On System Algebra: A Denotational Mathematical Structure for Abstract System Modeling

On System Algebra: A Denotational Mathematical Structure for Abstract System Modeling

DOI: 10.4018/978-1-60566-902-1.ch009
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Systems are the most complicated entities and phenomena in abstract, physical, information, and social worlds across all science and engineering disciplines. System algebra is an abstract mathematical structure for the formal treatment of abstract and general systems as well as their algebraic relations, operations, and associative rules for composing and manipulating complex systems. This article presents a mathematical theory of system algebra and its applications in system engineering, software engineering, and cognitive informatics. A rigorous treatment of abstract systems is described, and the algebraic relations and compositional operations of abstract systems are analyzed. System algebra provides a denotational mathematical means that can be used to model, specify, and manipulate generic “to be” and “to have” type problems, particularly system architectures and high-level system designs, in computing, software engineering, system engineering, and cognitive informatics.
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The Abstract System Theory

This section demonstrates that systems may be treated rigorously as a new mathematical structure beyond conventional mathematical entities. Based on this view, the concept of abstract systems and their mathematical models are introduced.

  • Definition 1. An abstract system is a collection of coherent and interactive entities that has stable functions and a clear boundary with the external environment.

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