How an Autonomous Cognitive Agent Can Create an Axiomatic Theory
Abstract
Can a computer autonomous agent “invent” an axiomatic method by itself and apply it in a certain mathematical theory. This article discusses this issue. Euclid’s “Elements” is used as a prototype for a possible axiomatic theory.
References
1. Евклид. НА ЧАЛА. Книги I–VI. (Пер. с греческого и комментарии Д.Д. Мордухай-Болтовского при редакционном участии М.Я. Выгодского и И.Н. Веселовского). М.-Л., ОГИЗ, Государственное издательство технико-теоретической литературы, 1948.
2. https://24smi.org/celebrity/4943-evklid.html
3. I. Newton. Philosophiæ Naturalis Principia Mathematica. 1687. И. Ньютон. Математические начала натуральной философии. М., Наука, 1989.
4. В.Г. Редько. Как автономный компьютерный агент может самостоятельно открывать законы природы. «Интегрированные модели и мягкие вычисления в искусственном интеллекте». Сборник научных трудов XI Международной научно-практической конференции (ИММВ-2022, Коломна, 16-19 мая 2022 г.). В 2-х томах. Т. 2. М., РАИИ, 2022, 108–118.
5. Д. Гильберт. Основания геометрии. М.-Л., ОГИЗ, Государственное издательство технико-теоретической литературы, 1948.
6. https://wiki5.ru/wiki/Logic_Theorist
7. http://shelf1.library.cmu.edu/IMLS/MindModels/logictheorymachine.pdf
8. A.N. Whitehead, B. Russell. Principia Mathematica. Cambridge, Cambridge University. Press, 2nd edition. Vol. I (XLVI + 674 p.) 1925; Vol. II (XXXI + 742 p.) 1927; Vol. III (VIII + 491 p.) 1927.
9. A. Newell, J.C. Shaw, H.A. Simon. Report on a general problem-solving program. “Proceedings of the International Conference on Information Processing”. Paris, UNESCO, 15-20 June 1959. Published in 1960 by UNESCO (Paris), R. Oldenbourg (München) and Butterworths (London), 256–264. See also: http://bitsavers.informatik.uni-stuttgart.de/pdf/rand/ipl/P-1584_Report_On_A_General_Problem-Solving_Program_Feb59.pdf
10. A. Newell. Unified Theories of Cognition. Cambridge, Massachusetts, Harvard University Press, 1990.
11. H. Gelernter, J. Hansen, D. Loveland. Empirical explorations of the geometry theorem proving machine. “Proceedings of the Western Joint Computer Conference”. 1960, Vol. 17, 143–147. Reprinted in “Computers and Thought”. E. Feigenbaum, J. Feldman (Eds.). New York, McGraw-Hill Book Co., 1963, 153–167. See also: https://dl.acm.org/doi/pdf/10.1145/1460361.1460381
12. H. Gelernter. Realization of a geometry theorem proving machine. “Proceedings of the International Conference Information Processing”, Paris, June 15-20 1959, 273–282. Reprinted in “Computers and Thought”. E. Feigenbaum, J. Feldman (Eds.). New York, McGraw-Hill Book Co., 1963, 134–152.
13. H.L. Gelernter, N. Rochester. Intelligent behavior in problem-solving machines. “IBM Journal of Research and Development”, Vol. 2 (1958), No 4, 336–345.
14. A. Ferro, G. Gallo. Automated theorem proving in elementary geometry. “Le Matematiche”. Vol. 43 (1988), No 1,2, 195–224. See also: https://lematematiche.dmi.unict.it/index.php/lematematiche/arti-cle/view/713/678
15. D.W. Loveland. Automated Theorem Proving: A Logical Basis. “Fundamental Studies in Computer Science”. Vol. 6. Amsterdam, New York, Oxford, North-Holland Publishing Company, 1978.
16. Сайт журнала “The Journal of Automated Reasoning”: https://www.springer.com/journal/10817
17. https://postnauka.ru/faq/26503
Review
For citations:
Red’ko V.G. How an Autonomous Cognitive Agent Can Create an Axiomatic Theory. SRISA Proceedings. 2023;13(1-2):46-51. (In Russ.)
Views:
19
Email this article 