  In \(\mathsf{S4LP}\) both implicit and explicit knowledge is represented, but in possible world justification model semantics a single accessibility relation serves for both. This is not the only way of doing it. More generally, an explicit knowledge accessibility relation could be a proper extension of that for implicit knowledge. This represents the vision of explicit knowledge as having stricter standards for what counts as known than that of implicit knowledge. Using different accessibility relations for explicit and implicit knowledge becomes necessary when these epistemic notions obey different logical laws, e.g., \(\mathsf{S5}\) for implicit knowledge and \(\mathsf{LP}\) for explicit.  The case of multiple accessibility relations is commonly known in the literature as Artemov-Fitting models, but will be called multi-agent possible world models here. (cf. Section 5.2).