Nikiforov
Vladimir O.
D.Sc., Prof.
LOGIC WITH EXCEPTION ON THE ALGEBRA OF FOURIER-DUAL OPERATIONS: NEURAL NET MECHANISM OF COGNITIVE DISSONANCE REDUCING
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Abstract
A mechanism of cognitive dissonance reducing is demonstrated with approach for non-monotonic fuzzy-valued logics by Fourier-holography technique implementation developing. Cognitive dissonance occurs under perceiving of new information that contradicts to the existing subjective pattern of the outside world, represented by double Fourier-transform cascade with a hologram – neural layers interconnections matrix of inner information representation and logical conclusion. The hologram implements monotonic logic according to “General Modus Ponens” rule. New information is represented by a hologram of exclusion that implements interconnections of logical conclusion and exclusion for neural layers. The latter are linked by Fourier transform that determines duality of the algebra forming operations of conjunction and disjunction. Hologram of exclusion forms conclusion that is dual to the “General Modus Ponens” conclusion. It is shown, that trained for the main rule and exclusion system can be represented by two-layered neural network with separate interconnection matrixes for direct and inverse iterations. The network energy function is involved determining the cyclic dynamics character; dissipative factor causing convergence type of the dynamics is analyzed. Both “General Modus Ponens” and exclusion holograms recording conditions on the dynamics and convergence of the system are demonstrated. The system converges to a stable status, in which logical conclusion doesn’t depend on the inner information. Such kind of dynamics, leading to tolerance forming, is typical for ordinary kind of thinking, aimed at inner pattern of outside world stability. For scientific kind of thinking, aimed at adequacy of the inner pattern of the world, a mechanism is needed to stop the net relaxation; the mechanism has to be external relative to the model of logic. Computer simulation results for the learning conditions adequate to real holograms recording are presented.
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