PriMera Scientific Engineering (ISSN: 2834-2550)

Research Article

Volume 5 Issue 4

The (Elementary) Mathematical Data Model Revisited

Christian Mancas*

September 30, 2024

DOI : 10.56831/PSEN-05-157

View PDF

Abstract

This paper presents the current version of our (Elementary) Mathematical Data Model ((E)MDM), which is based on the naïve theory of sets, relations, and functions, as well as on the first-order predicate calculus with equality. Many real-life examples illustrate its 4 types of sets, 4 types of functions, and 76 types of constraints. This rich panoply of constraints is the main strength of this model, guaranteeing that any data value stored in a database is plausible, which is the highest possible level of syntactical data quality. An (E)MDM example scheme is presented and contrasted with some popular family tree software products.

Keywords: (Elementary) Mathematical Data Model; MatBase; Naïve theory of sets relations and functions; First order predicate calculus with equality; Database design; Modelware

References

  1. Mancas C. “A first introduction to a data model based on the semi-naïve theory of sets, relations, and functions”. In Proc. 5th Conf. on Informatics (INFO-IASI’85), A.I. Cuza Univ., Iasi, Romania (1985): 314-320. (in Romanian).
  2. Mancas C. “A Deeper Insight into the Mathematical Data Model’. In Proc. 13th Int. Seminar on Database Management Systems (ISDBMS'90), ICI Bucharest, Romania (1990): 122-134.
  3. Mancas C. “Conceptual data modelling”. Ph. D. Dissertation (in Romanian), Politehnica Univ., Bucharest, Romania (1997).
  4. Mancas C. “Normalization versus correctness of conceptual data modelling”. Compulsory object constraints in the Elementary Mathematical Data Model too. In Proc. 1st Conf. on Informatics Theory and Technologies (CITTI’2000), Ovidius Univ., Constanta, Romania (2000): 207-216 (in Romanian).
  5. Mancas C. “On Modeling Closed Entity-Relationship Diagrams in an Elementary Mathematical Data Model”. In Proc. 6th East-European Conf. on Advances in Databases and Inf. Syst. (ADBIS 2002), Slovak Univ. of Techn., Bratislava, Slovakia 2 (2002): 165-174.
  6. Mancas C. “On Modeling the Relational Domain-Key Normal Form Using an Elementary Mathematical Data Model”. In Proc. 6th IASTED Int. Conf. on Soft. Eng. and App. (SEA 2002), ACTA Press, Calgary, Canada (2002): 767-772.
  7. Mancas C. “On Knowledge Representation Using an Elementary Mathematical Data Model”. In Proc. 1st IASTED Int. Conf. on Inf. and Knowl. Sharing (IKS 2002), ACTA Press, Calgary, Canada (2002): 206-211.
  8. Mancas C. “MatBase Constraint Sets Coherence and Minimality Enforcement Algorithms”. In: Benczur, A., Thalheim, B., Horvath, T. (eds.), Proc. 22nd ADBIS Conf. on Advances in DB and Inf. Syst., LNCS, Springer, Cham, Switzerland 11019 (2018): 263-277.
  9. Mancas C. “On Modelware as the 5th Generation of Programming Languages”. Acta Scientific Computer Sciences 2.9 (2020): 24-26.
  10. Mancas C. “Conceptual Data Modeling and Database Design: A Completely Algorithmic Approach”. Volume I: The Shortest Advisable Path. Apple Academic Press / CRC Press (Taylor & Francis Group), Palm Bay, FL (2015).
  11. Millennia. Legacy Family Tree (2024). https://legacyfamilytree.com/,
  12. RootsMagic. RootsMagic Essentials 10 (2024). https://www.rootsmagic.com/try/.
  13. GenoPro Ltd. GenoPro 2020 (2024). https://genopro.com/.
  14. Gramps. Gramps-Genealogical Research Software (2024). https://gramps-project.org/blog/.
  15. Calico Pie Ltd. Family Historian 7 (2024). https://www.family-historian.co.uk/.
  16. Individual Software. Family Tree Heritage (2023). https://www.individualsoftware.com/product/family-tree-heritage-platinum-9-2/.
  17. Incline Software. Ancestral Quest (2024). http://www.ancquest.com/index.htm.
  18. Mancas C. “On the paramount importance of database constraints”. J. Inf. Tech. & Soft. Eng. Henderson, NV 5.3 (2015): 1-4.
  19. Mancas C. “On the Preeminence of Data Quality”. Acta Scientific Computer Sciences 3.12 (2021b): 26-29.
  20. Mancas C, Dragomir S and Crasovschi L. “On Modeling First Order Predicate Calculus Using the Elementary Mathematical Data Model in MatBase DBMS”. In Proc. 25th IASTED Int. Conf. on Databases and App. (DBA 2003), ACTA Press, Calgary, Canada (2003): 1197-1202.
  21. Mancas C. “MatBase-a Tool for Transparent Programming while Modeling Data at Conceptual Levels”. In: Proc. 5th Int. Conf. on Comp. Sci. & Inf. Techn. (CSITEC 2019), AIRCC Pub. Corp. Chennai, India (2019): 15-27.
  22. Mancas C. “MatBase Metadata Catalog Management”. Acta Scientific Computer Sciences 2.4 (2020): 25-29.
  23. Mancas C and Dorobantu V. “On enforcing relational constraints in MatBase”. London Journal of Research in Computer Science and Technology 17.1 (2017): 39-45.
