 Adopting one or the other approach to quantification affects the notion of validity, even for non-temporal principles. For instance, the sentence \(\exists x(x= c)\) is valid in first-order logic, and it is valid in the constant domain semantics as well, but it is no longer valid in the varying domain semantics, because the object assigned to the constant \(c\) may not belong to the local domain. Another principle from plain first-order logic that distinguishes the two semantics is the scheme of Universal Instantiation (where \(\tau\) is any term free for substitution for \(x\) in \(\varphi\)):  \[\forall x \varphi(x) \to  \varphi(\tau), \]   which is, likewise, valid in the constant domain semantics but invalid in the varying domain semantics, for analogous reasons. The main distinction between the two semantics is, however, in terms of principles that involve interaction of temporal operators and quantification, such as the Barcan formula schemata and their converses. In the following two sections, we take a closer look at some important validities and non-validities in the respective semantics.