Deep cases may be treated as a type of unary operations which transform nouns (or noun phrases) to the corresponding noun case forms. As noun phrases usually occur in the form of noun cases and as intensional logic is one of the most important logical tools for the treatment of natural language, it seems reasonable to introduce deep case operations into the syntax of intensional logic. \par In this paper the logic CIL (Case Intensional Logic), an extension of Montague intensional logic IL [Montague, 1970] is described. The main characteristic of CIL is that operations (2) corresponding to the deep noun cases are explicitly introduced into its syntax. This logic is very convenient for translating natural language locutions, particlularly for the languages with free word order. The role of participant is expressed in an explicit form. Thus the underlying structure, especially the structure TR (tectogrammatical representation) [Sgall, Hajičova ${\&}$ Penevova, 1986], is much more closer to the corresponding intensional logic formula. The idea for such an approach can be found in inflective languages in which deep cases are usually expressed by the corresponding morpholofical forms. We show that such an extension is not unnatural and that the main features of intensional logic IL are not violated. In the sequel, we develop the syntax and semantics of CIL, define generalized semantics and, for the given axiomatization, prove the generalized completeness theorem.