Simple multiplicative proof nets with units

TL;DR

This paper introduces a straightforward proof net framework for multiplicative linear logic with units, featuring direct, strongly normalising cut elimination and a simple composition method based on path composition.

Contribution

It proposes a new simple notion of proof nets with units that simplifies cut elimination and composition, avoiding complex jump moves used in prior approaches.

Findings

Cut elimination is direct and strongly normalising.

Composition is simplified to path composition.

The approach leverages geometry-of-interaction in Setp category.

Abstract

This paper presents a simple notion of proof net for multiplicative linear logic with units. Cut elimination is direct and strongly normalising, in contrast to previous approaches which resorted to moving jumps (attachments) of par units during normalisation. Composition in the resulting category of proof nets is simply path composition: all of the dynamics happens in GoI(Setp), the geometry-of-interaction construction applied to the category of sets and partial functions.