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In this work we present a new rule-discovery method for distributed information system. DIS is the system that connects a number of information systems using network communication technology. This communication can be driven by request for knowledge needed to predict for maximal optimization which missing values can be replaced. In this work we recall the notion of a distributed information system to talk about handling semantic inconsistencies between sites. Semantic inconsistencies are due to different interpretations of attributes and their values on the concepts level among sites. Different interpretations can be also linked with a different way of treating null values among sites. Some attributes might be just hidden because of the security reason. In such case we have to be certain that the missing data can not be reconstructed from the available data by any known null value imputation method and that some information in IS can not be uncovered as well. Assuming that one attribute is hidden at one of the sites of DIS we will try to reconstruct this attribute. In this paper we will also show which values have to be hidden from users to guarantee that the hidden attribute can not be reconstructed.