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Polyteam Semantics

  • Miika Hannula
  • Juha Kontinen
  • Jonni VirtemaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10703)

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.

Keywords

Team semantics Dependency theory Expressive power 

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.University of AucklandAucklandNew Zealand
  2. 2.University of HelsinkiHelsinkiFinland
  3. 3.Hasselt UniversityHasseltBelgium

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