PriMera Scientific Engineering (ISSN: 2834-2550)

Research Article

Volume 8 Issue 6

Extending the (Elementary) Mathematical Data Model and MatBase with Two New Constraint Types: Inexistence and Anti-existence

Christian Mancas*

May 31, 2026

DOI : 10.56831/PSEN-08-272

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Abstract

This research paper introduces two new constraint types and four subtypes of database constraints added to our (Elementary) Mathematical Data Model, which are the duals of the existence and non-existence ones. They are formally defined, characterized, and exemplified with real-life instances. The well-formedness, satisfiability, coherence, and minimality of sets of all 7 subtypes of existence constraints are studied. Corresponding SQL-embedded pseudocode algorithms for managing such sets are provided and proved to be of constant complexity, sound, complete, and optimal. Also provided are algorithms for enforcing these new types of constraints, called inexistence and anti-existence. Their characterization proves that they have linear complexity in the sum of the arities of the function (Cartesian products) involved, and are sound, complete, and optimal as well. All these algorithms were implemented in both versions of our intelligent data and knowledge base management system prototype MatBase, which automatically generates code for enforcing all the 7 subtypes of existence constraints.

Keywords: (Elementary) Mathematical Data Model; MatBase; anti-existence constraint; inexistence constraint; existence constraint; non-existence constraint; conceptual data modeling; database design; non-relational constraints enforcement; null values management

References

  1. Mancas C. “On Enforcing Existence and Non-Existence Constraints in MatBase”. PriMera Scientific Engineering 4.6 (2024): 04-12. 
  2. Mancas C. “The (Elementary) Mathematical Data Model revisited”. PriMera Scientific Engineering 5.4 (2024): 78-91. 
  3. Mancas C. “MatBase Metadata Catalog Management”. Acta Scientific Computer Sciences 2.4 (2020): 25-29. 
  4. Chen PP. “The entity-relationship model. Toward a unified view of data”. ACM TODS 1.1 (1976): 9-36.
  5. Thalheim B. “Entity-Relationship Modeling: Foundations of Database Technology”. Springer-Verlag, Berlin, Germany (2000).
  6. Mancas C. “Conceptual Data Modeling and Database Design: A Completely Algorithmic Approach. Volume 1: The Shortest Advis able Path”. Apple Academic Press, Waretown, NJ (2015).
  7. Codd EF. “A relational model for large shared data banks”. CACM 13.6 (1970): 377-387.
  8. Abiteboul S, Hull R and Vianu V. “Foundations of Databases”. Addison-Wesley, Reading, MA (1995).
  9. Codd EF. “The 12 rules”. (1985) https://reldb.org/c/index.php/twelve-rules/
  10. Codd EF. “Extending the database relational model to capture more meaning”. ACM TODS 4.4 (1979): 397-434.
  11. Thalheim B and Schewe KD. “NULL ‘Value’ Algebra and Logic”. In: Heimbrrger A. et al. (Eds.). Information Modelling and Knowledge Bases XXII (2011): 354-367.
  12. Maier D. “Theory of Relational Databases”. Computer Science Press, U.S.A (1983).
  13. Mancas C. “MatBase Constraint Sets Coherence and Minimality Enforcement Algorithms”. In: Benczur A., Thalheim B., Horvath T. (Eds). Advances in DB and Information Systems, LNCS 11019 (2018): 263-277. 
  14. Mancas C. “Teaching Enforcement of Satisfiable, Coherent, and Minimal Database Constraint Sets Associated with Function Products to Computer Science M.Sc. Students”. Chapter 10 from Daimi K. (ed.). “Emerging Trends in Computer Science and Computer Engineering Education”. Springer Nature, Cham, Switzerland (2026).