The Use of Convolutional Polycategories in Problems of Artificial Intelligence

  • Georgy K. TolokonnikovEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1126)


Convolutional polycategories introduced by the author find application in the general theory of systems, in the theory of artificial neural networks, in other areas of artificial intelligence. The report gives further applications of convolutional polycategories in algebraic biology and logical calculi, covering the classical and intuitionistic predicate calculus. Based on the formalism of convolutional polycategories, a new categorical definition of information is given, reflecting its semantic component. This definition finds application in algebraic biology with a basic code example of DNA and RNA molecules in a cell. A polycategorical model is given for the method of typical quantifiers used in AI and stronger than the Robinson method and the inverse Maslov method. The model reveals the categorical basis of calculus and is used to study the properties of the calculus of typical quantifiers. The main results are of a fundamental theoretical nature for algebraic biology and AI.


Genetic code DNA Tensor product System theory Categories Topoi Logic Quantifiers Predicate calculus Artificial intelligence 


  1. 1.
    Tolokonnikov, G.K.: Mathematical foundations of the theory of biomachsystems. In: Biomachsystems. Theory and Applications, pp. 31–213. Rosinformagrotekh, Moscow (2016)Google Scholar
  2. 2.
    Tolokonnikov, G.K.: Convolution polycategories and categorical splices for modeling neural networks. In: Advances in Intelligent Systems and Computing, Volume 938, Advances in Computer Science for Engineering and Education II, Conference Proceedings ICCSEEA, pp. 259–267 (2019). ISSN 2194-5357. ISSN 2194-5365Google Scholar
  3. 3.
    Vasiliev, S.N., Zherlov, A.K., Fedosov, E.A., Fedunov, B.E.: Intelligent control of dynamic systems, 352 p. Fizmatlit, Moscow (2000)Google Scholar
  4. 4.
    Tolokonnikov, G.K.: Manifest: neurographs, neurocategories and categorical splices. Biomachsystems 1(1), 59–146 (2017)Google Scholar
  5. 5.
    Karande, A.M., Kalbande, D.R.: Weight assignment algorithms for designing fully connected neural network. Int. J. Intell. Syst. Appl. (IJISA) 10(6), 68–76 (2018)Google Scholar
  6. 6.
    Dharmajee Rao, D.T.V., Ramana, K.V.: Winograd’s inequality: effectiveness for efficient training of deep neural networks. Int. J. Intell. Syst. Appl. (IJISA) 6, 49–58 (2018)CrossRefGoogle Scholar
  7. 7.
    Hu, Z., Tereykovskiy, I.A., Tereykovska, L.O., Pogorelov, V.V.: Determination of structural parameters of multilayer perceptron designed to estimate parameters of technical systems. Int. J. Intell. Syst. Appl. (IJISA) 10, 57–62 (2017)Google Scholar
  8. 8.
    Awadalla, M.H.A.: Spiking neural network and bull genetic algorithm for active vibration control. Int. J. Intell. Syst. Appl. (IJISA) 10(2), 17–26 (2018)Google Scholar
  9. 9.
    Abuljadayel, A., Wedyan, F.: An approach for the generation of higher order mutants using genetic algorithms. Int. J. Intell. Syst. Appl. (IJISA) 10(1), 34–35 (2018)Google Scholar
  10. 10.
    Petoukhov, S.: Matrix genetics, algebra of genetic code, noise immunity. RHD, Moscow (2008)Google Scholar
  11. 11.
    Petoukhov, S., Petukhova, E., Hazina, L., Stepanyan, I., Svirin, V., Silova, T.: The genetic coding, united-hypercomplex numbers and artificial intelligence. In: Hu, Z., Petoukhov, S., He, M. (eds.) Advances in Artificial Systems for Medicine and Education, AIMEE. Advances in Intelligent Systems and Computing, vol. 658. Springer, Cham (2017)Google Scholar
  12. 12.
    He, M., Hu, Z.B., Petoukhov, S.V.: Triply stochastic cubes associated with genetic code numerical mappings. In: Advances in Intelligent Systems and Computing, vol. 754, pp. 606–616 (2018)Google Scholar
  13. 13.
    Holevo, A.S.: Introduction to quantum information theory. MTSNMO, Moscow (2002)Google Scholar
  14. 14.
    Chernavsky, D.S.: The problem of the origin of life and thinking from the point of view of modern physics. UFN 170(2), 157–183 (2000)CrossRefGoogle Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Federal Scientific Agro-Engineering Center VIMRussian Academy of SciencesMoscowRussia

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