In . , Fitting showed that the standard hierarchy of logics of justified knowledge is conservative (e.g.a logic with positive introspection operator ! is conservative over the logic without !). We do the same with most logics of justified belief, showing both conservation of sequent proofs and extensibility of models. A brief example shows that conservativity does not hold for logics of justified consistent belief. © 2011 Elsevier B.V.
Milnikel, R. S. (2012). Conservativity for logics of justified belief: Two approaches. Annals of Pure and Applied Logic, 163(7), 809–819. https://doi.org/10.1016/j.apal.2011.09.015