 One way to deal with definite descriptions is to switch from an extensional to an intensional account of individual terms. That is, rather than assigning to each term at each time instant an extension, i.e. an object from the domain, one may assign to each term an intension, i.e. a function from time instants to objects. A general framework in which individual terms are assigned both extensions and intensions is the Case Intensional First-Order Logic (CIFOL) proposed in Belnap and Müller (2014a; 2014b). In CIFOL, identity is extensional, predication is intensional, and individuals can be identified across times without making use of rigid designation. The framework is also interesting against the background of the debate on persistence as it remains metaphysically neutral with respect to the precise nature of the objects included in the overall domain.