Title: Polyteam Semantics,
Abstract: 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.