Daily Arxiv

This page organizes papers related to artificial intelligence published around the world.
This page is summarized using Google Gemini and is operated on a non-profit basis.
The copyright of the paper belongs to the author and the relevant institution. When sharing, simply cite the source.

Curved Boolean Logic: A Contextual Generalization of Propositional Logic with Algorithmic Consequences

Created by
  • Haebom

Author

Maximilian R.P. von Liechtenstein

Outline

Curved Boolean logic (CBL) generalizes propositional logic by allowing local truth assignments that do not extend to a single global evaluation, similar to curvature in geometry. We present a conservative, context-aware proof computation within the flat bound, with equivalent bundle and exclusive graph semantics. We formalize CBL-SAT and its underlying complexity (generally NP-complete), and present operators (CBL-AC and CBL-CONS) that eliminate contradictions early on in existing hardware. We model noise with iid, AR(1)-correlation, and adversarial boundary perturbations, and provide permutation-based significance with Benjamini-Hochberg FDR control. We provide a Colab-ready notebook (Supplementary Files) that reproduces all figures and statistics. We place CBL in relation to KCBS, CSW, and bundle frameworks, and briefly discuss the link between SAT/CSP and robustness/adapter stability in large-scale language models.

Takeaways, Limitations

Curved Boolean logic (CBL) generalizes traditional propositional logic to provide a new model of computation.
We present NP-completeness of the CBL-SAT problem.
The CBL-AC and CBL-CONS operators can improve computational efficiency by eliminating contradictions early.
It provides various perturbation methods for noise modeling and evaluates significance through Benjamini-Hochberg FDR control.
We present potential applications to large-scale language models and SAT/CSP problems.
Limitations of the study are not specifically stated, but further research may be needed to explore the practical application and complexity of the new logic framework, as well as comparison and analysis with other relevant frameworks.
👍