Propositional Dependence and Independence Logic

I will give a quick introduction to team semantics i.e. semantics in which meaning of formulas is defined relative to a set of assignments (valuations) rather than relative to a single assignment (valuation). I use this semantics in the context of propositional logic and describe a hierarchy of extensions of classical propositional logic obtained by adding distinguished relations between propositional atoms, such as dependence, inclusion and independence. I give semantic characterizations as well as complete axiomatizations of several such extensions, and will also list some open problems. This is joint work with Fan Yang.