On Contemporary Denotational Mathematics for Computational Intelligence

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, intelligence, and systems. New forms of mathematics are sought, collectively known as denotational mathematics, in order to deal 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 this paper. 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 computational intelligence are elaborated. A set of case studies is presented on the modeling of iterative and recursive systems architectures and behaviors by RTPA, the modeling of autonomic machine learning by concept algebra, and the modeling of granular computing by system algebra.