  24. Mancas C. “Algorithms for Key Discovery Assistance”. In: Repa, V., Bruckner, T. (eds). BIR 2016, Lecture Notes in Business Information Processing. Springer, Cham, Switzerland 261 (2016): 322-338.
  25. Mancas C. “MatBase E-RD Cycles Associated Non-Relational Constraints Discovery Assistance Algorithm”. In: Arai, K., Bhatia, R., Kapoor, S. (eds.), Intelligent Computing, Proc. 2019 Computing Conference, AISC Series. Springer, Cham, Switzerland 997.1 (2019): 390-409.
  26. Mancas C. “On Detecting and Enforcing the Non-Relational Constraints Associated to Dyadic Relations in MatBase”. J. of Electronic & Inf. Syst 2.2 (2020):1-8.
  27. Mancas C. “On Variable Geometry Database Keys and their Subkeys”. WJAETS 6.2 (2022): 71-80.
  28. Mancas C. “Matbase Autofunction Non-relational Constraints Enforcement Algorithms”. IJCSIT 11.5 (2019): 63-76.
  29. Mancas C. “On enforcing dyadic relationship constraints in MatBase”. WJAETS 09.02 (2023): 298-311.
  30. Mancas C. “On enforcing dyadic-type self-map constraints in MatBase”. IJFETR 05.01 (2023): 014-026.
  31. Mancas C. “On Enforcing Dyadic-Type Homogeneous Binary Function Product Constraints in MatBase”. JCSR 6.1 (2024): 31-42.
  32. Mancas C and Mancas DC. “On enforcing existence and non-existence constraints in MatBase”. PriMera Scientific Engineering 4.6 (2024): 04-12.
  33. Mancas C and Dragomir S. “MatBase Datalog Subsystem Metacatalog Conceptual Design”. In Proc. 8th IASTED Int. Conf. on Soft. Eng. and App. (SEA 2004), ACTA Press, Calgary, Canada (2004): 34-41.
  34. Mancas C. “On MatBase’s algorithm for preventing cycles in binary Cartesian function products”. WJAETS 7.1 (2022): 23-37.
  35. Chen PP. “The entity-relationship model: Toward a unified view of data”. ACM TODS 1.1 (1976):9-36.
  36. Thalheim B. “Entity-Relationship Modeling: Foundations of Database Technology”. Springer-Verlag, Berlin (2000).
  37. Gray PMD., et al. “The Functional Approach to Data Management”. Springer, Berlin Heidelberg, New York (2004).
  38. Mancas C and Dragomir S. “On the Equivalence between Entity-Relationship and Functional Data Modeling”. In Proc. 7th IASTED Int. Conf. on Soft. Eng. and App. (SEA 2003), ACTA Press, Calgary, Canada (2003): 335-340.
  39. Schultz P and Wisnesky R. Algebraic Data Integration. Expanded and corrected version of the paper published in J. Functional Programming, Cambridge Univ. Press 27 (2017): E24.
  40. Gosnell D and Broecheler M. “The Practitioner's Guide to Graph Data: Applying Graph Thinking and Graph Technologies to Solve Complex Problems”. O’Reilly Media, Inc., CA (2020).
  41. Neo4j. Get started with Neo4j (2024). https://neo4j.com/docs/getting-started/
  42. Microsoft. Azure Cosmos DB (2024). https://azure.microsoft.com/en-us/products/cosmos-db
  43. AWS. Amazon Neptune (2024). https://aws.amazon.com/neptune/
  44. Green T and Tannen V. “Models for incomplete and probabilistic information”. IEEE Data Engineering Bulletin 29.1 (2006): 17-24.
  45. Kenig B and Suciu D. “Integrity Constraints Revisited: From Exact to Approximate Implication”. In Proc. 23rd Intl. Conf. on DB Theory (ICDT 2020) 18 (2020).
  46. Roblot TK and Link S. “Possibilistic Cardinality Constraints and Functional Dependencies”. In: Comyn-Wattiau, I. et al. (eds.) Conceptual Modeling. ER 2016. LNCS, Springer, Cham 9974 (2016): 133-148.
  47. NASA. EOSCUBE: A Constraint Database System for High-Level Specification and Efficient Generation of EOSDIS Products. Phase 1; Proof-of-Concept. NASA, Washington D.C (2019).
  48. Morgan T. “Business Rules and Information Systems: Aligning IT with Business Goals”. Addison-Wesley Professional, Boston, MA (2002).
  49. von Halle B and Goldberg L. “The Business Rule Revolution. Running Businesses the Right Way”. Happy About, Cupertino, CA (2006).
  50. IBM Corp. Introducing Operational Decision Manager (2024). https://www.ibm.com/docs/en/odm/8.12.0?topic=manager-introducing-operational-decision.
  51. Dyer L., et al. (Scaling BPM Adoption from Project to Program with IBM Business Process Manager 2012). http://www.redbooks.ibm.com/redbooks/pdfs/sg247973.pdf.
  52. Red Hat Customer Content Services. Getting Started with Red Hat Business Optimizer (2024). https://access.redhat.com/documentation/en-us/red_hat_decision_manager/7.1/html/getting_started_with_red_hat_business_optimizer/index.
  53. Agiloft Inc. Agiloft Reference Manual (2022). https://www.agiloft.com/documentation/agiloft-developer-guide.pdf.
  54. The Data Appeal. Geographic Data (2024). https://datarade.ai/data-products/the-data-appeal-geographic-data-api-dataset-251m-poi-m-the-data-appeal-company.
  55. Insider Media Ltd. Top Companies Database (2024). https://www.insidermedia.com/membership/sample-data.
  56. Extensions Hub Yellow Pages Scraper (2024). https://chromewebstore.google.com/detail/yellow-pages-scraper-yell/mmibhnbgahgckfofpindpgaphgocbkhi?pli=1.
  57. DataForSEO. Amazon Product Database (2024). https://dataforseo.com/databases/amazon-database.