We introduce some new logics of imperfect information by adding atomic formulas corresponding to inclusion and exclusion dependencies to the language of first order logic. The properties of these logics and their relationships with other logics of imperfect information are then studied. Furthermore, a game theoretic semantics for these logics is developed. As a corollary of these results, we characterize the expressive power of independence logic, thus answering an open problem posed in (Grädel and Väänänen, 2010).

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We prove that the expressive power of first-order logic with team semantics plus contradictory negation does not rise beyond that of first-order logic (with respect to sentences), and that the totality atoms of arity k + 1 are not definable in terms of the totality atoms of arity k. We furthermore prove that all first-order nullary and unary dependencies are strongly first order, in the sense that they do not increase the expressive power of first order logic if added to it.