# Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic (Extended Abstract)

arXiv: https://arxiv.org/abs/2306.05106 · HTML: https://mlsanity.com/paper/2306.05106/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2023.

## Built on by (most cited first, 1 of 1)

- [On the Logical Content of Knowledge Bases](https://mlsanity.com/paper/2503.05355/) (2025)

## Abstract (arXiv)

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.