Safe Dependency Atoms and Possibility Operators in Team Semantics
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I consider the question of which dependencies are safe for a Team Semantics-based logic FO( D), in the sense that they do not increase its expressive power when added to it. I show that some dependencies, like totality, non-constancy and non-emptiness, are safe for all logics FO( D), and that other dependencies, like constancy, are not safe for FO( D) for some choices of D despite being strongly first order (that is, safe for FO(∅)). I furthermore show that the possibility operator ϕ, which holds in a team if and only if ϕ holds in some nonempty subteam, can be added to any logic FO( D) without increasing its expressive power.
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