  Since justification logics provide explicit justifications, while conventional logics of knowledge provide an implicit knowledge operator, it is natural to consider combining the two in a single system. The most common joint logic of explicit and implicit knowledge is \(\mathsf{S4LP}\) (Artemov and Nogina 2005). The language of \(\mathsf{S4LP}\) is like that of \(\mathsf{LP}\), but with an implicit knowledge operator added, written either \(\mathbf{K}\) or \(\Box\) . The axiomatics is like that of \(\mathsf{LP}\), combined with that of \(\mathsf{S4}\) for the implicit operator, together with a connecting axiom, \(t : X \rightarrow \Box X\), anything that has an explicit justification is knowable.