Perspectives on denotational mathematics: new means of thought

  • Authors:
  • Yingxu Wang;Yiyu Yao;Guoyin Wang

  • Affiliations:
  • Dept. of Electrical and Computer Engineering, University of Calgary, Canada;Dept. of Computer Science, University of Regina, Canada;Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, China

  • Venue:
  • Transactions on computational science II
  • Year:
  • 2008

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Abstract

The denotational and expressive needs in cognitive informatics,computational intelligence, software engineering, and knowledge engineeringlead to the development of new forms of mathematics collectively known asdenotational mathematics. Denotational mathematics is a category ofmathematical 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 denotationalmathematics are such as concept algebra, system algebra, Real-Time ProcessAlgebra (RTPA), Visual Semantic Algebra (VSA), fuzzy logic, and rough sets.A wide range of applications of denotational mathematics have been identifiedin many modern science and engineering disciplines that deal with complex andintricate mathematical entities and structures beyond numbers, Booleanvariables, and traditional sets.