2026-07-21T18:41:08Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:18005 2024-03-06T11:00:50Z ddc:004 open_access

Unifying Graded Linear Logic and Differential Operators Breuvart, Flavien Kerjean, Marie Mirwasser, Simon Linear Logic Denotational Semantics Functional Analysis Graded Logic Linear Logic refines Classical Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which can describe the resource management or the complexity analysis of a program. From another perspective, Differential Linear Logic is an extension which allows the linearization of proofs. In this article, we merge these two directions by first defining a differential version of Graded linear logic: this is made by indexing exponential connectives with a monoid of differential operators. We prove that it is equivalent to a graded version of previously defined extension of finitary differential linear logic. We give a denotational model of our logic, based on distribution theory and linear partial differential operators with constant coefficients. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Flavien Breuvart and Marie Kerjean and Simon Mirwasser 2023 Is Part Of LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSCD.2023.21 urn:nbn:de:0030-drops-180052 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.21 eng https://creativecommons.org/licenses/by/4.0/legalcode