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On Contemporary Denotational Mathematics for Computational Intelligence

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Transactions on Computational Science II

Part of the book series: Lecture Notes in Computer Science ((TCOMPUTATSCIE,volume 5150))

Abstract

Denotational mathematics is a category of expressive mathematical structures that deals with high-level mathematical entities beyond numbers and sets, such as abstract objects, complex relations, behavioral information, concepts, knowledge, processes, intelligence, and systems. New forms of mathematics are sought, collectively known as denotational mathematics, in order to deal with complex mathematical entities emerged in cognitive informatics, computational intelligence, software engineering, and knowledge engineering. The domain and architecture of denotational mathematics are presented in this paper. Three paradigms of denotational mathematics, known as concept algebra, system algebra, and Real-Time Process Algebra (RTPA), are introduced. Applications of denotational mathematics in cognitive informatics and computational intelligence are elaborated. A set of case studies is presented on the modeling of iterative and recursive systems architectures and behaviors by RTPA, the modeling of autonomic machine learning by concept algebra, and the modeling of granular computing by system algebra.

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Authors and Affiliations

  1. Theoretical and Empirical Software Engineering Research Centre (TESERC) International Center for Cognitive Informatics (ICfCI) Dept. of Electrical and Computer Engineering Schulich School of Engineering, University of Calgary, 2500 University Drive, NW, Calgary, Alberta, T2N 1N4, Canada

    Yingxu Wang

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  1. Yingxu Wang
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Editors and Affiliations

  1. Department of Computer Science, University of Calgary, 2500 University Drive N.W., Calgary, T2N 1N4, AB, Canada

    Marina L. Gavrilova

  2. OptimaNumerics Ltd., Cathedral House, 23-31 Waring Street, BT1 2DX, Belfast, UK

    C. J. Kenneth Tan

  3. Schulich School of Engineering, Department of Electrical and Computer Engineering, University of Calgary, 2500 University Drive, T2N 1N4, NW Calgary, AB, Canada

    Yingxu Wang

  4. Department of Computer Science, University of Regina, S4S 0A2, Regina, Saskatchewan, Canada

    Yiyu Yao

  5. School of Information Science & Technology, Southwest Jiaotong University, 610031, Chengdu, China

    Guoyin Wang

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Wang, Y. (2008). On Contemporary Denotational Mathematics for Computational Intelligence. In: Gavrilova, M.L., Tan, C.J.K., Wang, Y., Yao, Y., Wang, G. (eds) Transactions on Computational Science II. Lecture Notes in Computer Science, vol 5150. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87563-5_2

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  • DOI: https://doi.org/10.1007/978-3-540-87563-5_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87562-8

  • Online ISBN: 978-3-540-87563-5

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