Curved Boolean Logic: A Contextual Generalization of Propositional Logic with Algorithmic Consequences
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911203447537664 |
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| author | von Liechtenstein, Maximilian R. P. |
| author_facet | von Liechtenstein, Maximilian R. P. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04716 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Curved Boolean Logic: A Contextual Generalization of Propositional Logic with Algorithmic Consequences von Liechtenstein, Maximilian R. P. Logic in Computer Science Artificial Intelligence Computational Complexity Quantum Physics 68Q17, 68Q25 F.1.1; F.2.2; I.2.3 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. |
| title | Curved Boolean Logic: A Contextual Generalization of Propositional Logic with Algorithmic Consequences |
| topic | Logic in Computer Science Artificial Intelligence Computational Complexity Quantum Physics 68Q17, 68Q25 F.1.1; F.2.2; I.2.3 |
| url | https://arxiv.org/abs/2510.04716 |