 Jouko Väänänen (2007) formulated a new approach to IF logic that he dubbed dependence logic \((\mathbf{DL})\); for further work on \(\mathbf{DL}\), see e.g. Kontinen et al. (2013). The syntax of \(\mathbf{DL}\) is obtained from that of \(\mathbf{FO}\) by allowing atomic formulas of the following special form: 