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

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 cognitive informatics, 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.

[1]  Yingxu Wang,et al.  On Concept Algebra: A Denotational Mathematical Structure for Knowledge and Software Modeling , 2008, Int. J. Cogn. Informatics Nat. Intell..

[2]  Pierre F. Tiako,et al.  Software Applications: Concepts, Methodologies, Tools, and Applications , 2009 .

[3]  George J. Klir,et al.  Systems Profile: The Emergence of Systems Science , 1991 .

[4]  Angelo C. Loula,et al.  Artificial Cognition Systems , 2006 .

[5]  Simon Colton,et al.  Applying Lakatos-style reasoning to AI domains , 2010 .

[6]  Yingxu Wang,et al.  On the informatics laws and deductive semantics of software , 2006, IEEE Trans. Syst. Man Cybern. Syst..

[7]  Agnessa Babloyantz,et al.  Thermodynamics of evolution , 1972 .

[8]  Yingxu Wang On the Big-R Notation for Describing Iterative and Recursive Behaviors , 2006, 2006 5th IEEE International Conference on Cognitive Informatics.

[9]  George J. Klir Correspondence systems profile , 1988 .

[10]  Shamal Faily,et al.  Towards Tool-Support for Usable Secure Requirements Engineering with CAIRIS , 2010, Int. J. Secur. Softw. Eng..

[11]  Yingxu Wang,et al.  The Real-Time Process Algebra (RTPA) , 2002, Ann. Softw. Eng..

[12]  Alexander Mehler,et al.  Stratified Constraint Satisfaction Networks in Synergetic Multi-Agent Simulations of Language Evolution , 2006 .

[13]  Yingxu Wang,et al.  Cognitive informatics models of the brain , 2006, IEEE Trans. Syst. Man Cybern. Syst..

[14]  Yingxu Wang,et al.  RTPA: A Denotational Mathematics for Manipulating Intelligent and Computational Behaviors , 2008, Int. J. Cogn. Informatics Nat. Intell..

[15]  Yingxu Wang,et al.  Deductive Semantics of RTPA , 2008, Int. J. Cogn. Informatics Nat. Intell..

[16]  Yingxu Wang,et al.  Using Process Algebra to Describe Human and Software Behaviors , 2003 .

[17]  Jordi Vallverd,et al.  Thinking Machines and the Philosophy of Computer Science: Concepts and Principles , 2010 .

[18]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..

[19]  Yingxu Wang,et al.  The OAR Model of Neural Informatics for Internal Knowledge Representation in the Brain , 2007, Int. J. Cogn. Informatics Nat. Intell..

[20]  Leonid Perlovsky Modeling Field Theory of Higher Cognitive Functions , 2007 .

[21]  Yide Ma,et al.  An Efficient and Automatic Iris Recognition System Using ICM Neural Network , 2010 .

[22]  Lori Baker-Eveleth,et al.  The Influence of Computer-Based In-Class Examination Security Software on Students' Attitudes and Examination Performance , 2008, Int. J. Inf. Commun. Technol. Educ..

[23]  Yingxu Wang,et al.  The Theoretical Framework of Cognitive Informatics , 2007, Int. J. Cogn. Informatics Nat. Intell..