New Causal Models Address Cycles and Symmetric Constraints

The dominant framework for causal reasoning, Pearl's structural causal models (SCMs) based on directed acyclic graphs (DAGs), faces limitations when dealing with symmetric constraints and feedback loops. This research proposes an extension to address these structural restrictions, which are common in physical and economic systems. The paper introduces "causal zeros" to formalize symmetric constraints where causal direction only emerges under intervention, such as the ideal gas law. It also grounds both causal zeros and feedback cycles in "Causal Differential Equations" (CDEs), treating apparent instantaneous cycles as artifacts of suppressed time. This approach views the transient regime as an unrolled acyclic causal process, with causal zeros defining equilibrium manifolds. The work provides an extended do-calculus, identifiability conditions, and counterfactual semantics for these advanced causal models.