Self-referentiality of justified knowledge

The principal result of Justification Logic is the Realization Theorem, which states that behind major epistemic modal logics there are corresponding systems of evidence/justification terms sufficient for reading all provable knowledge assertions as statements about justifications. A knowledge/belief modality is self-referential if there are modal sentences that cannot be realized without using self-referential evidence of type "t is a proof of A(t)." Building on an earlier result that S4 and its justification counterpart LP describe knowledge that is self-referential, we show that the same is true for K4, D4, and T with their justification counterparts whereas for K and D self-referentiality can be avoided. Therefore, no single modal axiom from the standard axiomatizations of these logics is responsible for self-referentiality.