A probabilistic approach is introduced to classify and diagnose erroneous rules of operation resulting from a variety of misconceptions ("bugs") in a procedural domain of arithmetic. The model is contrasted with the deterministic approach which has commonly been used in the field of artificial intelligence, and the advantage of treating the variability of errors in response is shown. Item response theory (IRT) is a useful model in integrating the theory of cognitive processes with educational practice. Erroneous rules of operation in signed-number subtraction problems can be represented as points in a geometric space by utilizing IRT (rule space). This approach seems promising in assessing the state of knowledge as reflected by erroneous rules and in utilizing the information obtained from behaviors of "bugs." (Author/PN)