Abstract: The subject of the research is a logical approach to data analysis and the development of software tools capable of identifying hidden patterns, even with a limited amount of data. The input data consists of indicators of the diagnosis of patients, their diagnoses and the experience of doctors obtained in the course of medical practice.
The research method is the development of software tools based on systems of multivalued predicate logic for the analysis of patient data. This approach considers the source data as a set of general rules, among which it is possible to distinguish those rules that are sufficient to explain all the observed data. These rules, in turn, are generative for the area under consideration and help to better understand the nature of the objects under study. The novelty of the study lies in the use of multivalued logic to analyze a limited amount of medical data of patients in order to determine the most likely diagnosis with a given accuracy. The proposed approach makes it possible to detect hidden patterns in the symptoms and results of patient examinations, classify them and identify unique signs of various forms of gastritis. Unlike neural networks, logical analysis is transparent and does not require training on large amounts of data.
The conclusions of the study show the possibility of such an approach for diagnosis with a lack of information, as well as the offer of alternatives if the required accuracy of diagnosis is not achieved.

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.