ISSN 2071-8594

Russian academy of sciences

Editor-in-Chief

Gennady Osipov

A.V. Pavlov, P.V. Kochetkov Algebra of fourier-dual operations: conceptual thinking generation

Abstract.

Two steps of conceptual thinking on the figurative one basis generation have been considered: the first step is inductive concepts generation by set of examples processing, and the second one is connections of the generated concepts with the yet existed ones establishing. The task has been considered in the framework of biologically inspired approach, i.e. both figurative and conceptual forms of information are represented and processed by the patterns of inner representation. A model based on the algebra of Fourier-dual operations for the both steps of the task solving has been proposed. Inductive concepts generation is implemented by sub-pattern of common features in the generalized on a set of examples pattern revealing under the criteria of the sub-patterns mutual correlation. A measure for revealing efficiency in dependence on both: a number of examples in the learning set and the sub-pattern of individual features information measures is proposed. Three layered neural network for the model implementation has been proposed. Computer simulations in the framework of “Darii” syllogism inversion results have been demonstrated.

Keywords:

Figurative thinking, Conceptual thinking, Associative memory, Induction, Inductive concepts generation, Fourier-duality, Correlation, Neural networks, Pattern of inner representation

PP. 27-42

REFERENCES

1. .Kuznetsov O.P. Bystrye processy mozga i obrabotka obrazov // Novosti iskusstvennogo intellekta. 1998. №2. http://raai.org/library/ainews/1998/2/DISTR.ZIP
2. Golitsyt G.A., Fominyh I.B. Neironnye seti I expertnye systemy: perspectivy integratcii // Novosti iskusstvennogo intellekta. 1996, №4. P.121-145.
3. Borisyuk G N, Borisyuk R M, Kazanovich Ya B, Ivanitskii G R Models of neural dynamics in brain information processing — the developments of ’the decade’ // Phys. Usp. 451073–1095 (2002); DOI: 10.1070/PU2002v045n10ABEH001143.
4. Hayes B.K., Heit E., Swendsen H. Inductive reasoning // Wiley Interdisciplinary Reviews: Cognitive Science.2010. V. 1, Issue 2. P. 278-292.
5. Vagin, V.N., Golovina, E.Yu., and Zagoryanskaya, A.A., Dostovernyi i pravodpodobnyi vyvod v intellektual’nykh sistemakh (Reliable and Probable Conclusion in Intelligent Systems), Vagin, V.N. and Pospelov, D.A., Eds., Moscow; FIZMALIT, 2008..
6. Barskii A.B. Logicheskie neironnye seti.- М.: Binom, 2007. 351 P.
7. V. K. Finn J.S. Mill’s inductive methods in artificial intelligence systems. Part II // Scientific and Technical Information Processing December 2011, Volume 38, Issue 6, pp 385-402.
8. V.K. Finn J.S. Mill’s inductive methods in artificial intelligence systems. Part II // Scientific and Technical Information Processing December 2012, Volume 39, Issue 5, pp 241-260.
9. M.I. Zabezhailo. To the Computational Complexity of Hypotheses Generation in JSM-method. Part I. // Iskusstvennyy intellekt i prinyatie resheniy. 2015. №1. P.3 – 17.
10. M. I. Zabezhailo To the Computational Complexity of Hypotheses Generation in JSM-method. Part I // Iskusstvennyy intellekt i prinyatie resheniy. 2015. №2. P.3 – 17.
11. Patrick Cavanagh Holographic and trace strength models of rehearsal effects in the item recognition task // Memory & Cognition 1976. Vol. 4. Issue 2. P.186-199
