Polyteam Semantics

Miika Hannula, Juha Kontinen, Jonni Virtema

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 ( $$\mathsf {ESO}$$ ). The analogous result is shown to hold for poly-independence logic and all $$\mathsf {ESO}$$ -definable properties.