Hierarchical knowledge representation formalisms provide more efficient tool for simulating the knowledge domains contents models compared to descriptive logics based models. These formalisms allow constructing complicated semantic structures, associated with given professional problems that needed searching for the solutions. Application of hierarchical formalisms to professional activity domains is associated with claim of formalization the inference operator concept, as the foundation for realization the decision searching processes. The universal unified inference operator definition is introduced. It uses task structure invariants and complex knowledge, synthesized by processing the subject area knowledge base. Such a base is represented by enumerable sets of elementary and simple knowledge extracted from subject domain content. The possibility of any task reducibility into tasks combination from four special classes is settled. Every inference operator allows implementation as set of tasks solving processes described by knowledge synthesis rules. Such an operator is supplied by knowledge structure tracing mappings as the tool for tasks solutions extracting from synthesized knowledge. Universal concepts and invariants are proposed for tasks decomposition and knowledge synthesis rules descriptions. The tasks structures and tasks solving processes rules serve to be the foundation for inference operator formal description. The rule premises types are represented by templates, conditions and procedures calls as well as rules’ conclusions templates. Rules’ premises templates provide components recognitions and analysis for sets of associated knowledge. Conditions and procedures calls allow describing complex situation of knowledge synthesis as specified at rules’ conclusions. Task structure is created by the task decomposition process. It defines the subtasks based processes that implement the scenario of tasks solving.