 It is worth pointing out here that we do not require, in general, that \(Y\) and \(Z\) are disjoint. Because of the downwards closure property, which we will discuss soon, this additional condition would make no difference for the semantics of dependence logic proper; but in the case of certain extensions and variants of dependence logic, that additional requirement would conflict with the principle of locality according to which the satisfaction conditions of an expression depend only on the values of the variables which occur free in it (Galliani 2012).