Polyteam Semantics
  Team semantics is the mathematical framework of modern logics of dependence
and independence in which formulae are interpreted by sets of assignments
(teams) instead of single assignments as in first-order logic. In order to
deepen the fruitful interplay between team semantics and database dependency
theory, we define "Polyteam Semantics" in which formulae are evaluated over a
family of teams. We begin by defining a novel polyteam variant of dependence
atoms and give a finite axiomatisation for the associated implication problem.
We also characterise the expressive power of poly-dependence logic by
properties of polyteams that are downward closed and definable in existential
second-order logic (ESO). The analogous result is shown to hold for
poly-independence logic and all ESO-definable properties.
