Curved Boolean Logic: A Contextual Generalization of Propositional Logic with Algorithmic Consequences
This is an incremental theoretical framework with potential applications in SAT/CSP and robustness in large language models.
The paper introduces Curved Boolean Logic (CBL), a generalization of propositional logic that allows local truth assignments without a single global valuation, and shows it is NP-complete for CBL-SAT while providing operational operators to prune contradictions on classical hardware.
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.