 Finally, note how a plausibility relation defines, semantically, layers or spheres of equally-plausible worlds, with the spheres themselves ordered according to their plausibility so that every strong belief characterizes one of the spheres. This will turn every plausibility model into a sphere model (Grove 1988; Spohn 1988), making it perfectly fit to model  belief revision.  Still, even though in \(\cL_{\left\{ [{\leq}], K \right\}}\) there are formulas expressing that \(\varphi\) holds in the most plausible sphere (the mentioned \(B\varphi\), given by \(\langle{\leq}\rangle[{\leq}]\varphi)\), no formula can express, e.g., that \(\varphi\) holds in the next to most plausible worlds. One way to fix this ‘problem’ is to define (now semantically) the strict plausibility relation \({&lt;} := {\leq} \cup {\not\geq}\) (with \(\geq\) the converse of \(\leq\), defined in the standard way, \({\geq} := \left\{ (u,w) \in W \times W \mid w \leq u \right\})\), and then introduce a standard modality for it: