In most database systems with production rule facilities, rules respond to operations on centralized data and rule processing is performed in a centralized, sequential fashion. In parallel and distributed database environments, for maximum autonomy it is desirable for rule processing to occur separately at each site ornode, responding tooperations on data at that site. However, since rules at one site may read or modify data and interact with rules at other sites, independent rule processing at each site may be impossible or incorrect. We describe mechanisms that allow rule processing to occur separately at each site and guarantee correctness: parallel or distributed rule processing is provably equivalent to rule processing in the corresponding centralized environment. Our mechanisms include locking schemes, communication protocols, and rule restrictions. Based on a given parallel or distributed environment and desired level of transparency, the mechanisms may be combined or may be use...