Book/Algebraic Models for Accounting Systems

Rambaud, Salvador Cruz; Pérez, José García; Nehmer, Robert A.; Robinson, Derek J S Robinson (2010). Algebraic Models for Accounting Systems. local page: Cambridge at the University Press. ISBN 978-981-4287-11-1. 

Research Synopsis

This book is being used as the main reference book to integrate my work on Algebra of Systems with pragmatic accounting practice. It turns out that accounting, as described by Prof. Gautam Dasgupta, should be also be described as abstract-counting. For digitally realize these accounting models, one might to refer to the book Digital Accounting: The Effects of the Internet and ERP on Accounting. The idea of The Accounting System as an Algebraic Automaton can also be found in this paper.

Excerpts

The book presents and develops a proof-based, algebraic ap- proach to the study of accounting systems. The analysis provides a description of single firms in terms of abstract algebraic objects such as automata. It concentrates on the process of producing infor- mation from data provided by the environment through the double- entry system. This process, although considered by many to be the core of accounting, has often been ignored in accounting research. ... The reduction of accounting systems to these types of languages will lead to a much stronger method of modeling information systems.

— Algebraic Models for Accounting Systems, Section 1.2, Page 8

On a final note, recently Demski has tried to answer to the question “Is accounting an academic discipline?” After analyzing the meaning of “discipline” and “academic”, his immediate conclusion was negative. However, Demski was not pleased with this answer and therefore he preferred to analyze the ten indicators of the ac- counting as an academic discipline, ending with “... accounting is not today an academic discipline; it is an ever-narrowing insular vocational enterprise. But it could and should, in my opinion, be an academic discipline. Even if you disagree with my assessment, you should consider whether the state of academic accounting is, in your view, what it could and should be. The stakes in this game are enormous and serious”.

— Algebraic Models for Accounting Systems, Page 2 and 3, Paragraph 3,

Principle Data Structures in Accounting Systems

1. Balance Vector
2. Directed Graph (or Digraph)
3. Automaton (State Machine)
4. Monoid

Decision problems for Accounting Systems

1. Decide whether a given transaction is allowable.
2. Decide whether a given balance vector is allowable.
3. Decide whether a given transaction is feasible.
4. Decide whether a final balance vector could actually have occurred by correctly applying a sequence of allowable transactions to a given initial balance vector.
5. Decide whether two accounting systems on the same account set are equivalent, i.e., if they have the same feasible transactions and hence the same monoid.
6. Decide whether a given accounting system is of a specific type such as those described in Chapter 7.