Causality is a central concept in a wide range of research areas, yet there is still no universally agreed axiomatisation of causality. We view causality both as an extension of probability theory and as a study of \textit{what happens when one intervenes on a system}, and argue in favour of taking Kolmogorov's measure-theoretic axiomatisation of probability as the starting point towards an axiomatisation of causality. To that end, we propose the notion of a \textit{causal space}, consisting of a probability space along with a collection of transition probability kernels, called \textit{causal kernels}, that encode the causal information of the space. Our proposed framework is not only rigorously grounded in measure theory, but it also sheds light on long-standing limitations of existing frameworks including, for example, cycles, latent variables and stochastic processes.

翻译：因果性是众多研究领域的核心概念，但目前仍缺乏普遍认同的因果性公理化体系。我们将因果性既视为概率论的延伸，也视为对"干预系统时会发生什么"的研究，并主张以科尔莫戈罗夫的概率测度论公理化作为因果性公理化的出发点。为此，我们提出"因果空间"概念，它由概率空间及一组称为"因果核"的转移概率核构成，这些因果核编码了空间中的因果信息。我们提出的框架不仅严格建立在测度论基础之上，还揭示了现有框架中长期存在的局限性，例如循环结构、潜变量和随机过程等问题。