. ACM ToDS 6.1 (1981): 140-173.