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.
This research was supported by a Marsden grant from Government funding, administered by the Royal Society of New Zealand, and grants 292767 and 308712 of the Academy of Finland.
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Hannula, M., Kontinen, J., Virtema, J. (2018). Polyteam Semantics. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2018. Lecture Notes in Computer Science(), vol 10703. Springer, Cham. https://doi.org/10.1007/978-3-319-72056-2_12
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