  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.
