We study hidden-variable models from quantum mechanics, and their abstractions in purely probabilistic and relational frameworks, by means of logics of dependence and independence, based on team semantics. We show that common desirable properties of hidden-variable models can be defined in an elegant and concise way in dependence and independence logic. The relationship between different properties, and their simultaneous realisability can thus been formulated and a proved on a purely logical level, as problems of entailment and satisfiability of logical formulae. Connections between probabilistic and relational entailment in dependence and independence logic allow us to simplify proofs. In many cases, we can establish results on both probabilistic and relational hidden-variable models by a single proof, because one case implies the other, depending on purely syntactic criteria. We also discuss the no-go theorems by Bell and Kochen-Specker and provide a purely logical variant of the latter, introducing non-contextual choice as a team-semantical property.

翻译：我们研究量子力学的隐性可变模型,及其在纯粹概率和关系框架中的抽象性,其依据是团队语义的依附性和独立性逻辑。我们表明,在依赖性和独立性逻辑中,可以以优雅和简洁的方式界定隐性可变模型的共同可取特性;因此,不同属性之间的关系及其同时的可变性可以在纯粹逻辑层面上得到制定和证明,作为逻辑公式的必然和可比较性问题。依赖性和独立性的概率性与关联性必然因素之间的联系使我们得以简化证据。在许多情况下,我们可以通过单一证据来确定概率和关联性隐性模型的结果,因为一个案例意味着另一个案例,取决于纯粹的合成标准。我们还讨论贝尔和科钦-斯派克的禁标,并提供后者的纯逻辑变式,将非理论性选择引入团队模拟属性。