Gheorghiu, Alexander;
Gu, Tao;
Pym, David;
(2024)
Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic.
Studia Logica
10.1007/s11225-024-10158-6.
(In press).
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Abstract
Proof-theoretic semantics (P-tS) is an innovative approach to grounding logical meaning in terms of proofs rather than traditional truth-conditional semantics. The point is not that one provides a proof system, but rather that one articulates meaning in terms of proofs and provability. To elucidate this paradigm shift, we commence with an introduction that contrasts the fundamental tenets of P-tS with the more prevalent model-theoretic approach to semantics. The contribution of this paper is a P-tS for a substructural logic, intuitionistic multiplicative linear logic (IMLL). Specifically, we meticulously examine and refine the established P-tS for intuitionistic propositional logic. Subsequently, we present two novel and comprehensive forms of P-tS for IMLL. Notably, the semantics for IMLL in this paper embodies its resource interpretation through its number-of-uses reading (restricted to atoms). This stands in contrast to the conventional model-theoretic semantics of the logic, underscoring the value that P-tS brings to substructural logics.
| Type: | Article |
|---|---|
| Title: | Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s11225-024-10158-6 |
| Publisher version: | https://doi.org/10.1007/s11225-024-10158-6 |
| Language: | English |
| Additional information: | This article is licensed under a Creative Commons Attribution 4.0 International License, 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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence 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. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Keywords: | Logic, Semantics, Proof theory, Proof-theoretic semantics, Substructural logic, Resources, 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 > Dept of Computer Science |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10199842 |
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