Presenting the basic essence of limiting generalizations paradigm by algebra predicate structures

Authors

  • Виталий Иванович Булкин Makiivka economic-humanitarian institute Оstrovsky str., 16, Makiivka, Ukraine, 86157, Ukraine https://orcid.org/0000-0001-6212-1009
  • Юрий Александрович Прокопчук Institute of Technical Mechanics of the National Academy of Sciences of Ukraine 15 Leshko-Popel St, Dnipropetrovsk, Ukraine, 49005, Ukraine https://orcid.org/0000-0002-8544-1838

DOI:

https://doi.org/10.15587/1729-4061.2014.22134

Keywords:

paradigm of limiting generalizations, directed graphs of domains, pattern systems, algebra of predicates, algebra-predicate structures

Abstract

At the present stage of computer technology advancement, there are problems of using sequential algorithms and exclusively binary encoding. These problems require creating computational tools with a new design and using non-binary coding techniques. In this study, a method of formal representation of elementary tests, their domains and pattern systems in the language of predicate algebra was developed for the first time. Formalization of the recalculation rules between the domains of different levels of generality, using the mathematical tool of the algebra of predicates, was carried out. The developed mathematical models, specifying the rules for domain value recalculation, are represented as the corresponding AP structures. For a hardware implementation of the obtained models, the method of presenting algebra-predicate structures in the form of associative-logic converters was used. The obtained AP structures can be used for creating intelligent parallel-action systems, operating in real time.

Author Biographies

Виталий Иванович Булкин, Makiivka economic-humanitarian institute Оstrovsky str., 16, Makiivka, Ukraine, 86157

Associate professor

Department of the applied mathematics and information technologies

Юрий Александрович Прокопчук, Institute of Technical Mechanics of the National Academy of Sciences of Ukraine 15 Leshko-Popel St, Dnipropetrovsk, Ukraine, 49005

