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It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (<jats:inline-formula><jats:tex-math>$$\\mathrm IMLL$$<\/jats:tex-math><\/jats:inline-formula>). The starting point is a review of Sandqvist\u2019s B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the<jats:italic>generalized<\/jats:italic>elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for<jats:inline-formula><jats:tex-math>$$\\mathrm IMLL$$<\/jats:tex-math><\/jats:inline-formula>, in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established.<\/jats:p>","DOI":"10.1007\/978-3-031-43513-3_20","type":"book-chapter","created":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T14:02:36Z","timestamp":1694613756000},"page":"367-385","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Proof-Theoretic Semantics for\u00a0Intuitionistic Multiplicative Linear Logic"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7144-6910","authenticated-orcid":false,"given":"Alexander V.","family":"Gheorghiu","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5749-0758","authenticated-orcid":false,"given":"Tao","family":"Gu","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6504-5838","authenticated-orcid":false,"given":"David J.","family":"Pym","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,9,14]]},"reference":[{"issue":"2","key":"20_CR1","doi-asserted-by":"publisher","first-page":"514","DOI":"10.2307\/2275217","volume":"58","author":"G Allwein","year":"1993","unstructured":"Allwein, G., Dunn, J.M.: Kripke models for linear logic. 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