Complete logics for elementary team properties

In this paper, we introduce a logic based on team semantics, called FOT, whose expressive power is elementary, i.e., coincides with first-order logic both on the level of sentences and (possibly open) formulas, and we also show that a sublogic of FOT, called FOT?, captures exactly downward closed elementary (or first-order) team properties. We axiomatize completely the logic FOT, and also extend the known partial axiomatization of dependence logic to dependence logic enriched with the logical constants in FOT?.