On contemporary denotational mathematics for computational intelligence

  • Authors:

  • Yingxu Wang

  • Affiliations:

  • Theoretical and Empirical Software Engineering Research Centre, International Center for Cognitive Informatics, Dept. of Electrical and Computer Engineering, Schulich School of Engineering, Univer ...

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

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Abstract

Denotational mathematics is a category of expressive mathematicalstructures that deals with high-level mathematical entities beyond numbers andsets, such as abstract objects, complex relations, behavioral information, concepts,knowledge, processes, intelligence, and systems. New forms of mathematicsare sought, collectively known as denotational mathematics, in order todeal 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 thispaper. 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 computationalintelligence are elaborated. A set of case studies is presented on themodeling of iterative and recursive systems architectures and behaviors byRTPA, the modeling of autonomic machine learning by concept algebra, andthe modeling of granular computing by system algebra.