Rewriting Structured Cospans: A Syntax For Open Systems
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 syst...
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| Main Author | |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
12.06.2019
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| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.1906.05443 |
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| 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. |
|---|---|
| AbstractList | 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. |
| Author | Cicala, Daniel |
| Author_xml | – sequence: 1 givenname: Daniel surname: Cicala fullname: Cicala, Daniel |
| BackLink | https://doi.org/10.48550/arXiv.1906.05443$$DView paper in arXiv |
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| Snippet | The concept of a system has proliferated through natural and social sciences.
While myriad theories of systems exist, there is no mathematical general theory... |
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| Title | Rewriting Structured Cospans: A Syntax For Open Systems |
| URI | https://arxiv.org/abs/1906.05443 |
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