Semantic Analysis of Subexponential Modalities in Distributive Non-commutative Linear Logic

Daniel Rogozin (University College London)

Semantic Analysis of Subexponential Modalities in Distributive Non-commutative Linear Logic

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arxiv 2308.04521 v1 pith:RD6SLZWK submitted 2023-08-08 cs.LO

Daniel Rogozin (University College London) This is my paper · ORCID

classification cs.LO

keywords distributivemodalitiescalculusconsiderkripkelambeksubexponentialsubexponentials

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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.

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