Transactions on Computational Science II

1. Front Matter

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2. Regular Papers

   1. Perspectives on Denotational Mathematics: New Means of Thought

      • Yingxu Wang, Yiyu Yao, Guoyin Wang

      Pages 1-5

   2. On Contemporary Denotational Mathematics for Computational Intelligence

      • Yingxu Wang

      Pages 6-29

   3. Mereological Theories of Concepts in Granular Computing

      • Lech Polkowski

      Pages 30-45

   4. On Mathematical Laws of Software

      • Yingxu Wang

      Pages 46-83

   5. Rough Logic and Its Reasoning

      • Qing Liu, Lan Liu

      Pages 84-99

   6. On Reduct Construction Algorithms

      • Yiyu Yao, Yan Zhao, Jue Wang

      Pages 100-117

   7. Attribute Set Dependence in Reduct Computation

      • Pawel Terlecki, Krzysztof Walczak

      Pages 118-132

   8. A General Model for Transforming Vague Sets into Fuzzy Sets

      • Yong Liu, Guoyin Wang, Lin Feng

      Pages 133-144

   9. Quantifying Knowledge Base Inconsistency Via Fixpoint Semantics

      • Du Zhang

      Pages 145-160

   10. Contingency Matrix Theory I: Rank and Statistical Independence in a Contigency Table

       • Shusaku Tsumoto, Shoji Hirano

       Pages 161-179

   11. Applying Rough Sets to Information Tables Containing Possibilistic Values

       • Michinori Nakata, Hiroshi Sakai

       Pages 180-204

   12. Toward a Generic Mathematical Model of Abstract Game Theories

       • Yingxu Wang

       Pages 205-223

   13. A Comparative Study of STOPA and RTPA

       • Natalia Lopez, Manuel Núñez, Fernando L. Pelayo

       Pages 224-245

3. Back Matter

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The denotational and expressive needs in cognitive informatics, computational intelligence, software engineering, and knowledge engineering have led 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 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. This issue of Springer’s Transactions on Computational Science on Denotational Mathematics for Computational Intelligence presents a snapshot of current research on denotational mathematics and its engineering applications. The volume includes selected and extended papers from two international conferences, namely IEEE ICCI 2006 (on Cognitive Informatics) and RSKT 2006 (on Rough Sets and Knowledge Technology), as well as new contributions. The following four important areas in denotational mathem- ics and its applications are covered: Foundations and applications of denotational mathematics, focusing on: a) c- temporary denotational mathematics for computational intelligence; b) deno- tional mathematical laws of software; c) a comparative study of STOPA and RTPA; and d) a denotational mathematical model of abstract games.

• approximate reasoning
• artificial intelligence
• autonomic computing
• brain models
• cognitive models
• cognitive psychology
• cognitive science
• computational intelligence
• concept algebra
• cybernetics
• decision grids
• decision mak
• modeling
• sets
• software architecture

• Department of Computer Science, University of Calgary, Canada

  Marina L. Gavrilova

• OptimaNumerics Ltd., Belfast, UK

  C. J. Kenneth Tan

• Schulich School of Engineering, Department of Electrical and Computer Engineering, University of Calgary, NW Calgary, Canada

  Yingxu Wang

• Department of Computer Science, University of Regina, Regina, Canada

  Yiyu Yao

• School of Information Science & Technology, Southwest Jiaotong University, Chengdu, China

  Guoyin Wang

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