We investigate the conceptual link between action refinement for a process algebra which contains the TCSP-parallel composition operator and recursion on the one hand and action refinement for the Hennessy-Milner-Logic on the other. We show that the assertion p ⊨ ϕ ⇔ P[a↪Q] ⊨ ϕ[a↪Q] where ⋅[a↪Q] denotes the refinement operator both on process terms and formulas holds in the considered framework under weak and reasonable restrictions.