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Rule interpreters usually start with an initial database and perform the inference procedure in cycles, ending with a final datahase. In a real time enVlrOnl1lent it is possible to receive IIpdates to the initial database after the inference procedure has started or even after it has ended. \Ve present an algorithm for ll1cremental mallltenance of the deductive database in the presence of such updates. Interestingly, the sallle algorithm is llseful for parallel and distributed rule processlllg in the following sense. \\'hen the processors evaluating a program operate asynchronously. then they may have different t'letL'S of the database. The incremental maintenance procedure we pre~ent can be used to synchronize these views.

Incremental evaluation of rules and its relationship to parallelism