English

A categorical reduction system for linear logic

Logic in Computer Science 2020-10-09 v2

Abstract

Diagram chasing is not an easy task. The coherence holds in a generalized sense if we have a mechanical method to judge whether given two morphisms are equal to each other. A simple way to this end is to reform a concerned category into a calculus, where the instructions for the diagram chasing are given in the form of rewriting rules. We apply this idea to the categorical semantics of the linear logic. We build a calculus directly on the free category of the semantics. It enables us to perform diagram chasing as essentially one-way computations led by the rewriting rules. We verify the weak termination property of this calculus. This gives the first step towards the mechanization of diagram chasing.

Keywords

Cite

@article{arxiv.1912.00629,
  title  = {A categorical reduction system for linear logic},
  author = {Ryu Hasegawa},
  journal= {arXiv preprint arXiv:1912.00629},
  year   = {2020}
}
R2 v1 2026-06-23T12:32:46.921Z