I consider the question of which dependencies are safe for a Team Semantics-based logic $FO(\mathcal{D})$, in the sense that they do not increase its expressive power over sentences when added to it. I show that some dependencies, like totality, non-constancy and non-emptiness, are safe for all logics $FO(\mathcal{D})$, and that other dependencies, like constancy, are not safe for $FO(\mathcal{D})$ for some choices of $\mathcal{D}$ despite being strongly first order (that is, safe for $FO(\varnothing )$). 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 $\text{FO}(\mathcal{D})$ without increasing its expressive power over sentences.

我考虑以下问题：对于基于团队语义的逻辑，哪些依赖项是安全的$FØ（\mathcal{d}）$，从某种意义上讲，它们在添加到句子时不会增加其对句子的表达能力。我证明了某些依赖关系，例如总计，非恒定性和非空性，对于所有逻辑都是安全的$FØ（\mathcal{d}）$，并且其他依赖项（例如恒定性）对于 $FØ（\mathcal{d}）$ 对于某些选择 $\mathcal{d}$ 尽管是强烈的第一订单（也就是说，对于 $FØ（\varnothing ）$）。我还表明，可能运营商⋄ φ，后者持有一支球队当且仅当φ持有一些非空的工作小组，可以添加到任何逻辑$\text{FO}（\mathcal{d}）$ 而不增加其对句子的表达能力。