Data base (DB) technology is a large field, comprising DB design methods, DB theory, DB models, DB management, and DB applications. In recent years, formally defined DB models have become an important topic. In knowledge representation, being the Artificial Intelligence area most closely related to DB research, the general trend moves towards the standard description of models by predicate logic. For DB design, an architecture on 3 abstraction levels is a widely accepted standard. It distinguishes between the conceptual level, the internal level, and the external level. On the conceptual level the problem relevant aspects are exclusively considered, whereas on the internal level the physical aspects (implementation details), and on the external level specific applications are treated. Each level has its respective schemas. In this paper we focus on already designed FAIM conceptual schemas (a design method is available): A mathematical model is developed for them. Each FAIM conceptual schema consists of association types (FAIM) with action types thereon (insert/retrieve/modify/delete) and inference typēs̄ (FAIM), all of which are formally defined (FAIM) by first order logic with equality. Associations, actions, and inferences are instances of association, action, and inference types. Associations are modelled relations among modelled living beings, things (so-called individuals), or abstract concepts (so-called designators). An object (individual or designator) must be modelled as an individual if either its name may be subject to change, or if its name is a compound name. Objects play so-called roles within associations. Actions are modelled events, inferences modelled rules. The use of predicate logic leads to particularly exact, unambiguous, and expressive definitions. Nevertheless only few models have been rigorously defined for conceptual schemas. Within the scope of further developments FAIM is going to be a model of knowledge representation schemas.