Pattern recognition problem using properties of parts of a recognizable objects and relations between them is NP-hard. That is why quick recognition of an object with many elements is a difficult problem. To overcome such a difficulty the use of upper bound of steps for an algorithm solving such a problem based on logic-objective approach is suggested. The possibility of the use of Prolog language family for image recognition is investigated. An example of such a problem for which the use of these upper bounds of complexity permits to decrease the time of its solution is presented.