Abstract Within the field of causal inference, it is desirable to learn the structure of causal relationships holding between a system of variables from the correlations that these variables exhibit; a sub-problem of which is to certify whether or not a given causal hypothesis is compatible with the observed correlations. A particularly challenging setting for assessing causal compatibility is in the presence of partial information; i.e. when some of the variables are hidden/latent. This paper introduces the possible worlds framework as a method for deciding causal compatibility in this difficult setting. We define a graphical object called a possible worlds diagram, which compactly depicts the set of all possible observations. From this construction, we demonstrate explicitly, using several examples, how to prove causal incompatibility. In fact, we use these constructions to prove causal incompatibility where no other techniques have been able to. Moreover, we prove that the possible worlds framework can be adapted to provide a complete solution to the possibilistic causal compatibility problem. Even more, we also discuss how to exploit graphical symmetries and cross-world consistency constraints in order to implement a hierarchy of necessary compatibility tests that we prove converges to sufficiency.

中文翻译：

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因果兼容性的组合解决方案

摘要 在因果推理领域，需要从变量表现出的相关性中学习变量系统之间的因果关系结构；它的一个子问题是证明给定的因果假设是否与观察到的相关性兼容。评估因果兼容性的一个特别具有挑战性的设置是存在部分信息；即当某些变量隐藏/潜在时。本文介绍了可能世界框架作为在这种困难环境中决定因果兼容性的一种方法。我们定义了一个称为可能世界图的图形对象，它简洁地描述了所有可能观察的集合。从这个构造中，我们使用几个例子明确地展示了如何证明因果不相容。实际上，我们使用这些结构来证明其他技术无法证明的因果不相容性。此外，我们证明了可能世界框架可以适用于为可能的因果兼容性问题提供完整的解决方案。更重要的是，我们还讨论了如何利用图形对称性和跨世界一致性约束来实现我们证明收敛到充分性的必要兼容性测试的层次结构。