A new area of application of methods of algebra of logic and to valued logic, which has emerged recently, is the problem of recognizing a variety of objects and phenomena, medical or technical diagnostics, constructing modern machines, checking test problems, etc., which can be reduced to constructing an optimal extension of the logical function to the entire feature space. For example, in logical recognition systems, logical methods based on discrete analysis and propositional calculus based on it are used to build their own recognition algorithms. In the general case, the use of a logical recognition method provides for the presence of logical connections expressed by the optimal continuation of a k-valued function over the entire feature space, in which the variables are the logical features of the objects or phenomena being recognized. The goal of this work is to develop a logical method for object recognition consisting of a reference table with logical features and classes of non-intersecting objects, which are specified as vectors from a given feature space. The method consists of considering the reference table as a logical function that is not defined everywhere and constructing an optimal continuation of the logical function to the entire feature space, which determines the extension of classes to the entire space.

翻译：逻辑代数与多值代数方法的一个新应用领域是识别各种对象与现象、医学或技术诊断、构建现代机器、检验测试问题等，这些问题可归结为在全体特征空间上构造逻辑函数的最优延拓。例如，在逻辑识别系统中，基于离散分析和以此为基础的命题演算的逻辑方法被用于构建自身的识别算法。通常，逻辑识别方法的使用需要存在由k值函数在全体特征空间上的最优连续所表达的逻辑联系，其中变量是被识别对象或现象的逻辑特征。本工作的目标是开发一种对象识别的逻辑方法，该方法由包含逻辑特征的参考表和非相交对象类别组成，这些类别被定义为给定特征空间中的向量。该方法将参考表视为一个未完全定义的逻辑函数，并在整个特征空间上构造逻辑函数的最优延拓，从而确定类别向整个空间的扩展。