The Sup Connective in IMALL: A Categorical Semantics
arXiv:2205.02142 · doi:10.1016/j.tcs.2026.115845
Abstract
We explore a proof language for intuitionistic multiplicative additive linear logic, incorporating the sup connective that introduces additive pairs with a probabilistic elimination, and sum and scalar products within the proof-terms. We provide an abstract characterisation of the language, revealing that any symmetric monoidal closed category with biproducts and a monomorphism from the semiring of scalars to the semiring Hom(I,I) is suitable for the job. Leveraging the binary biproducts, we define a weighted codiagonal map which is at the core of the sup connective.