  In this paper, we consider the full Lambek calculus enriched with
subexponential modalities in a distributive setting. We show that the
distributive Lambek calculus with subexponentials is complete with respect to
its Kripke frames via canonical extensions. In this approach, we consider
subexponentials as S4-like modalities and each modality is interpreted with a
reflexive and transitive relation similarly to usual Kripke semantics.
