The Relativity of Causal Knowledge
This work addresses the need for collaborative causal reasoning in AI, though it appears incremental as it builds on existing mathematical frameworks.
The paper tackles the problem of imperfect and subjective structural causal models by introducing the relativity of causal knowledge, using category and sheaf theory to encode models with convex probability measures and define relative causal knowledge formally.
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.