In modal logic, describes a theory of identity in which sentences of the form $a=b$, where $a$ and $b$ are names, can be assigned different truth values at different possible worlds. This is to say that a semantics with possible worlds has a contingent theory of identity when it has models in which there exist worlds $w$ and $w^{\prime }$ and an identity sentence $a=b$ such that $a=b$ is true at $w$ and not true at $w^{\prime }$. Contingent identity is opposed to necessary identity, according to which the truth of a statement $a=b$ entails the truth of $\square \left(a=b\right)$.