To actualize an automatic certification system for a theorem in a broad sense which is used for an on-line manual of a machine, CAD for computer programming, translating operation assistance between different languages, knowledge management, and digital nervous system.

Keys of data of this retrieval system are comprehensively classified into key storing data prescribing an associating function, key storing data defining an object, key storing data of thesauruses, key storing data regarding classifications, key storing data on rules for inference, and key storing data regarding solution examples of problems; and specific data types suitable for computer processing are given to them and processed by algorithm having advantages of an object-oriented database, a knowledge database, and a commercial on-line database using the thesauruses.