Normalization by second order graphs: A visual alternative to simplify systems: A visual alternative to simplify systems

Abstract

This issue stems from the need for tools to analyze and make decisions around complex systems, where they apply the rules for linearly dependent sets, with the purpose of providing a visual tool, which serves to support complexity reduction processes. Two great precedents are Armstrong's Axioms, which has been applied from its publication to the present for database normalization, the other is set theory, a fundamental pillar of the Structured Query Language; based on them, together with the second-order logic, which adds qualifiers for subsets or properties, this work has been prepared, with an explanatory metrology with a qualitative approach, in an axiomatic system. As a result, a support tool has been provided to analyze complex systems naturally, by breaking cycles and detecting patterns, without interfering with existing models; however, for large systems it can be difficult to address it in its entirety, so it is recommended to divide by subsystems. With this work a technique has been accomplished, repeatable by anyone, but with a strong theoretical foundation. This work has great utility for the normalization of relational databases and an enormous potential for application in the design of systems beyond computational systems, it is also useful for understanding dependencies by their axiomatic nature.