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arXiv · 2205.02142

The Sup Connective in IMALL: A Categorical Semantics

Alejandro Díaz-Caro·Octavio Malherbe
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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.

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Alejandro Díaz-Caro, Octavio Malherbe. 2022-05-04. The Sup Connective in IMALL: A Categorical Semantics. https://doi.org/10.1016/j.tcs.2026.115845

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