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The purpose of this study is to introduce a probabilistic approach to classify and diagnose erroneous rules of operation resulting from a variety of misconceptions ('bugs') in a procedural domain of arithmetic. The model contrasts the deterministic approach which has commonly been used in the field of artificial intelligence and shows an advantage in treating the variability of errors in responses. Item response theory (IRT) turned out to be a useful model in integrating the theory of cognitive processes with educational practice. In this paper, erroneous rules of operation in signed-number subtraction problems are represented as points in a geometric space by utilizing IRT. We named this space '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 into educational evaluation.