Issue title: Cognitive Informatics, Cognitive Computing, and
Their Denotational Mathematical Foundations (I)
Article type: Research Article
Authors: Wang, Yingxu;
Affiliations: Visiting Professor, Dept. of Computer Science,
Stanford University, Stanford, CA 94305-9010, USA. yingxuw@stanford.edu | International Center for Cognitive Informatics (ICfCI),
Theoretical and Empirical Software Engineering Research Centre (TESERC), Dept.
of Electrical and Computer Engineering, Schulich School of Engineering,
University of Calgary, 2500 University Drive, NW, Calgary, Alberta, Canada T2N
1N4. yingxu@ucalgary.ca
Note: [] Address for correspondence: International Center for Cognitive
Informatics (ICfCI), Theoretical and Empirical Software Engineering Research
Centre (TESERC), Dept. of Electrical and Computer Engineering, Schulich School
of Engineering, University of Calgary, 2500 University Drive, NW, Calgary,
Alberta, Canada T2N 1N4
Abstract: The abstract, rigorous, and expressive needs in cognitive
informatics, intelligence science, software science, and knowledge science lead
to new forms of mathematics collectively known as denotational mathematics.
Denotational mathematics is a category of expressive mathematical structures
that deals with high level mathematical entities beyond numbers and sets, such
as abstract objects, complex relations, behavioral information, concepts,
knowledge, processes, and systems. Denotational mathematics is usually in the
form of abstract algebra that is a branch of mathematics in which a system of
abstract notations is adopted to denote relations of abstract mathematical
entities and their algebraic operations based on given axioms and laws. Four
paradigms of denotational mathematics, known as concept algebra, system
algebra, Real-Time Process Algebra (RTPA), and Visual Semantic Algebra (VSA),
are introduced in this paper. Applications of denotational mathematics in
cognitive informatics and computational intelligence are elaborated.
Denotational mathematics is widely applicable to model and manipulate complex
architectures and behaviors of both humans and intelligent systems, as well as
long chains of inference processes.
Keywords: Cognitive informatics, denotational mathematics, concept algebra, system algebra, process algebra, RTPA, visual semantic algebra, intelligence science, AI, computational intelligence, software engineering, knowledge engineering, cognitive computing, case studies
DOI: 10.3233/FI-2009-0019
Journal: Fundamenta Informaticae, vol. 90, no. 3, pp. 283-303, 2009
Received 12 March 2009
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Accepted 12 March 2009
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Published: 2009
