The semi-Join of two relations R and S is denoted as R SJ_FS, where F is a formula which specifies a join predicate. A semi-join is derived from projection and join as follows:

where Attr(R) denotes the set of all attributes of R. Thus, the result of the semi-join is a subset of the tuples of R, constituted by those tuples which give a contribution to the join of R with S.