Basic Elements of Logical Graphs

TL;DR

This paper explores a graphical notation for multiplicative intuitionistic linear logic, demonstrating its implementation in Standard ML to facilitate graph traversal, isomorphism, and a foundation for a graphical logic language.

Contribution

It introduces a novel graphical notation for linear logic and provides a functional implementation, advancing tools for logic visualization and manipulation.

Findings

Graphical notation captures symmetries in linear logic

Implementation in Standard ML enables efficient graph traversal

Foundation laid for a graphical language for logic formulas

Abstract

We considers how a particular kind of graph corresponds to multiplicative intuitionistic linear logic formula. The main feature of the graphical notation is that it absorbs certain symmetries between conjunction and implication. We look at the basic definitions and present details of an implementation in the functional programming language Standard ML. This provides a functional approach to graph traversal and demonstrates how graph isomorphism be implemented in just a few lines of readable code. This works takes the initial steps towards a graphical language and toolkit for working with logic formula and derivations.