Dependence and independence

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 y⃗ are totally determined by the variables x^→. We show that y ⃗⊥_x^→y^→ gives rise to a natural logic capable of formalizing basic intuitions about independence and dependence. We show that y ⃗⊥_x^→y^→ 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.