Gheorghiu, Alexander;
Gu, Tao;
Pym, David;
(2023)
Proof-theoretic Semantics for Intuitionistic
Multiplicative Linear Logic.
In: Ramanayake, Revantha and Urban, Josef, (eds.)
Procceedings of the 32nd International Conference on Automated Reasoning with Analytic Tableaux and Related Methods.
(pp. pp. 367-385).
Springer: Prague, Czech Republic.
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Abstract
This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of Sandqvist’s B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the generalized elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for IMLL , in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established.
| Type: | Proceedings paper |
|---|---|
| Title: | Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic |
| Event: | 32nd International Conference, TABLEAUX 2023 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/978-3-031-43513-3_20 |
| Publisher version: | https://doi.org/10.1007/978-3-031-43513-3_20 |
| Language: | English |
| Additional information: | Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. |
| Keywords: | Logic, Semantics, Proof Theory, Proof-theoretic Semantics, Substructural Logic, Multiplicative Connectives |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10176106 |
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