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.
Keywords
Cite
@article{arxiv.2510.04716,
title = {Curved Boolean Logic: A Contextual Generalization of Propositional Logic with Algorithmic Consequences},
author = {Maximilian R. P. von Liechtenstein},
journal= {arXiv preprint arXiv:2510.04716},
year = {2025}
}
Comments
v3: Restores original v1 content; later additions are retracted pending a normalization audit