A distinctive property of relational database systems is the ability to perform data updates and queries in atomic blocks called transactions, with the well known ACID properties. To date, the ability of systems performing reasoning to maintain the ACID properties, even over data held within a relational database, has been largely ignored. This article studies an approach to reasoning over data from OWL 2 RL ontologies held in a relational database, where the ACID properties of transactions are maintained. Taking an incremental approach to maintaining materialised views of the result of reasoning, the approach is demonstrated to support a query and reasoning performance comparable to or better than other OWL reasoning systems, yet adding th...