Integration of logical and imaginative thinking by Fourier holography techniques: Implementation in nonmonotonic reasoning

  • A. M. Alekseev
  • A. M. Konstantinov
  • A. V. Pavlov


The possibility of integrating the principles of imaginative and logical thinking by means of Fourier holography is demonstrated. The proposed approach develops the concept of logical-linguistic modeling based on fuzzy-valued logics with allowance for some recent results in brain neurophysiology. The possible implementation of nonmonotonic reasoning in holography is illustrated by experimental results.


Fuzzy Number Linguistic Variable Logical Thinking Logical Inference Nonmonotonic Reasoning 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Collier, R.J., Burckhardt, C.B., and Lin, L.H., Optical Holography, New York: Academic Press, 1971.Google Scholar
  2. 2.
    Kuznetsov, O.P., Nonclassical Paradigms in Artificial Intelligence, Izv. Ross. Akad. Nauk, Ser. Teor. Sist. Upravl., 1995, no. 5, pp. 3–23.Google Scholar
  3. 3.
    Sudakov, K.V., The Holographic Principle of Systemic Organization in Living Activity, Usp. Fiziol. Nauk, 1997, vol. 28, pp. 3–32.Google Scholar
  4. 4.
    Pribram, K.H., Nonlocality and Localization: Holographic Hypothesis of Brain Functioning in Perception and Memory (Russian Translation), in Synergetics and Psychology (Issue 1: Methodological Problems), Moscow: Izdat. MGSU “Soyuz,” 1997.Google Scholar
  5. 5.
    Arbib, M., Metaphorical Brain, New York: Wiley, 1972.zbMATHGoogle Scholar
  6. 6.
    Pribram, K.H., Languages of the Brain: Experimental Paradoxes and Principles in Neuropsychology, New York: Wadsworth, 1971.Google Scholar
  7. 7.
    Val’kman, Yu.R., et al., Texts, Contexts, and Universums in Graphical Images and Languages, Trudy mezhdunarodnoi konferentsii “Intellektual’nye sistemy (Divnomorskoe, 3–10.09.2003) (Proc. Intern. Conf. “Intellectual Systems,” Divnomorskoe, September 3–10, 2003), Moscow: Fizmatlit, 2003, vol. 1, pp. 213–219.Google Scholar
  8. 8.
    Bykov, V.S., Val’kman, Yu.R., and Rykhal’skii, A.Yu., Modeling Imaginative Thinking in Computer Technologies: Image as a Result of Reflection, Trudy mezhdunarodnoi konferentsii “Intellektual’nye sistemy” (Proc. Intern. Conf. “Intellectual Systems,” September 3–10, 2005), Moscow: Fizmatlit, 2005, vol. 2, pp. 250–255.Google Scholar
  9. 9.
    Golitsyn, G.A. and Fominykh, I.B., Neuron Networks and Expert Systems: Prospects for Integration, Novosti Iskusstv. Intell., 1996, no. 4.Google Scholar
  10. 10.
    Kuznetsov, O.P., Modeling Optical Phenomena in Neuron Networks, Opt. Zh., 2003, vol. 70, no. 8, pp. 25–33 [J. Opt. Technol. (Engl. Transl.), 2003, vol. 70, pp. 548–555].Google Scholar
  11. 11.
    Zadeh, L.A., The Concept of a Linguistic Variable and Its Application to Approximate Reasoning, New York: Elsevier, 1973.Google Scholar
  12. 12.
    Pavlov, A.V., Using the Methods of Fourier Holography to Construct Logic Processors, Opt. Zh., 2002, vol. 69, no. 10, pp. 42–48 [J. Opt. Technol. (Engl. Transl.), 2002, vol. 69, pp. 735–740].Google Scholar
  13. 13.
    Borisyuk, G.N., Borisyuk, R.M., Kazanovich, Ya.B., and Ivanitskii, G.R., Models of Neuron Dynamics in Brain Information Processing: The Developments of “The Decade,” Usp. Fiz. Nauk, 2002, vol. 172, no. 10, pp. 1189–1214 [Phys. Usp. (Engl. Transl.), 2002, vol. 45, pp. 1073–1096].CrossRefGoogle Scholar
  14. 14.
    Pavlov, A.V., Implementing a Linear Predictor Model by Fourier Holography, Opt. Zh., 2005, vol. 72, no. 2, pp. 43–47 [J. Opt. Technol. (Engl. Transl.), 2005, vol. 72, pp. 199–202].Google Scholar
  15. 15.
    Pavlov, A.V. and Shevchenko, Ya.Yu., Implementing a Logical Conclusion on Linguistic Scales by the Method of Fourier Holography, Opt. Zh., 2004, vol. 71, no. 7, pp. 44–51 [J. Opt. Technol. (Engl. Transl.), 2004, vol. 71, pp. 454–460].Google Scholar
  16. 16.
    Antoniou, G., Nonmonotonic Reasoning, Cambridge (Ma): MIT Press, 1997.zbMATHGoogle Scholar
  17. 17.
    Benferhat, S., Dubois, D., and Prade, H., Nonmonotonic Reasoning, Conditional Objects, and Possibility Theory, Artif. Intell., 1997, vol. 92, pp. 259–276.zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Likasiewicz, T., Weak Nonmonotonic Perobabilistic Logics, Artif. Intell., 2005, vol. 168, pp. 119–161.CrossRefGoogle Scholar
  19. 19.
    Hunter, A., Proc. 11th Int. Workshop on Nonmonotonic Reasoning,
  20. 20.
    Ishikawa, S., Fuzzy Inferences by Algebraic Method, Fuzzy Sets Syst., 1997, vol. 87, pp. 181–200.zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Ishikawa, S., Quantum-Mechanical Approach to a Fuzzy Theory, Fuzzy Sets Syst., 1997, vol. 90, pp. 277–306.zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Ishikawa, S., Fuzzy Logic in Measurements, Fuzzy Sets Syst., 1998, vol. 100, pp. 291–300.zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Landauer, R., Irreversibility and Heat Generation in the Computing Process, IBM J. Res. Dev., 1961, vol. 5, pp. 183–192 [reprinted: IBM J. Res. Dev., 2000, vol. 44, pp. 261–269].MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Arbib, M. and Bota, M., Language Evolution: Neural Homologies and Neuroinformatics, Neural Netw., 2003, vol. 16, pp. 1237–1260.CrossRefGoogle Scholar

Copyright information

© Allerton Press, Inc. 2007

Authors and Affiliations

  • A. M. Alekseev
    • 1
  • A. M. Konstantinov
    • 1
  • A. V. Pavlov
    • 1
    • 2
  1. 1.St. Petersburg State University of Information Technology, Mechanics, and OpticsSt. PetersburgRussia
  2. 2.Vavilov Optical InstituteState Scientific Center of the Russian FederationSt. PetersburgRussia

Personalised recommendations