Belief Maintenance under Retraction in Large Language Models

Retracting an inferred belief requires withdrawing its support while reassessing the conclusions that depend on it. Such changes are nonmonotonic (NMR): removing one justification can invalidate a conclusion, restore an alternative, or enable a new inference. We investigate how large language models (LLMs) perform this belief maintenance by formalizing two procedures: editing an existing reasoning state and rebuilding it from revised information. Within a temporal argumentation framework, we compare these procedures under shared counterfactuals and support cuts. We establish conditions for agreement on belief values and show that identical current values can conceal differences in support histories that emerge under subsequent retraction. Using NMR-Retraction, we evaluate whether LLMs perform support withdrawal and belief revision or preservation in accordance with the semantics of each procedure. Experiments reveal substantial difficulties in downstream retraction and history-dependent revision, despite stronger performance in accepting counterfactual assumptions. Supervised fine-tuning improves performance on unseen graphs, showing that these maintenance capabilities can be strengthened through training. Together, these findings highlight the importance of procedural knowledge for reliable belief maintenance in LLM reasoning.