Probabilistic Dependence Logic Pietro Galliani Abstract: Given a finite model M, it is possible to associate to every sentence φ of Backslash Logic and Dependence Logic the value of the corresponding imperfect information game H(φ), that is, the best average payoff that the Verifier can guarantee when both players are allowed to play random moves. Hodges' compositional semantics can then be adapted to this new logic, and the value of atomic dependence formulas in the resulting framework is seen to correspond to one of Kivinen and Mannila's measures of approximate functional dependency.