The rule space model permits measurement of cognitive skill acquisition, diagnosis of cognitive errors, and detection of the strengths and weaknesses of knowledge possessed by individuals. Two ways to classify an individual into his or her most plausible latent state of knowledge include: (1) hypothesis testing--Bayes' decision rules for minimum errors; and (2) bug distribution--how bugs, incorrect rules used to solve problems, are clustered and related. A 40-item test containing subtraction of fraction items was given to 535 junior high school students. A computer program was used on the PLATO system to diagnose erroneous rules of operation. Two common erroneous problem-solving rules were used to illustrate the rule space model. The results were then compared with the results obtained from a conventional artificial intelligence approach. (GDC)