{"ID":2859827,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.04716","arxiv_id":"2510.04716","title":"Curved Boolean Logic: A Contextual Generalization of Propositional Logic with Algorithmic Consequences","abstract":"Curved Boolean Logic (CBL) generalizes propositional logic by allowing local truth assignments that do not extend to a single global valuation, analogous to curvature in geometry. We give equivalent sheaf and exclusivity-graph semantics and a context-aware proof calculus that is conservative in the flat limit. We formalize CBL-SAT and basic complexity (NP-complete in general) and present operational operators (CBL-AC and CBL-CONS) that prune contradictions earlier on classical hardware. We model noise with iid, AR(1)-correlated, and adversarial bounded perturbations and provide permutation-based significance with Benjamini-Hochberg FDR control. A Colab-ready notebook (ancillary files) regenerates all figures and statistics. We position CBL relative to KCBS, CSW, and sheaf frameworks and outline links to SAT/CSP and robustness/adapter stability in large language models.","short_abstract":"Curved Boolean Logic (CBL) generalizes propositional logic by allowing local truth assignments that do not extend to a single global valuation, analogous to curvature in geometry. We give equivalent sheaf and exclusivity-graph semantics and a context-aware proof calculus that is conservative in the flat limit. We forma...","url_abs":"https://arxiv.org/abs/2510.04716","url_pdf":"https://arxiv.org/pdf/2510.04716v3","authors":"[\"Maximilian R. P. von Liechtenstein\"]","published":"2025-10-06T11:34:08Z","proceeding":"cs.LO","tasks":"[\"cs.LO\",\"cs.AI\",\"cs.CC\",\"quant-ph\"]","methods":"[\"Language Model\"]","has_code":false}