Conservativity for Logics of Justified Belief

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In [1], 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, but taking a semantic approach rather than Fitting’s syntactic one. A brief example shows that conservativity does not hold for logics of justified consistent belief.