It has been widely recognized that many future database applications, including engineering processes, manufacturing and communications, will require some kind of rule based reasoning. It is conceivable that large knowledge bases cannot, and perhaps should not, for space reasons, reside in main memory. In this paper we study methods for storing and manipulating large rule bases using relational database management systems. First, we provide a matching algorithm similar to the Rete Network used in OPS5, which can be used to efficiently identify applicable rules. The second contribution of this paper, is our proposal for concurrent execution strategies which surpass, in terms of performance, the sequential OPS5 execution algorithm. Since the problem of identifying applicable rules is the same as the problems of supporting triggers and materialized views in a conventional relational database system, our approach provides some new ideas for the solution of these problems as well. Finally, the proposed method is fully parallelizable, which makes its use even more attractive, as it can be used in parallel computing environmenta.