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We investigate the possibility to use update propagation methods for optimizing the evaluation of continuous queries. Update propagation allows for the efficient determination of induced changes to derived relations resulting from an explicitly performed base table update. In order to simplify the computation process, we propose the propagation of updates with different degrees of granularity which corresponds to an incremental query evaluation with different levels of accuracy. We show how propagation rules for diferent update granularities can be systematically derived, combined and further optimized by using Magic Sets. This way, the costly evaluation of certain subqueries within a continuous query can be systematically circumvented allowing for cutting down on the number of pipelined tuples considerably.