Abstract. 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.
The cognitive models of information representation are fundamental research areas in cognitive informatics, which attempts to reveal the mechanisms and potential of the brain in learning and knowledge representation. Because memory is the foundation of all forms of natural intelligence, a generic model of memory, particularly the long-term memory, may explain the fundamental mechanism of internal information representation and the forms of learning results. This article presents the Object-Attribute-Relation (OAR) model to formally represent the structures of internal information and knowledge acquired and learned in the brain. The neural informatics model of human memory is introduced with particular focus on the long-term memory. Then, the OAR model that explains the mechanisms of internal knowledge and information representation in the brain is formally described, and the physical and physiological meanings of this model are explained. Based on the OAR model, knowledge structures and learning mechanisms are rigorously explained. Further, the magnitude of human memory capacity is rigorously estimated on the basis of OAR, by which the memory capacity is derived to be in the order of 108,432 bits.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.