Abstract: The object of study in this article involves logical algorithms for recognition and diagnostics, which are designed for functioning in weakly formalized areas of knowledge. Directional search trees and logical neural networks can be classified as such algorithms. The proposed implementation of a logical algorithm for searching for objects within a given domain, which are correspondent to a set of properties, is based upon the application of logical functions, which are formed with  variable-valued predicates. The representation of the training sample in the form of variable-valued logic function allows not only to eliminate redundancy in the description of objects, but also to construct all possible classes of objects by all attributes, and also, using the constructed functions, to reveal hidden regularities in the subject domain.The basis for constructing variable-valued logical functions is a set of production rules, each of which contains both a set of properties and an object defined by them. Integration and optimization of rules are performed using logical operations. The scientific novelty of this study is due to the following.  The author proposes knowledge extraction from the initial databases containing information on the properties of the analyzed objects using variable-valued predicates. Then a method is proposed for obtaining all possible classes of structures of telecommunication networks, which makes it possible to reveal additional properties and to make an intelligent choice of the desired topology.