A model-theoretic treatment of conditional logic due to philosopher David Lewis (1941–2001) that provides a precise semantic interpretation of the notion of similarity between possible worlds. While the notion of similarity is frequently captured by a number of accessibility relations—in which $w{R}_{\phi }{w}^{\prime }$ is read as ‘$w^{\prime }$ is among the most similar worlds to $w$ with respect to formula $\phi$’—systems of spheres permit a more fine-grained account by permitting degrees of similarity between worlds. In a system of spheres model with set of possible worlds $W$, each possible world $w$ is assigned a nested set ${\text{\$}}_w$ of non-empty subsets of $W$, i.e., a set of spheres of worlds where

• • ${\text{\$}}_w=\left\{S_i\mid i\in I\right\}$ where for all $i,j\in I$, $S_i\subseteq W$ and either $S_i⊊S_j$ or $S_j⊊S_i$

The larger a sphere $S_i\in {\text{\$}}_w$ is, the more permissive it is with respect to the possible worlds it treats as equivalent. If ${\text{\$}}_w=\left\{S_0,S_1\right\}$, the situation in $S_0=\left\{w,w^{\prime }\right\}$ an $S_1=\left\{w,w^{\prime },w^{″}\right\}$ represents that $w^{\prime }$ is more similar to $w$ than $w^{″}$ (i.e., $w^{″}$ is more remote than $w^{\prime }$).