A semantic device first employed in the set-up semantics for relevant logic introduced by Richard Sylvan (1935–1996) and Val Plumwood (1939–2008). A Routley star $\star$ is a unary bijective function mapping each possible world $w$ (or set-up) to a corresponding ‘star world’ $w^{\star }$ that meets at least the following criterion:

• • $w^{\star \star }=w$

In semantics with the Routley star, the truth condition for negated formulae then become:

• • $\neg \phi$ is true at $w$ if $\phi$ is not true at $w^{\star }$.

The Routley star is designed to permit non-classical evaluations at worlds, e.g., by designing a model in which an atomic formula $p$ is true at a world $w$ but not true at its star world $w^{\star }$, both $p$ and $\neg p$ are true at $p$. Assuming that standard truth and falsity conditions for conjunctions and disjunctions hold at worlds, the negation that arises from the Routley star is a De Morgan negation, as it is involutive and satisfies De Morgan’s laws. It may be noted that in models in which $w=w^{\star }$ for all worlds $w$, the above truth condition converges with the classical account of negation, i.e.,

• • $\neg \phi$ is true at $w$ if $\phi$ is not true at $w$ (i.e., $w^{\star }$).