A method to perform nonmonotonic relational rule computations is presented, called the split technique, The goal is to avoid redundant computations with rules that can insert and delete sets of tuples specified by the rule body. The method is independent of the control strategy that governs rule firing. Updatable relations are partitioned, as the computation progresses, into blocks of tuples such that tuples within a block are indiscernible from each other based on the computation so far. Results of previous rule firings are remembered as “relational equations” so that a new rule firing does not recompute parts of the result that can be determined from the existing equations. Seminaive evaluation falls out as a special case when all rules specify inserts. The method is amenable to parallelization.