A Fibrational Approach to Multiplicative Additive Indexed Linear Logic - Archive ouverte HAL
Preprints, Working Papers, ... (Preprint) Year : 2023

A Fibrational Approach to Multiplicative Additive Indexed Linear Logic

Une approche fibrationnelle de la logique indexée multiplicative additive

Abstract

In this paper, we achieve a modular and fairly concise presentation of the semantic ideas that lie behind the multiplicative-additive fragment of indexed linear logic. We generalize the basic definition of its syntax, utilizing objects of appropriate categories, referred to as "loci", in place of sets of resources. We prove that this generalized proof system enjoys cut-elimination. We then present its semantics, exploiting the notion of categorical fibration. We interpret formulae defined under a loci as elements of its fiber. We observe that, while multiplicative connectives (i.e., the star-autonomous structure) are confined to each fiber, the additives (i.e., the product and coproduct structures) live within the entire fibration. Finally, we build various examples of categorical models for our system.
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Dates and versions

hal-03978764 , version 1 (08-02-2023)

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  • HAL Id : hal-03978764 , version 1

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Flavien Breuvart, Thomas Ehrhard, Nicolas Munnich, Federico Olimpieri. A Fibrational Approach to Multiplicative Additive Indexed Linear Logic. 2023. ⟨hal-03978764⟩
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