We introduce abstract intermediate justification logics by extending arbitrary intermediate propositional logics with a subset of specific axioms of (classical) justification logic. We study these intermediate justification logics semantically out of various perspectives by combining the well-known semantical access points to intermediate logics through algebraic and Kripke-frame based models with the usual semantic machinery used by Mkrtychevs, Fittings or Lehmanns and Studers 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. We consider especially the particular instances of intuitionistic, classical and Godel justification logics because of their previous presence in the literature.