Relational Mathematics Continued

TL;DR

This paper extends relational mathematics with new results on domain construction, relational calculus, and visualizations, broadening the theoretical framework and practical tools for relational reasoning.

Contribution

It introduces novel formulae for domain construction, a relational calculus for binary mappings, and visualizations, expanding the theoretical and practical scope of relational mathematics.

Findings

New formulae for existential and inverse image

A relational calculus for binary mappings

Visualizations illustrating relational concepts

Abstract

This is in some sense an addendum to the book Relational Mathematics by the first-named author. It originated from work on diverse other topics during which a lot of purely relational results with broad applicability have been produced. These include results on domain construction with novel formulae for existential and inverse image, a relational calculus for binary mappings, and the development of a formally derived relational calculus of Kronecker-, strict fork-, and strict join-operators. The many visualizations in this report make it also a scrap- and picture book for examples.