... Pre-test-based methods are, e.g., [48,50,78,54,55,25,37,66,24,64,65,59,60,22,61,58,23,26], including a few industrial attempts, e.g., [16,3]. Other methods provide simplifications that may require the availability of both the old and the new state, assuming that the database keeps track of the old state before committing an update, [82,83]. In [46], an adaptation of subsumption checking (called partial subsumption) is used to generate simplification as the "difference" (called residual ) between an integrity constraint and a clause representing an update. ...