# A Probabilistic Calculus of Actions

arXiv: https://arxiv.org/abs/1302.6835 · HTML: https://mlsanity.com/paper/1302.6835/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2013.

## Built on by (most cited first, 14 of 14)

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- [The Minimal Search Space for Conditional Causal Bandits](https://mlsanity.com/paper/2502.06577/) (2025)
- [Learning by Analogy: A Causal Framework for Composition Generalization](https://mlsanity.com/paper/2512.10669/) (2025)
- [A Survey on Causal Representation Learning and Future Work for Medical Image Analysis](https://mlsanity.com/paper/2210.16034/) (2022)
- [CausalOps -- Towards an Industrial Lifecycle for Causal Probabilistic Graphical Models](https://mlsanity.com/paper/2308.01375/) (2023)
- [Causal Models for Growing Networks](https://mlsanity.com/paper/2504.01012/) (2025)
- [The Design and Composition of Structural Causal Decision Processes](https://mlsanity.com/paper/2605.02681/) (2026)

## Abstract (arXiv)

We present a symbolic machinery that admits both probabilistic and causal information about a given domain and produces probabilistic statements about the effect of actions and the impact of observations. The calculus admits two types of conditioning operators: ordinary Bayes conditioning, P(y|X = x), which represents the observation X = x, and causal conditioning, P(y|do(X = x)), read the probability of Y = y conditioned on holding X constant (at x) by deliberate action. Given a mixture of such observational and causal sentences, together with the topology of the causal graph, the calculus derives new conditional probabilities of both types, thus enabling one to quantify the effects of actions (and policies) from partially specified knowledge bases, such as Bayesian networks in which some conditional probabilities may not be available.