Transactions on Computational Science II, Volume 2

Front Cover
Springer Science & Business Media, Sep 16, 2008 - Computers - 245 pages
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.
 

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Contents

New Means of Thought
1
On Contemporary Denotational Mathematics for Computational Intelligence
6
Mereological Theories of Concepts in Granular Computing
30
On Mathematical Laws of Software
46
Rough Logic and Its Reasoning
84
On Reduct Construction Algorithms
100
Attribute Set Dependence in Reduct Computation
118
A General Model for Transforming Vague Sets into Fuzzy Sets
133
Quantifying Knowledge Base Inconsistency Via Fixpoint Semantics
145
Rank and Statistical Independence in a Contigency Table
161
Applying Rough Sets to Information Tables Containing Possibilistic Values
180
Toward a Generic Mathematical Model of Abstract Game Theories
205
A Comparative Study of STOPA and RTPA
224
Author Index
246
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