A Measure-Theoretic Axiomatisation of Causality

• URL: http://arxiv.org/abs/2305.17139v3
• Date: Thu, 6 Jun 2024 09:06:33 GMT
• Title: A Measure-Theoretic Axiomatisation of Causality
• Authors: Junhyung Park, Simon Buchholz, Bernhard Schölkopf, Krikamol Muandet,
• Abstract summary: We argue in favour of taking Kolmogorov's measure-theoretic axiomatisation of probability as the starting point towards an axiomatisation of causality. Our proposed framework is rigorously grounded in measure theory, but it also sheds light on long-standing limitations of existing frameworks.
• Score: 55.6970314129444
• License: http://creativecommons.org/licenses/by/4.0/
• 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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