arXiv2024
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.