A knowledge base (KB) is composed of logical constructs representing knowledge about a world. We assume that such a world can be modeled by using notions of (nave) set theory, e.g. elements, sets, relations, functions, and thus that knowledge about this set theoretical model are expressed by (a variant or a fragment) of first order logic. In this paper we are interested by identification problems concerning individual entities in world. These individual entities are represented by elements in the model and these elements are represented by special symbols called surrogates in the knowledge base. Surrogates should be in one-to-one correspondence with the set of world entities. Our aim is to define a KB faithful, or unambiguous, with respect to the identification of world entities and to propose mechanisms allowing a user to design, build, maintain such a KB, and also to repair an ambiguous KB. In this paper we consider individual entities, nevertheless similar identification problems occur for other notions such as classes of entities or relationships between entities.