Scientific and Technical Information Processing

, Volume 40, Issue 6, pp 375–385 | Cite as

The algebra of Fourier-dual operations: Logic with exception

Article

Abstract

In the development of an approach to the implementation of fuzzy logics on neural networks with interconnections via the scheme of Fourier holography, a model of logic with exception is proposed, which is associated with the basic Generalized Modus Ponens rule. The exception is recalled from the associative memory by an inference formed by the basic rule and it modifies the original inference. The results of numerical simulation are based on the experimental data.

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References

  1. 1.
    Vagin, V.N., Golovina, E.Yu., Zagoryanskaya, A.A., and Fomina, M.V., Dostovernyi i pravdopodobnyi vyvod v intellektual’nykh sistemakh, (The Trustworthy and Plausible Conclusion in Intellectual Systems), 2nd ed., Moscow: FIZMATLIT, 2008.Google Scholar
  2. 2.
    Reiter, R., A logic for default reasoning, Art. Intell., 1980, vol. 13, nos. 1–2, pp. 81–132.CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Antoniou, G., Nonmonotonic Reasoning, Cambridge, MA: MIT, 1997.MATHGoogle Scholar
  4. 4.
    Benferhat, S., Dubois, D., and Prade, H., Nonmonotonic reasoning, conditional objects and possibility theory, Art. Intell., 1997, vol. 92, nos. 1–2, pp. 259–276.CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Lukasiewicz, T., Weak nonmonotonic probabilistic logics, Art. Intell., 2005, vol. 168, nos. 1–2, pp. 119–161.CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Vin’kov, M.M. and Fominykh, I.B., Nonmonotonic reasoning in artificial intelligence systems, Novosti Iskusstv. Intell., 2005, no. 4, pp. 12–23.Google Scholar
  7. 7.
    Astanin, S.V. and Kalashnikova, T.G., Model of non-monotonic reasoning on the basis of fuzzy logics, Materialy mezhd. NTK “Intellektual’nye SAPR”, (Proc. Int. Sci.-Techn. Conf. “Intellectual CAD”), Taganrog, 2000.Google Scholar
  8. 8.
    Golitsyn, G.A. and Fominykh, I.B., Neuron nets and expert systems: Integration perspectives, Novosti Iskusstv. Intell., 1996, no. 4, pp. 121–145.Google Scholar
  9. 9.
    Fominykh, I.B., Integrated models and technologies of creative task solution, Trudy VI Mezhdunarodnoi konferentsii “Integrirovannye modeli i myagkie vychisleniya v iskusstvennom intellekte” (Proc. 6th Int. Conf. “Integrated Models and Soft Calculations in Artificial Intellect”), Kolomna, 2011, pp. 149–157.Google Scholar
  10. 10.
    Kuznetsov, O.P., Quick processes of mind and image treatment, Novosti Iskusstv. Intell., 1998, no. 2.Google Scholar
  11. 11.
    Borisyuk, G.N., Borisyuk, R.M., Kazanovich, Ya.B., and Ivanitskii, G.R., Models of?neural dynamics in?brain information processing?— the developments of “the decade”, Phys.-Usp., 2002, vol. 45, pp. 1073–1095.CrossRefGoogle Scholar
  12. 12.
    Pavlov, A.V., Mathematical models of optical methods in data processing, J. Comput. Syst. Sci. Int., 2000, vol. 39, pp. 441–447.Google Scholar
  13. 13.
    Pavlov, A.V., Application of the Fourier-holography technique to the implementation of logical-linguistic models, J. Comput. Syst. Sci. Int., 2003, vol. 42, pp. 275–281.MATHGoogle Scholar
  14. 14.
    Pavlov, A.V., On algebraic foundations of holographic paradigm in artificial intellect: Algebra Fourier-dual operators, V-ya Mezhdunarodnaya nauchno-prakticheskaya konferentsiya “Integrirovannye modeli i myagkie vychisleniya v iskusstvennom intellekte”, (Proc. 5th Int. Sci.-Pract. Conf. “Integrated Models and Soft Computing in Artificial Intellect”), V. 1, P. 140–148. Moscow, Fizmatlit, 2009, 2009.Google Scholar
  15. 15.
    Pavlov, A.V., Approach to integration of logic and image reasoning by Fourier-holography method, Nov. Iskusst. Intell., 2006, no. 4.Google Scholar
  16. 16.
    Dubois, D. and Prade, H., Fuzzy numbers: An overview, in Analysis of Fuzzy Information, Bezdek, J.C., Ed., Vol. 1, Boca Raton, FL. 1987.Google Scholar
  17. 17.
    Zade, L., Conception of linguistic variable and its application to acceptance of approximate decisions, Matematika. Novoe v Zarubezhnoi Nauke, 1976, no. 3.Google Scholar
  18. 18.
    Pavlov, A.V. and Alekseev, A.M., Realization of fuzzy logics with exclusions by Fourier-holography method, Mezhd. nauchno-tekhnicheskie konferentsii IEEE AIS’07 CAD-2007, (Proc. Int. Sci.-Techn. Conf. IEEE AIS’07 CAD-2007), Divnomorskoe, Russia, 2007; Proc. Conf. vol. 2, Moscow, Fizmatlit, pp. 155–160.Google Scholar
  19. 19.
    Alekseev, A.M. and Pavlov, A.V., Implementation of fuzzy logic with exclusions by Fourier-holography method, J. Optical Technol., 2008, vol. 75, pp. 242–246.CrossRefGoogle Scholar
  20. 20.
    Shansi, M., Raju, K., and Avadhani, P.S., Reasoning with fuzzy censors, IEEE Trans. Syst., Man, Cybern., 1994, vol. 24, pp. 1061–1064.CrossRefGoogle Scholar
  21. 21.
    Mesiar, R. and Pap, E., Different interpretations of triangular norms and related operations, Fuzzy Sets and Systems, 1998, vol. 96, pp.183–189.CrossRefMATHMathSciNetGoogle Scholar
  22. 22.
    Novak, V., Perfil’eva, I., and Mochkorzh, I., Matematicheskie printsipy nechetkoi logiki (Mathematical Principles of Fuzzy Logic), Moscow: Fizmatlit, 2006.Google Scholar
  23. 23.
    Kuleshov, A.M., Shubnikov, E.I., and Smaeva, S.A., On optimality of holographic compatible filter, Opt. Spektrosk., 1986, vol. 60, pp. 1273–1276.Google Scholar
  24. 24.
    Aleksandrina, S.A. and Kuleshov, A.M., Effect of spectrum low space frequencies on signal parameters in holographic correlator, Opt. Spektrosk., 1990, vol. 68, pp. 652–655.Google Scholar
  25. 25.
    Alekseev, A.M. and Pavlov, A.V., Approximation of transfer function of the 4f scheme of Fourier holography upon fuzzy-valued logics implementation, Optics Spectrosk., 2010, vol. 108, pp. 137–142.CrossRefGoogle Scholar
  26. 26.
    Kuznetsov, O.P., Markovskii, A.V., and Shipilina, L.B., Golograficheskie mekhanizmy obrabotki obraznoi informatsii (Holographic Mechanisms of Image Information Treatment), Moscow: Inst. Prob. Upravl. Ross. Akad. Nauk, 2007.Google Scholar

Copyright information

© Allerton Press, Inc. 2013

Authors and Affiliations

  1. 1.St. Petersburg State University of Information Technologies, Mechanics, and OpticsSt. PetersburgRussia

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