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# Elimination and cut-elimination in multiplicative linear logic

We associate to every proof structure in multiplicative linear logic an ideal which represents the logical content of the proof as polynomial equations. We show how cut-elimination in multiplicative proof nets corresponds to instances of the Buchberger algorithm for computing Gröbner bases in elimination theory.

• 5 publications
• 2 publications
12/15/2017

### Taylor expansion in linear logic is invertible

Each Multiplicative Exponential Linear Logic (MELL) proof-net can be exp...
12/30/2021

### Super Exponentials in Linear Logic

Following the idea of Subexponential Linear Logic and Stratified Bounded...
05/30/2022

### Exponentials as Substitutions and the Cost of Cut Elimination in Linear Logic

This paper introduces the exponential substitution calculus (ESC), a new...
05/17/2020

### Bouncing threads for infinitary and circular proofs

We generalize the validity criterion for the infinitary proof system of ...
07/31/2020

### The Multiplicative-Additive Lambek Calculus with Subexponential and Bracket Modalities

We give a proof-theoretic and algorithmic complexity analysis for system...
04/22/2018

### Subatomic systems need not be subatomic

Subatomic systems were recently introduced to identify the structural pr...
02/14/2019

### An application of parallel cut elimination in multiplicative linear logic to the Taylor expansion of proof nets

We examine some combinatorial properties of parallel cut elimination in ...