  In (Fitting 2005) a stronger version of the semantics was also introduced. A model \(\mathcal{M} = \langle \mathcal{G} , \mathcal{R} , \mathcal{E} , \mathcal{V}\rangle\) is called fully explanatory if it meets the following condition. For each \(\Gamma \in \mathcal{G}\), if \(\mathcal{M} , \Delta \Vdash X\) for all \(\Delta \in \mathcal{G}\) such that \(\Gamma \mathcal{R} \Delta\) , then \(\mathcal{M} , \Gamma \Vdash t : X\) for some justification term \(t\). Note that the condition, \(\mathcal{M} , \Delta \Vdash X\) for all \(\Delta \in \mathcal{G}\) such that \(\Gamma \mathcal{R} \Delta\) , is the usual condition for \(X\) being believable at \(\Gamma\) in the Hintikka/Kripke sense.  So, fully explanatory really says that if a formula is believable at a possible world, there is a justification for it.