The statements of the practically useful problems of intelligent activity

Actuality of the classification based on general principles and terminology well-determined by mathematical apparatus is shown. The mathematical apparatus is suggested that allows to introduce mathematical abstractions for all the notions used in task specifications. A multilevel classification of tasks is proposed in that the basic classification of tasks is expressed rather abstractedly. Further, on the lower levels of abstractions special properties of domains are introduced and formally represented, and refined specification of tasks and new inherent tasks are suggested.