Classical constraint systems require that the set of variables which exist in a problem be known ab initio. However, there are some applications in which the existence of certain variables is dependent on conditions whose truth or falsity can only be determined dynamically. In this paper, we show how this conditional existence of variables can be handled in a mathematically well-founded fashion by viewing a constraint network as a set of sentences in free logic. Based on these ideas, we have developed, implemented and applied, a constraint language in which any sentence in full first-order free logic, about a many-sorted universe of discourse which subsumes the reals, is a well-formed constraint.