Rewriting Structured Cospans: A Syntax for Open Systems
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.