A Measure-Theoretic Axiomatisation of Causality
This foundational work provides a rigorous mathematical basis for causality, impacting fields like statistics and AI, though it is incremental in building on probability theory.
The paper tackles the lack of a universally agreed axiomatisation of causality by proposing a measure-theoretic framework based on causal spaces and kernels, which addresses limitations like cycles and latent variables in existing approaches.
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.