A binary relation $R$ holding between possible worlds in frames for intuitionistic and modal logic. When for two worlds $w$, $w^{\prime }$, $wR{w}^{\prime }$ holds in a model, $w^{\prime }$ is said to be ‘accessible from’ $w$. Accessibility provides a basis for the typical truth condition for a formula $\square \phi$ where $\square$ is a necessity operator:

• • $\square \phi$ is true at $w$ if for all $w^{\prime }$ such that $wR{w}^{\prime }$ (i.e., at all accessible worlds $w^{\prime }$) $\phi$ is true at $w^{\prime }$.

One natural application of accessibility is found in tense logic, in which the interpretation of $R$ is that $wR{w}^{\prime }$ whenever $w^{\prime }$ represents a state in the future of $w$. Generalizations of the accessibility relation are common. In many semantics for conditional logic, there exists an accessibility relation corresponding to each formula $\phi$ in the language so that $w{R}_{\phi }{w}^{\prime }$ is often interpreted as representing that $w^{\prime }$ is among the most similar worlds to $w$ at which $\phi$ is true. In semantics for relevant logics, a ternary relation $R$ between possible worlds (or set-ups), provides the apparatus for the truth condition for relevant conditionals:

• • $\phi \to \psi$ is true at $w$ if for all $w^{\prime }$ and $w^{″}$ such that $Rw{w}^{\prime }{w}^{″}$, if $\phi$ is true at $w^{\prime }$, then $\psi$ is true at $w^{″}$.