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.

翻译：本文在分布式框架下研究了添加子指数模态的完整Lambek演算。我们证明，具有子指数模态的分布式Lambek演算通过典范扩张在Kripke框架下是完备的。在该方法中，我们将子指数模态视为类S4模态，且每个模态通过自反且传递的关系进行解释，这与通常的Kripke语义类似。