Behavior of relational databases is studied within the framework of Relational Discrete Event Systems (RDESes) and Models (RDEMs). Production system and recurrence equation RDEMs are introduced, and their expressive powers are compared. Non-deterministic behavior is defined for both RDEMs and the expressive power of deterministic and non-deterministic production rule programs is also compared. This comparison shows that non-determinism increases expressive power of production systems. A formal concept of a production system interpreter is defined, and several specific interpreters are proposed. One interpreter, called parallel deterministic, is shown to be better than others in many respects, including the conflict resolution module of OPS5.