12. Rosenblatt F. Principles of neurodynamics // Washington: Spartan Books, 1962.
13. Minsky M., Papert S. Perceptrons // Cambridge: MIT Press, 1969.
14. V.V. Anshelevich, B.R. Amirikian, A.V. Lukashin, and M. D. Frank-Kamenetskii On the Ability of Neural Networks to Perform Generalization by Induction // Biological Cybernetics, 1989. V. 61. P. 125 – 128.
15. Pavlov A.V. Mathematical Models of Optical Methods in Data Processing// Journal of Computer and Systems Sciences International. 2000. №3. P.441 – 448.
16. Pavlov A.V. Ob algebraicheskih osnovaniyah golograficheskoi paradigm v iskusstvennom intellekte: algebra Fourier-dual’nyh operatorov // V mezdunarodnaya nauchno-prakticheskaya konferentsia: Integrirovannye modeli I myagkie vychislenia v iskusstvennom intellekte, 28-30 .05. 2009 ., Kolomna. Trudy konferentsii. – М.Fizmatlit,2009. Т.1, P.140-148.
17. Glezer V.D., Ivanov V.A., Sherbach T.A. Otvet retseptivnykch poleii neironov zritel’noii kory koshki na slozgnye stimuly //Phys. Journal USSR. 1972. V.58. №3.
18. Glezer V.D., Ivanov V.A., Sherbach T.A. Issledovanie retseptivnykch poleii neironov zritel’noii kory koshki kak filtrov prostranstvennyh chastot // Phys. Journal USSR. 1973. V.59. №2.
19. Glezer V.D.,Dudnik K.N. et al. Zritel’noe opoznanie I ego neiropfiziologicheskie mechanizmy. L.: Nauka, 1975.
20. Glezer V.D. Zrenie I myshlenie. SPb.: Nauka, 1993. 341 P.
21. Glezer V.D. The Role of Spatial–Frequency Analysis, Primitives, and Interhemispheric Asymmetry in the Identification of Visual Images // Human Physiology. 2000. V.26. №.5. P.636 – 640.
22. Pavlov A.V. Realizatsia pravdopodobnyh vyvodov na neirosetiyah so sviaziami po scheme holographii Fourier // Iskusstvennyy intellekt i prinyatie resheniy. 2010, №1. P.3-14.
23. B. A. Kobrinskii The significance of visual-image presentations for medical intelligent systems // Scientific and Technical Information Processing December 2013, V. 40, Issue 6, pp 337-341.
24. Marr D. Vision: a computational investigation into the human representation and processing of visual information. Freedman Hill, 1982. 397 p.
25. Mesiar R., Pap E., Different interpretations of triangular norms and related operations // Fuzzy Sets and Systems. 1998. V.96. P.183 – 189.
26. Averkin A.N., Batyrshin I.Z., et.al. Nechetkie mnozhestva v modelyah upravleniya I iskusstvennogo intellekta / Under ed. by Pospelov D.A. – M.: Nauka, 1986.
27. V.A. Kotel’nikov On the transmission capacity of ’ether’ and wire in electric communications // Physics-Uspekhi (Advances in Physical Sciences) 49 736–744 (2006) DOI: 10.1070/PU2006v049n07ABEH006160
28. Dubois D., Prade H. Fuzzy numbers: an overview // in: Ed. by J.C.Bezdek, Analysis of Fuzzy Information.- Boca Raton, FL, 1987. V.1. P. 3 – 39.
29. Yaglom. A.M Korrelyaеtscionnaya teoriya stacionarnyh sluchaynyh funktsyi // L.: Gidrometeoizdat, 1981. 280 P.
30. Ventscel E.S. Teoriya veroyatnosteii. M.: Vyshaya shkola, 1999.
31. Subnikov E.I.. Signal to noise ratio under images correlation comparison // Optics and Spectroscopy. 1987. V.62. i.2. P .450 – 456.
32. Foster D.J., Wilson M.A. Reverse replay of behavioural sequences in hippocampal place cells during the awake state // Nature, 2006. V. 440. PP. 680-3.
33. O.P.Kuznetsov Cognitive semantics and artificial intelligence // Scientific and Technical Information Processing, December 2013, Volume 40, Issue 5, pp 269-276.