A generalization of the notion of a possible world invented by Richard Sylvan (1935–1996) and Val Plumwood (1939–2008) as a device for models of the relevant logic of first degree entailment. By convention, the set of formulae true at any possible world is generally construed as consistent and complete, i.e., for any formula $\phi$, precisely one member of $\left\{\phi ,\neg \phi \right\}$ is true at a possible world $w$. However, relevant logics must deny theses such as $\left(\phi \wedge \neg \phi \right)\to \psi$; a possible world-type approach much include some object at which a contradiction may be true or a tautology may be false. Set-ups serve as such ‘impossible worlds’ by allowing initial assignments of literals to be inconsistent (in which both $p$ and $\neg p$ are made true for some atom $p$) and incomplete (in which neither $p$ nor $\neg p$ are true for some atom $p$).