DeepAI AI Chat
Log In Sign Up

Confluence as a cut elimination property

05/23/2023
by   Gilles Dowek, et al.
0

The goal of this note is to compare two notions, one coming from the theory of rewrite systems and the other from proof theory: confluence and cut elimination. We show that to each rewrite system on terms, we can associate a logical system: asymmetric deduction modulo this rewrite system and that the confluence property of the rewrite system is equivalent to the cut elimination property of the associated logical system. This equivalence, however, does not extend to rewrite systems directly rewriting atomic propositions.

READ FULL TEXT

page 1

page 2

page 3

page 4

07/22/2022

Elimination and cut-elimination in multiplicative linear logic

We associate to every proof structure in multiplicative linear logic an ...
08/09/2020

The New Normal: We Cannot Eliminate Cuts in Coinductive Calculi, But We Can Explore Them

In sequent calculi, cut elimination is a property that guarantees that a...
04/22/2018

Subatomic systems need not be subatomic

Subatomic systems were recently introduced to identify the structural pr...
07/30/2020

Logic of fusion

The starting point of this work is the observation that the Curry-Howard...
04/26/2023

Cut-restriction: from cuts to analytic cuts

Cut-elimination is the bedrock of proof theory with a multitude of appli...
06/24/2019

Transitivity of Subtyping for Intersection Types

The subtyping relation for intersection type systems traditionally emplo...
05/02/2023

On the convergence of reduction-based and model-based methods in proof theory

In the recent past, the reduction-based and the model-based methods to p...