Conservativity for logics of justified belief: Two approaches

In [7], 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.