Towards a formalization of budgets

TL;DR

This paper develops a formal algebraic theory of rational budgets using the tuplix calculus, emphasizing totalized models for rational numbers, demonstrated through a university department case study.

Contribution

It introduces a novel formal algebraic framework for rational budgets based on the tuplix calculus, addressing the need for rigorous budget modeling.

Findings

The theory effectively models rational budgets with totalized rational numbers.

Application to a university department budget illustrates practical utility.

Highlights the importance of totalized models for accurate budget representation.

Abstract

We go into the need for, and the requirements on, a formal theory of budgets. We present a simple algebraic theory of rational budgets, i.e., budgets in which amounts of money are specified by functions on the rational numbers. This theory is based on the tuplix calculus. We go into the importance of using totalized models for the rational numbers. We present a case study on the educational budget of a university department offering master programs.