Causal Relevance as Predictive Utility: A Directional and State-Dependent Framework

We introduce the Causal Relevance Index (CRI), a measure of predictive utility contributed by external inputs to a dynamical system. Unlike traditional approaches such as mutual information or Granger causality, CRI quantifies the actual reduction in prediction error.

We further define a Directionality Index (DI), capturing asymmetry in predictive usefulness between forward and reverse configurations.

Our results show that causality is not binary, but a continuous and state-dependent quantity. We also demonstrate that traditional methods may detect spurious causality, while CRI remains sensitive only to meaningful predictive contributions.

Causality is not the presence of information, but the usefulness of information.