Lossless outer joins with incomplete information

In the relational model of data, Rissanen's Theorem provides the basis for the usual normalization process based on decomposition of relations. However, many difficulties occur if information is incomplete in databases and nulls are required to represent missing or unknown data. We concentrate here on the notion of outer join and find some reasonable conditions to guarantee that outer join will also preserve the lossless join property for two relations. Next we provide a generalization of this result to several relations.