Algebra of Fourier-dual operations: conceptual thinking generation

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.