  To be precise, a semantics for \(\mathsf{J}_{CS}\), where \(CS\) is any constant specification, is to be defined. Formally, a possible world justification logic model for \(\mathsf{J}_{CS}\) is a structure \(\mathcal{M} = \langle \mathcal{G} , \mathcal{R} , \mathcal{E} , \mathcal{V}\rangle\) . Of this, \(\langle \mathcal{G} , \mathcal{R}\rangle\) is a standard \(\mathsf{K}\) frame, where \(\mathcal{G}\) is a set of possible worlds and \(\mathcal{R}\) is a binary relation on it.  \(\mathcal{V}\) is a mapping from propositional variables to subsets of \(\mathcal{G}\), specifying atomic truth at possible worlds.