In addition to logical coherence, the theory of basic operations has psychological sanction. Consequently, operations which would have been inadmissible were these considered from the perspective of standard logic are accepted because these operations occur and find consistent use in the logic of the child. The operations of cognitive algebra are more general than those associated with standard logic and therefore a variety of logics may be derived by use of the basic operations. These include deontic and dialectic logics, among others. In conjunction with progressive group theory, new operations comparable to the operations of standard logic and operations of a higher order which involve evaluations of structural coherence, completeness, balance, symmetry, and the like may be rigorously defined.
Cognitive algebra facilitates the identification of antecedent and consequent operational abilities.
Each level of cognition is linked to the stages which precede and follow. Cognitive algebra may provide a useful formalism to logicians. Standard logic has long seemed ossified with few new paradigms or logics. It has occupied a secure niche as a court of last resort in the tribunal of Newtonian physics, but developments in quantum mechanics, subatomic theory, and mathematics call for its reappraisal. Cognitive algebra provides a sufficiently general paradigm for the disciplined investigation of alternative frameworks to standard logic.