Abstract: The object of the research is the subject area, which is a precedent relationship between objects and their characteristics used in solving image recognition problems.Intellectual analysis of data is one of the necessary stages in the solution of poorly formalized problems; therefore, in many cases the accuracy of the solution of the task depends on the method of building knowledge bases, analyzing them and minimizing them. The development of common formal methods for revealing logical patterns in any given subject area seems to be a very pressing problem, as it provides the opportunity to form optimal knowledge bases, which greatly simplifies the solution and improves its quality. In this paper, the author use the apparatus for differentiating Boolean functions to analyze and minimize knowledge bases, which are the directions of modern discrete mathematics and find their application in problems of dynamic analysis and synthesis of discrete digital structures. The main results of the study are a constructed logical function that analyzes the relationship between objects and characteristics that characterize them, which is an opportunity to reveal all the laws of a given subject area; as well as the method of minimizing knowledge bases obtained on the basis of logical data analysis, revealing a minimal set of decision rules, sufficient for solving the task.

Abstract: In this article the authors offer a method for constructing logical operations to analyze and correct the results of the operation of sigma-pi neural networks designed to solve recognition problems. The aim of the research is to reveal the logical structure of implicit regularities formed as a result of training the neural network. The method proposed by the authors restores the training sample based on the values of the sigma-pi weighting coefficients of the neuron, analyzes the relationships of this structure and allows to detect implicit regularities, which contributes to the increase of the adaptive properties of the sigma-pi neuron. To solve this problem, the authors perform a logical-algebraic analysis of the subject area within the framework of which the cigma-pi of a neuron is trained, a logical decision function is constructed, its properties and applicability to the correction of the work of a neuron are investigated. It is widely known that the combined approach to the organization of the recognition algorithms increases their effectiveness. The authors argue that the combination of the neural network approach and the use of logical correctors allows, in cases of an incorrect response, to indicate the object closest to the requested attributes from the sample on which the sigma-pi neuron was trained. This significantly improves the quality of the automated solution of intellectual problems, i.e. ensuring the accuracy of achieving the right solution by using the most effective systems for analyzing the original data and developing more accurate methods for their processing.

Abstract: The subject of the research are methods and algorithms aimed at practical solution of problems of pattern recognition in the weakly formalized fields of knowledge, such as medical field, technical field, geological reconnaissance diagnostics, forecasting and construction of expert systems. The solutions of such problems entered into use a large number of incorrect (heuristic) algorithms. The authors focus on such aspects as the need for the development of the theory of corrective operations, the necessity for the synthesis of correct algorithms minimum complexity, solving the stability issues by using mathematical methods. Special attention is paid to the construction of the algorithm, correct on the whole set of recognizable objects, based on existing algorithms and decision rules drawn up for the studied area. The logical approach may be a technology of constructing a theory of the synthesis of the correct recognition algorithms based on existing family of algorithms. The article shows that these methods allow creating algorithms that implement certain expert conclusion, despite the lack of adequate mathematical models of the relationships between image and its properties, incomplete and contradictory of data. The main conclusion of the research is in a logical analysis of a given subject area, in terms of variables valued logic. The authors propose approaches to the design of procedures for recognition of precedents on the basis of incorrect set of algorithms and constructed logical decision rules. The main contribution of the authors in the study of the topic is the proposed algorithm, expanding the area of the solutions obtained and correct on the whole set of recognizable objects. The novelty of the study is the use of variables valued logic that improves the correctness of encoded information and increase the expressiveness of the conclusions.