A Syntactic Realization Theorem for Justification Logics

Justification logics are refinements of modal logics where modalities are replaced by justification terms. They are connected to modal logics via so-called realization theorems. We present a syntactic proof of a single realization theorem that uniformly connects all the normal modal logics formed from the axioms d, t, b, 4, and 5 with their justification counterparts. The proof employs cut-free nested sequent systems together with Fitting’s realization merging technique. We further strengthen the realization theorem for KB5 and S5 by showing that the positive introspection operator is superfluous.