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As one of the basic problems of knowledge discovery and data analysis, knowledge reduction can make the discovery of implicit knowledge in data easier and the representation simpler. In this paper, relations of attribute reduction between object and property oriented formal concept lattices are discussed. And beautiful results are obtained that attribute reducts and attribute characteristics in the two concept lattices are the same based on new approaches to attribute reduction by means of irreducible elements. It turns out to be meaningful and effective in dealing with knowledge reduction, as attribute reducts and attribute characteristics in the object and property oriented formal concept lattices can be acquainted by only investigating one of the two concept lattices.