  Semantically, possible world justification models for  \(\mathsf{LP}\) need no modification, since they already have  all the machinery of Hintikka/Kripke models. One models the \(\Box\)   operator in the usual way, making use of just the accessibility  relation, and one models the justification terms as described in  Section 3.1 using both accessibility and the evidence function. Since  the usual condition for \(\Box X\) being true at a world is  one of the two clauses of the condition for \(t : X\)  being true, this immediately yields the validity of  \(t : X \rightarrow \Box X\), and soundness follows easily. Axiomatic completeness is also rather straightforward.