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  • Lev Beklemishev, Daniyar Shamkanov. Some abstract versions of Gödel's second incompleteness theorem based on non-classical logics, ArXiv: 1602.05728, Feb. 2016.
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News
June 2, 2026
HSE Study Reveals Imbalance in the Generative AI Market
Researchers at HSE University analysed how effectively the global generative artificial intelligence market converts investment into real revenue, concluding that AI is currently developing faster than it is paying off. The results have been published in the journal Foresight and STI Governance.
June 2, 2026
Discovering Science through Russian Language: HSE Prep Year Students Present at International Conference in Kazan
On May 23, 2026, the V International Scientific and Practical Conference ‘Discovering the World of Science’ took place in Kazan at the Preparatory Faculty for International Students of Kazan Federal University. Four students of the HSE International Preparatory Year took part in the event: two delivered their presentations in person, while two participated online. Their work was supervised by Acting Director of the International Prep Year Irina Isaeva and lecturer Ekaterina Kozhemyakova.
May 25, 2026
HSE Scientists Train Neural Network to 'Hear' Faults in Electric Motors
Researchers at the AI and Digital Science Institute of the HSE Faculty of Computer Science have developed a new method—the Signature-Guided Data Augmentation (SGDA) framework—that achieves 99% accuracy in motor fault detection and 86% accuracy in fault classification. The application of this approach can reduce industrial equipment repair costs, minimise downtime, and improve production safety. The study results have been published in Engineering Applications of Artificial Intelligence.

 

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Lev Beklemishev, Daniyar Shamkanov. Some abstract versions of Gödel's second incompleteness theorem based on non-classical logics, ArXiv: 1602.05728, Feb. 2016.

2016. No. 1602.05728.
Lev Beklemishev, Shamkanov D.
We study abstract versions of G\"odel's second incompleteness theorem and formulate generalizations of L\"ob's derivability conditions that work for logics weaker than the classical one. We isolate the role of contraction rule in G\"odel's theorem and give a (toy) example of a system based on modal logic without contraction invalidating G\"odel's argument.
Research target: Philosophy, Ethics, and Religious Studies Mathematics Computer Science
Priority areas: IT and mathematics mathematics
Language: English
Text on another site
Keywords: Goedel theoremfixed pointssubstructural logics
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