Abstract: With expanding of the knowledge base scale and increasingly complication of its structure, the problems of the limited capability of first-order logic expose to be more and more serious, thus the application that based on knowledge representation of higher-order logic is quite necessary.The original research based on KDK and KDK* will inevitably lead to development and research of higher first-order logic.This paper first summarizes the knowledge discovery that based on the knowledge base, then introduces the representation language of the high-order logic knowledge-Escher, KDK and KDK*.At last, expands the connotation of Double-Bases Cooperating Mechanism under the background of first-order logic, and illustrate the equivalence theorem of KDK* process model logic that is facing the high-order logic.