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 | |
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| 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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| Summary: | 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. |
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| DOI: | 10.48550/arxiv.1906.05443 |