English

Rewriting Structured Cospans: A Syntax For Open Systems

Category Theory 2019-06-14 v1

Abstract

The concept of a system has proliferated through natural and social sciences. While myriad theories of systems exist, there is no mathematical general theory of systems. In this thesis, we take a first step towards formulating such a theory. Our focus is on developing a syntax for compositional systems equipped with a rewriting theory. We pull from category theory and linguistics to accomplish this. The basic syntactical unit is a structured cospan and rewriting is introduced via the double pushout method. Two versions of rewriting are proposed: one that tracks intermediate steps and another disregards them. Benefits and drawbacks of both versions are discussed. We apply our results to the decomposition of closed systems, obtaining a structurally inductive viewpoint of rewriting such systems.

Cite

@article{arxiv.1906.05443,
  title  = {Rewriting Structured Cospans: A Syntax For Open Systems},
  author = {Daniel Cicala},
  journal= {arXiv preprint arXiv:1906.05443},
  year   = {2019}
}
R2 v1 2026-06-23T09:52:13.337Z