Out of Scope, Still Active: Do Language Models Respect Reasoning Scope?

Large language models increasingly solve complex problems by exploring hypotheses, revising intermediate conclusions, and moving between local stages of reasoning. Such reasoning is hierarchical and requires selective carry-over: after a local stage ends, conclusions that remain supported should carry forward, while those supported only locally should stop guiding inference. We introduce reasoning with scope (RWS), an analytical framework based on scoped computation in programs, to study how LLMs carry information across reasoning stages. Across controlled settings and natural reasoning traces, information from a completed scope can continue to influence later reasoning, while still-supported conclusions can be weakened. Crossed tests show that models respond more strongly to where a conclusion was derived than to whether it remains supported. This pattern changes substantially when the same reasoning is expressed more rigorously as an executable program: in natural-language reasoning, models often treat supported and unsupported conclusions similarly, whereas under executable scope their behavior can differ by nearly 90 percentage points. Reliable reasoning therefore requires tracking not only what has been inferred, but also which inferences remain justified as reasoning moves across stages.