The cognitive goals classification problem relates to constructing the substantially full system of independent classes of such goals correlated with various philosophical, linguistic and psychological concepts and models. The formalized and unified systems of universal basic qualifiers of cognitive goals and knowledge synthesis operations, agreed with concept of knowledge representation formalisms, are considered. It allows presenting of any cognitive goal as combinations of the goals from basic classes and defining complex knowledge synthesis processes. The created classifications are based on specifications of weakly formalized and ambiguous concepts of cognitive goal and cognitive operation, offered by B. Bloom. Such a classification is broad, tangled and ambiguous. Realization of goal from any offered class often suppose realization of goals from other classes and needs accommodation of a hardly realized multiplicity of relations between goals and operations. Coordination of the created classification with knowledge representation formalisms invariants is realized by such a compression of cognitive goal and operation concepts that imply independence of goals and operations of different classes. Relation of aggregation does not connect the elements of defined classes. It allows considering the simulated classes of cognitive goals in the narrow sense bounded by specific formalized requirements to their general properties and realization, own for each such class. The universal hierarchy of formalized classes of computable knowledge processing operations is unique for all knowledge representation formalisms. It is adapted to hierarchy of cognitive goals classes and is based on set-theoretic, algebraic, logical and topological aspects of such operations. Transforming the mathematical concepts into the functional invariants for cognitive goals realizations for any knowledge representation formalism is coordinated with the universal invariants of knowledge algebraic and semantic structures. The constructed versions of qualifiers expand theoretical and application-oriented opportunities for the concept of knowledge representation formalisms, keeping its generality, abstractness and universality.