Equational zero vector accounting systems, based on duality principles and the double-entry model, were designed as ontological control systems to help prevent and detect fraud and errors inherent in non-equational, single-entry systems. Non-equational systems lend themselves to fraud and errors to a larger degree because the internal control inherent in an equational zero vector system has no substitute. We use an analytical analysis methodology to show that an equational zero vector system provides superior inherent internal control over data completeness and data reliability. In the accounting information systems area, the most popular modern non-equational system, the resource-event-agent model, is increasingly being promoted as a replacement for the equational zero vector accounting system. We contend that, although non-equational accounting system frameworks can be modelled with controls, they do not achieve the degree of control inherent in an equational zero vector accounting system without becoming an equational zero vector accounting system. Copyright © 2010 Inderscience Enterprises Ltd.