A Measure-Theoretic Axiomatisation of Causality

Author:

Junhyung Park, Simon Buchholz, Bernhard Schölkopf, Krikamol Muandet

Keyword:

Computer Science, Artificial Intelligence, Artificial Intelligence (cs.AI), Statistics Theory (math.ST)

journal:

date:

2023-05-18 16:00:00

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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