  We study abstract intermediate justification logics, that is arbitrary
intermediate propositional logics extended with a subset of specific axioms of
(classical) justification logics. For these, we introduce various semantics by
combining either Heyting algebras or Kripke frames with the usual semantic
machinery used by Mkrtychev's, Fitting's or Lehmann's and Studer's models for
classical justification logics. We prove unified completeness theorems for all
intermediate justification logics and their corresponding semantics using a
respective propositional completeness theorem of the underlying intermediate
logic. Further, by a modification of a method of Fitting, we prove unified
realization theorems for a large class of intermediate justification logics and
accompanying intermediate modal logics.
