Reasoning involving notions of dependence and independence occurs in a variety of situations, and it is of interest to study dependence and independence as basic logical concepts in their own right. Indeed, this desideratum has been one motivation for the development of the "independence friendly logic" of Hintikka, and for the "dependence logic" programme of Väänänen. In the talk I will show that certain sheaf models naturally support an extension of classical logic with independence relations, leading to logical principles for reasoning about independence. No prior knowledge of sheaf theory will be assumed.