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.

翻译：弯曲布尔逻辑（CBL）通过允许局部真值赋值不扩展至单一全局赋值来推广命题逻辑，类似于几何中的曲率概念。我们给出了等价的层与互斥图语义，以及一个在平坦极限下保持保守的情境感知证明演算。我们形式化了CBL-SAT问题及其基本复杂度（通常为NP完全），并提出了可在经典硬件上提前修剪矛盾的操作算子（CBL-AC与CBL-CONS）。我们通过独立同分布、AR(1)相关及对抗性有界扰动对噪声进行建模，并提供基于置换的显著性检验及Benjamini-Hochberg错误发现率控制。一个可直接在Colab运行的笔记本（辅助文件）可复现所有图表与统计结果。我们将CBL与KCBS、CSW及层理论框架进行对比定位，并概述其与SAT/CSP问题及大语言模型中鲁棒性/适配器稳定性的关联。