用几何曲率思想扩展逻辑，让局部真值不依赖全局一致，提升系统鲁棒性。
Curved Boolean Logic: A Contextual Generalization of Propositional Logic with Algorithmic Consequences
- 引入局部真值与曲率类比，打破传统逻辑必须全局一致的限制
- CBL-SAT问题在一般情况下为NP完全，但可在经典硬件上提前消解矛盾
- 适用于建模噪声、大模型鲁棒性分析，适合逻辑与复杂系统研究者
弯曲布尔逻辑（CBL）通过允许不扩展为单一全局赋值的局部真值赋值，推广了命题逻辑，类比于几何中的曲率。我们给出了等价的层论与排斥图语义，并构建了一个上下文感知的证明演算，其在平坦极限下保持保守性。形式化了CBL-SAT问题，揭示其一般情形下为NP完全；提出操作算子CBL-AC与CBL-CONS，在经典硬件上可提前剪枝矛盾。通过独立同分布、AR(1)相关及对抗有界扰动建模噪声，采用基于置换的显著性检验并控制贝尼尼-霍赫伯格错误发现率（FDR）。配套Colab笔记本可重现实验图表与统计结果。将CBL置于KCBS、CSW及层框架中进行定位，并指出其与SAT/CSP及大语言模型鲁棒性/适配器稳定性之间的潜在联系。
原文摘要 · Abstract (English)
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.
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