The initial concept of knowledge representation formalism is based on unified invariants for algebraic and semantic structures of knowledge. These invariants are proposed to be the implementation of independent knowledge properties specifications for notions of knowledge construction and knowledge transformation. Abstract knowledge spaces are defined as special class of formalisms with marked binary trees as unified knowledge structure format. These formalisms offer more sophisticated opportunities for knowledge representation and transformation in comparison with set-theoretic formalisms, learning spaces and descriptive logics. Tasks setting format and inference operator, as foundation for tasks solution procedure, are investigated in the submitted paper as additional invariants and considered to be the elements for subsequent development of the concept of knowledge representation formalisms. These invariants are specified for extensive class of abstract knowledge spaces application areas and submitted by thoroughly analyzed specification for simple and complex knowledge and also for tasks, constructed with the sets of elementary knowledge and subject semantic relations. Knowledge formalism inference operator is defined as a goals-controlled system operated by rules of goal knowledge synthesis that applies forward and backwards chaining inference schemes. The rule antecedents belong to classes named as templates, conditions and procedures calls. Rules consequents are elements of the templates class and define subject areas knowledge structures as composition performed over template antecedents implementations. Task solution is extracted from goal knowledge structure synthetized by inference operator with one of abstract knowledge space tracing operations.