Transporting the partitioning to the concept level

In concept theory, it is possible to make a distinction between the intensional/concept level, which is the level of human thinking, and the extensional/set theoretical level, which is the level of computer science. At the intensional level, concepts are dealt with, whereas, at the extensional level set of objects/classes are considered. As a set of objects falls under many different concepts, an arrow exists which is directed only from the intensional to the extensional level. In this paper, a methodology is proposed for transporting at the concept level mappings of graphs from semantic to object level. This idea is important for both reasons. Within the concept level effective algorithms which have correspondently classes of objects supported by computer systems are not yet available, but can be defined. On the other hand, within appropriate concept structures it is possible determining all the concepts under which a set of objects falls.