  Single world justification models were developed considerably before the more general possible world justification models we have been discussing, (Mkrtychev 1997). Today they can most simply be thought of as possible world justification models that happen to have a single world. The completeness proof for \(\mathsf{J}\) and the other justification logics mentioned above can easily be modified to establish completeness with respect to single world justification models, though of course this was not the original argument. What completeness with respect to single world justification models tells us is that information about the possible world structure of justification models can be completely encoded by the admissible evidence function, at least for the logics discussed so far. Mkrtychev used single world justification models to establish decidability of \(\mathsf{LP}\), and others have made fundamental use of them in setting complexity bounds for justification logics, as well as for showing conservativity results for justification logics of belief (Kuznets 2000, Kuznets 2008, Milnikel 2007, Milnikel 2009). Complexity results have further been used to address the problem of logical omniscience.