Positive reasoning and negative reasoning have been applied to be very useful in practice as clear from the record of many real life applications, especially in medicine. These reasoning mechanisms play important role in cutting the search space, reflecting experts' decision, supporting decision by the cooperation of experts and computers. This paper proposes the concepts of extended negative rule, minimal rule and explores their properties. Furthermore, an algorithm for finding all minimal positive rule and minimal negative rule is given. This algorithm is effective to discover positive and negative rules which have not redundant formula. These rules support to deduce the other important positive and negative rules. Experiments are carried out on data sets of UCI machine learning repository to analyze the performance study.
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