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 for more than one team simultaneously. We begin by defining a novel polyteam variant of dependence atoms and give a finite axiomatization for the associated implication problem. We also characterize the expressive power of poly-dependence logic formulae 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.