Aggregate characteristics of discrete models appearing in different artificial intelligence problems are considered. It is shown that if an investigated object is a collection of its elements and its description contains properties of these elements and relations between them then a predicate calculus language is convinient for its simulation. In such a case a lot of problems are NP-hard. Upper bounds of steps for two essentially different decision algorithms are presented. A problem of transformation of an investigated object and the number of its decision steps is regarded. A many-level approach (consisting in the extraction of subformulas of goal conditions) to the decision of these problems is described. It allows to decrease the used time.