Dependence and

We introduce an atomic formula ~y ⊥~x ~z intuitively saying that the variables ~y are independent from the variables ~z if the variables ~x are kept constant. We contrast this with dependence logic D based on the atomic formula =(~x, ~y), actually equivalent to ~y ⊥~x ~y, saying that the variables ~y are totally determined by the variables ~x. We show that ~y ⊥~x ~z gives rise to a natural logic capable of formalizing basic intuitions about independence and dependence. We show that ~y ⊥~x ~z can be used to give partially ordered quantifiers and IF-logic an alternative interpretation without some of the shortcomings related to so called signaling that interpretations using =(~x, ~y) have.