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arXiv · 2305.17139

A Measure-Theoretic Axiomatisation of Causality

Junhyung Park·Simon Buchholz·Bernhard Schölkopf·Krikamol Muandet
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Abstract

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.

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Junhyung Park, Simon Buchholz, Bernhard Schölkopf, Krikamol Muandet. 2023-05-19. A Measure-Theoretic Axiomatisation of Causality. https://arxiv.org/abs/2305.17139

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