Knowledge representation research is not only formal, it is also descriptive and normative. Its aim is to implement a formal system which captures a practically relevant body of cognitive faculties employed by humans. It capitalizes on its technical strength to extend human knowledge representation and reasoning capabilities. In this monograph, the author develops formalisms for his own notion of a vivid knowledge representation and reasoning system, characterized by the presence of two kinds of negation (weak and strong) and the requirements of restricted reflexivity, constructivity, and non-explosiveness.