Dense relations are determined by their endomorphism monoids

We introduce the class of dense relations on a set X and prove that for any finitary or infinitary dense relation rho on X, the relational system (X, rho) is determined up to semi-isomorphism by the monoid End (X, rho) of endomorphisms of (X, rho). In the case of binary relations, a, semi-isomorphism is an isomorphism or an anti-isomorphism.