The purpose of this study was to validate the results of cognitive diagnoses using the rule-space model and to demonstrate the usefulness of cognitive diagnoses for instruction. The results of the study strongly indicated that the rule-space model can effectively diagnose students' knowledge states and can point out ways for remediating their errors quickly with minimum effort. It was also found that the designing of instructional units for remediation can be effectively guided by the rule-space model, because the determination of all possible ideal item-score patterns, given an incidence matrix, is based on a tree structure of cognitive attributes, knowledge states, and items. (61pp.)