Method of a distributed construction and the use of a level description of goal conditions within the framework of a logic-predicate approach to AI problems is described in the paper. The previously proposed logical-predicate approach to solving AI problems is briefly described. Many of these problems are NP-complete or NP-hard. According to a set of goal conditions, the author has earlier proposed construction of their level (hierarchical) descriptions, the use of which significantly decreases the computational complexity of the problems. The construction of such descriptions is performed only once, and then the resulting descriptions are reused. Both the distributed construction of level descriptions of goal conditions and their distributed use make it possible to decrease the time complexity of solving AI problems.