The article is devoted to the application of Formal Concept Analysis to the development of domain semantic models. The paper deals with the problem of axiomatization of classes of cases from various domains. The research is based on the model theoretical approach to the formalization of domains and on Formal Concept Analysis. We consider the four-level semantic model that conceptually describes the given domain. The third level of the semantic model is the set of domain cases. To describe sets of domain cases we use formal contexts; the objects of these formal contexts are models formalizing domain cases. We represent classes of domain cases as classes of models having different signatures. Theories of classes of domain cases and axiomatizable classes of domain cases are investigated. They are defined as intents and extents of formal concepts of the corresponding formal contexts. It is shown that the introduced notion of theory of class of cases, i.e., theory of class containing models with different signatures, is a generalization of the notion of theory of a class of models in the classical sense.