Dependence and Independence Erich Grädel, Jouko Väänänen Abstract: We introduce an atomic formula \vec{y} ⊥_\vec{x} \vec{z} intuitively saying that the variables \vec{y} are independent from the variables \vec{z} if the variables \vec{x} are kept constant. We contrast this with dependence logic D based on the atomic formula =(\vec{x}, \vec{y}), actually a special case of \vec{y} ⊥_\vec{x} \vec{z}, saying that the variables y are totally determined by the variables \vec{x}. We show that \vec{y} ⊥_\vec{x} \vec{z} gives rise to a natural logic capable of formalizing basic intuitions about independence and dependence. We show that \vec{y} ⊥_\vec{x} \vec{z} can be used to give partially ordered quantifiers and IF-logic a compositional interpretation without some of the shortcomings related to so called signaling that interpretations using =(\vec{x}, \vec{y}) have.