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: 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.