Co-Professor

Department of system analysis and control problems

References

  1. Бондаренко, М. Ф. Основи теорії багатозначних структур і кодування в системах штучного інтелекту [Текст] / М. Ф. Бондаренко, З. Д. Коноплянко, Г. Г. Четвериков. – Х. : Фактор-Друк, 2003. – 336 с.
  2. Прокопчук, Ю. А. Принцип предельных обобщений: методология, задачи, приложения [Текст]: монография / Ю. А. Прокопчук. – Днепропетровск: Ин-т технической механики НАНУ и НКАУ, 2012.– 384 с.
  3. Прокопчук, Ю. А. Модели когнитивных архитектур и процессов на основе парадигмы предельных обобщений [Текст] / Ю. А. Прокопчук // Кибернетика и вычисл. техника. – 2013. – Вып. 171. – С. 37–51.
  4. Булкин, В. И. Представление алгебропредикатных структур в виде ассоциативно-логических преобразователей [Текст] / В. И. Булкин // Искусственный интеллект. – № 3.– С. 6–17.
  5. Samsonovich, A. V.: Toward a Unified Catalog of Implemented Cognitive Architectures (Review) [Text] / A. V. Samsonovich, K. R. Johansdottir, A. Chella, B. Goertzel // Biologically Inspired Cognitive Architectures 2010: Proc. 1st Annual Meeting of BICA Society, Frontiers in Artificial Intelligence and Applications – 2010. – Vol. 221. – P. 195–244
  6. Затуливетер, Ю. С. Графодинамические системы с сетецентрическим управлением в математически однородном поле компьютерной информации [Текст] / Ю. С. Затуливетер, Е. А. Фищенко // Управление большими система-ми. – 2010. – № 30–1. – С. 567–604.
  7. Малинецкий, Г. Г. Теория самоорганизации. На пороге IV парадигмы [Текст] / Г. Г. Малинецкий // Компьютерные исследования и моделирование. – 2013. – Т. 5, № 3. – С. 315−366.
  8. Rasmussen, D. A Neural model of rule generation in inductive reasoning [Text] / D. Rasmussen, C. Eliasmith // Topics in Cognitive Science . – 2011 – Vol. 3 (1). – P. 140–153.
  9. Edelman, G. M. Biology of consciousness [Text] / G. M. Edelman, J. A. Gally, B. J. Baars // Front. Psychology. – 2011. – P. 2–4.
  10. Dixon, J. A. Multifractal Dynamics in the Emergence of Cognitive Structure [Text] / J. A. Dixon, J. G. Holden, D. Mirman, D. G. Stephen // Topics in Cognitive Science. – 2012. – Vol. 4. – P. 51–62.
  11. Бутенко, Д. В. Гомеостатическая нейросеть [Текст] / Д. В. Бутенко, Е. В. Албегов, Л. Н. Бутенко // Нейрокомпьютеры: разработка, применение. – 2013. – № 2. – C. 45–53.
  12. Иващенко, А. В. Мультиагентные технологии для разработки сетецентрических систем управления [Текст] / А. В. Иващенко, О. В. Карсаев и др. // Известия Южного федерального университета. Технические науки. – 2011. – Т. 116, № 3. – C. 11–23.
  13. Байрак, С. А. Параллельные процессоры для построения интеллектуальных систем [Текст] : матер. II междунар. научн.-техн. конф. / С. А. Байрак, Д. Н. Одинец и др. // Открытые семантические технологии проектирования интеллектуальных систем. – Минск : БГУИР, 2012. – С. 135–140.
  14. Каляев, И. А. Высокопроизводительные реконфигурируемые вычислительные системы нового поколения [Текст] / И. А. Каляев, А. И. Дордопуло и др. // Вычислительные методы и программирование: новые вычислительные технологии. – 2011. – Т. 12, №2. – С. 82–89.
  15. Brodtkorb, A. R. Graphics processing unit (GPU) programming strategies and trends in GPU computing [Text] / A. R. Brodtkorb, T. R. Hagen, M. L. Saetra // Journal of Parallel and Distributed Computing. – 2013. – Vol. 73, Issue 1. – P. 4–13.
  16. Бухановский, А. В. Перспективная технология «облачных» вычислений второго поколения [Текст] / А. В. Бухановский, В. Н. Васильев и др. // Изв. вузов. Приборостроение. – 2011. – Т. 54, № 10. – С. 7–15.
  17. Вереник, Н. Л. Разработка проблемно-ориентированных процессоров семантической обработки информации [Текст] / Н. Л. Вереник, Е. Н. Сейткулов, М. М. Татур // Электроника инфо. – 2012. – № 8. – С. 95–98.
  18. Бондаренко, М. Ф. Мозгоподобные структуры [Текст]: Справ. пос.; Т. 1. / М. Ф. Бондаренко, Ю. П. Шабанов-Кушнаренко; под ред. И. В. Сергиенко. – К.: Наукова думка, 2011. – 460 с.
  19. Глушков, В. М. Основные архитектурные принципы повышения производительности ЭВМ [Текст] : избр. тр.; Т. 2 / В. М. Глушков. – К.: Наукова думка, 1990. – 267 с.
  20. Gates, B. Business at the Speed of Thought : Using a Digital Nervous System (Penguin Joint Venture Readers) [Text] / B. Gates. – Pearson Education Limited, 2001. – 112 р.
  21. Bondarenko, M. F. (2003). Fundamentals of theory of multivalued structures and coding in the systems of artificial intelligence. Kharkov, Factor-Druk, 336.
  22. Prokopchuk, Y. A. (2012). Principle of Limiting Generalizations: Methodology, Problems, and Applications. Monograph. Dnepropetrovsk, Institute of Technical Mechanics of the NAS and the State Space Agency of Ukraine Publ., 384.
  23. Prokopchuk, Y. (2013). Models of cognitive architectures and processes on the basis of a paradigm of limiting generalizations. Cybernetics and computer engineering, 171, 37–51.
  24. Bulkin, V. I. (2012). Presentation of algebra predicate structures as associative-logical transformers. J Artificial intelligence, 3, 6–17.
  25. Samsonovich, A. V. (2010). Toward a Unified Catalog of Implemented Cognitive Architectures (Review) J Biologically Inspired Cognitive Architectures: Proc. 1st Annual Meeting of BICA Society, Frontiers in Artificial Intelligence and Applications – 2010, 221, 195–244.
  26. Zatuliveter, Y. S. (2010). Graph dynamic network-centric management system in a mathematically uniform field of computer information. J Management of large systems, 30 (1), 567–604.
  27. Malinetsky, G. G. (2013). Self-organization theory. On a threshold of the IV paradigm. J Computer researches and modelling, 5(3), 315−366.
  28. Rasmussen, D. (2011). A Neural model of rule generation in inductive reasoning. J Topics in Cognitive Science, 3 (1), 140–153.
  29. Edelman, G. M. (2011). Biology of consciousness. J Front. Psychology, 2–4.
  30. Dixon, J. A. (2012). Multifractal Dynamics in the Emergence of Cognitive Structure. J Topics in Cognitive Science, 4, 51–62.
  31. Butenko, D. V. (2013). Gomeostatic neuronet. J Neurocomputers: development, application, 2, 45–53.
  32. Ivashchenko, A. V. (2011). Multiagent technologies for development of network-centric control systems. J News of the Southern federal university. Technical sciences. 116 (3), 11–23.
  33. Bayrak, S. A. (2012). Parallel processors for creation of intellectual systems. Open semantic technologies of design of intellectual systems. Minsk: BGUIR, 135–140.
  34. Kalyaev, I. A. (2011). High-performance reconfigurable computing systems of new generation. J Computing methods and programming: new computing technologies, 12 (2), 82–89.
  35. Brodtkorb, A. R. (2013). Graphics processing unit (GPU) programming strategies and trends in GPU computing. Journal of Parallel and Distributed Computing, 73 (1), 4–13.
  36. Bukhanovsky, A. V. (2011). Perspective technology of “cloudy” calculations of the second generation. J News of higher education institutions. Instrument making, 54 (10), 7–15.
  37. Verenik, N. L. (2012). Development of problem-oriented processors of semantic information processing. J Electronics info, 8, 95–98.
  38. Bondarenko, M. F. (2011). Brainlike structures. Kiev: Naukova dumka, 460.
  39. Glushkov, V. М. (1990). Basic architectural principles of increase of the productivity of computers. Kiev, USSR : Naukova dumka, 2, 267.
  40. Gates, B. (2001). Business at the Speed of Thought : Using a Digital Nervous System (Penguin Joint Venture Readers), Pearson Education Limited, 112.

Downloads

Published

2014-04-09

How to Cite

Булкин, В. И., & Прокопчук, Ю. А. (2014). Presenting the basic essence of limiting generalizations paradigm by algebra predicate structures. Eastern-European Journal of Enterprise Technologies, 2(4(68), 9–15. https://doi.org/10.15587/1729-4061.2014.22134

Issue

Vol. 2 No. 4(68) (2014): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

License

Copyright (c) 2014 Виталий Иванович Булкин, Юрий Александрович Прокопчук

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.