On Enforcing Satisfiable, Coherent, and Minimal Sets of Self-Map Constraints in MatBase

TL;DR

This paper introduces a formal framework and an efficient algorithm for enforcing consistent, minimal sets of self-map constraints in a novel database system, ensuring data integrity and coherence.

Contribution

It provides a rigorous formalization of self-map constraints and a pseudocode algorithm for their enforcement in the MatBase system, guaranteeing satisfiability, coherence, and minimality.

Findings

Algorithm guarantees constraint set properties

Ensures fast, sound, complete enforcement

Demonstrates practical implementation in MatBase

Abstract

This paper rigorously and concisely defines, in the context of our (Elementary) Mathematical Data Model ((E)MDM), the mathematical concepts of self-map, composite mapping, totality, one-to-oneness, non-primeness, ontoness, bijectivity, default value, (null-)reflexivity, irreflexivity, (null-)symmetry, asymmetry, (null-)idempotency, anti-idempotency, (null-)equivalence, acyclicity, (null-)representative system mapping, the properties that relate them, and the corresponding corollaries on the coherence and minimality of sets made of such mapping properties viewed as database constraints. Its main contribution is the pseudocode algorithm used by MatBase, our intelligent database management system prototype based on both (E)MDM, the relational, and the entity-relationship data models, for enforcing self-map, atomic, and composite mapping constraint sets. We prove that this algorithm guarantees the satisfiability, coherence, and minimality of such sets, while being very fast, sound, complete, and minimal. In the sequel, we also presented the relevant MatBase user interface as well as the tables of its metacatalog used by this algorithm.