Perspectives on Denotational Mathematics: New Means of Thought

  • Yingxu Wang
  • Yiyu Yao
  • Guoyin Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5150)

Abstract

The denotational and expressive needs in cognitive informatics, computational intelligence, software engineering, and knowledge engineering lead to the development of new forms of mathematics collectively known as denotational mathematics. Denotational mathematics is a category of mathematical structures that formalize rigorous expressions and long-chain inferences of system compositions and behaviors with abstract concepts, complex relations, and dynamic processes. Typical paradigms of denotational mathematics are such as concept algebra, system algebra, Real-Time Process Algebra (RTPA), Visual Semantic Algebra (VSA), fuzzy logic, and rough sets. A wide range of applications of denotational mathematics have been identified in many modern science and engineering disciplines that deal with complex and intricate mathematical entities and structures beyond numbers, Boolean variables, and traditional sets.

Keywords

Cognitive informatics computational intelligence denotational mathematics concept algebra system algebra process algebra RTPA visual semantic algebra rough set granular computing knowledge engineering AI natural intelligence 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Yingxu Wang
    • 1
  • Yiyu Yao
    • 2
  • Guoyin Wang
    • 3
  1. 1.Dept. of Electrical and Computer EngineeringUniversity of CalgaryCanada
  2. 2.Dept. of Computer ScienceUniversity of ReginaCanada
  3. 3.Institute of Computer Science and TechnologyChongqing University of Posts and TelecommunicationsChina

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