The theory of joins in relational data bases

Answering queries in a relational database often requires that the natural join of two or more relations be computed. However, not all joins are semantically meaningful. This paper gives an efficient algorithm to determine whether the join of several relations is semantically meaningful (lossless) and an efficient algorithm to determine whether a set of relations has a subset with a lossy join. These algorithms assume that all data dependencies are functional. Similar techniques also apply to the case where data dependencies are multivalued.