The Syntax of the Accounting Language: A First Step

TL;DR

This paper explores the algebraic structure of T accounts and double entry bookkeeping, proposing a formal language framework to reconcile different measurement perspectives in accounting.

Contribution

It extends Ellerman's propositions by framing accounting procedures as a formal language, facilitating the reconciliation of stock and flow measurement perspectives.

Findings

T accounts and DEB have a compatible algebraic structure.

A formal language approach can unify different measurement perspectives.

The paper provides a foundational step for further algebraic analysis in accounting.

Abstract

We review and interpret two basic propositions published by Ellerman (2014). The propositions address the algebraic structure of T accounts and double entry bookkeeping (DEB). The paper builds on this previous contribution with the view of reconciling the two, apparently dichotomous, perspectives of accounting measurement: the one that focuses preferably on the stock of wealth and to the one that focuses preferably on the flow of income. The paper claims that T-accounts and DEB have an underlying algebraic structure suitable for approaching measurement from either or both perspectives. Accountants preferences for stocks or flows can be framed in ways which are mutually consistent. The paper is a first step in addressing this consistency issue. It avoids the difficult mathematics of abstract algebra by applying the concept of syntax to accounting numbers such that the accounting procedure qualifies as a formal language with which accountants convey meaning.