In a previous work we introduced a non-associative non-commutative logic extended by multimodalities, called subexponentials, licensing local application of structural rules. Here, we further explore this system, exhibiting a classical one-sided multi-succedent classical analogue of our intuitionistic system, following the exponential-free calculi of Buszkowski, and de Groote, Lamarche. A large fragment of the intuitionistic calculus is shown to embed faithfully into the classical fragment.

翻译：在先前的工作中，我们引入了一种由多模态（称为次指数）扩展的非结合非交换逻辑，允许结构规则的局部应用。本文进一步探索该体系，遵循Buszkowski以及de Groote、Lamarche的无指数演算，给出了我们直觉主义系统的经典单边多后继经典对应。研究表明，直觉主义演算的大多数片段可忠实嵌入经典片段中。