 If constants are treated as rigid designators, the principle of Necessity of Identity \(\tau_1 = \tau_2 \rightarrow A(\tau_1 = \tau_2)\) is valid, for both variables and constants (recall that \(A \varphi = H \varphi \land \varphi \land G\varphi\)). However, the language may also contain individual terms for which this principle fails. A core example are definite descriptions, such as “the Pope”, which may pick out different objects at different times. Importantly, proper names and definite descriptions require a different semantic treatment and are not freely inter-substitutable. For example “The Pope has been the sovereign of the Vatican City since 1929” is true, whereas “Jorge Mario Bergoglio has been the sovereign of the Vatican City since 1929” is false. Moreover, in a temporal setting, the question arises how to deal with definite descriptions that refer to objects that do no longer or not yet exist, such as “the first child to be born in South Africa in 2050”. The problems get even more intricate in a branching time setting, where time and modality are combined. Note, for instance, that some definite descriptions that are temporally rigid may be modally non-rigid. For more on definite descriptions in the context of temporal logic, see Rescher and Urquhart (1971, Chapters XIII and XX) and Cocchiarella (2002).