Decision-Relative Observation Quotients for Sequential Control
This paper studies when a reinforcement-learning system should acquire additional information before acting. It introduces causal observability: a finite criterion for whether an observation regime preserves the intervention-relevant distinctions needed for a declared decision. The central result shows that observation refinement has strictly greater sequential control value when a coarse observation aliases cases requiring incompatible continuation-optimal actions, and it yields a cost-sensitive rule for deciding when refinement is worthwhile. The paper formalizes this criterion in Lean and evaluates its one-step decision projection on controlled partially observable structural causal models, with MiniGrid used as an external protocol check.