The Relativity of Causal Knowledge

Gabriele D’Acunto, Claudio Battiloro
Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, PMLR 286:863-881, 2025.

Abstract

Recent advances in *artificial intelligence* reveal the limits of purely predictive systems and call for a shift toward causal *and* collaborative reasoning. Drawing inspiration from the revolution of Grothendieck in mathematics, we introduce the *relativity of causal knowledge*, which posits structural causal models (SCMs) are inherently imperfect, subjective representations embedded within networks of relationships. By leveraging category theory, we arrange SCMs into a functor category and show that their observational and interventional probability measures naturally form convex structures. This result allows us to encode non-intervened SCMs with convex spaces of probability measures. Next, using sheaf theory, we construct the *network sheaf and cosheaf of causal knowledge*. These structures enable the transfer of causal knowledge across the network while incorporating interventional consistency and the perspective of the subjects, ultimately leading to the formal, mathematical definition of *relative causal knowledge*.

Cite this Paper

BibTeX
@InProceedings{pmlr-v286-d-acunto25a, title = {The Relativity of Causal Knowledge}, author = {D'Acunto, Gabriele and Battiloro, Claudio}, booktitle = {Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence}, pages = {863--881}, year = {2025}, editor = {Chiappa, Silvia and Magliacane, Sara}, volume = {286}, series = {Proceedings of Machine Learning Research}, month = {21--25 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v286/main/assets/d-acunto25a/d-acunto25a.pdf}, url = {https://proceedings.mlr.press/v286/d-acunto25a.html}, abstract = {Recent advances in *artificial intelligence* reveal the limits of purely predictive systems and call for a shift toward causal *and* collaborative reasoning. Drawing inspiration from the revolution of Grothendieck in mathematics, we introduce the *relativity of causal knowledge*, which posits structural causal models (SCMs) are inherently imperfect, subjective representations embedded within networks of relationships. By leveraging category theory, we arrange SCMs into a functor category and show that their observational and interventional probability measures naturally form convex structures. This result allows us to encode non-intervened SCMs with convex spaces of probability measures. Next, using sheaf theory, we construct the *network sheaf and cosheaf of causal knowledge*. These structures enable the transfer of causal knowledge across the network while incorporating interventional consistency and the perspective of the subjects, ultimately leading to the formal, mathematical definition of *relative causal knowledge*.} }
Endnote
%0 Conference Paper %T The Relativity of Causal Knowledge %A Gabriele D’Acunto %A Claudio Battiloro %B Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2025 %E Silvia Chiappa %E Sara Magliacane %F pmlr-v286-d-acunto25a %I PMLR %P 863--881 %U https://proceedings.mlr.press/v286/d-acunto25a.html %V 286 %X Recent advances in *artificial intelligence* reveal the limits of purely predictive systems and call for a shift toward causal *and* collaborative reasoning. Drawing inspiration from the revolution of Grothendieck in mathematics, we introduce the *relativity of causal knowledge*, which posits structural causal models (SCMs) are inherently imperfect, subjective representations embedded within networks of relationships. By leveraging category theory, we arrange SCMs into a functor category and show that their observational and interventional probability measures naturally form convex structures. This result allows us to encode non-intervened SCMs with convex spaces of probability measures. Next, using sheaf theory, we construct the *network sheaf and cosheaf of causal knowledge*. These structures enable the transfer of causal knowledge across the network while incorporating interventional consistency and the perspective of the subjects, ultimately leading to the formal, mathematical definition of *relative causal knowledge*.
APA
D’Acunto, G. & Battiloro, C.. (2025). The Relativity of Causal Knowledge. Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 286:863-881 Available from https://proceedings.mlr.press/v286/d-acunto25a.html.

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