Cognitive Informatics (CI) is a transdisciplinary field that studies the internal information processing mechanisms of the brain, the underlying Abstract Intelligence (aI) theories and Intelligent Mathematics (IM), and their engineering applications in cognitive computing, computational intelligence, and cognitive systems. Cognitive Computing (CC) is a cutting-edge paradigm of General AI (GAI) methodologies and systems based on CI, which implements computational intelligence by autonomous inferences and perceptions mimicking the mechanisms of the brain.
Cognitive robots (CRs) are a cutting-edge technology of autonomous robots that is capable of learning and reasoning mimicking the brain.
Knowledge is the 3rd level of cognitive entities in the brain beyond data and information. It is recently discovered that: a) The basic structural model of human knowledge is a formal concept; and b) The basic unit of knowledge is a binary relation (bir) as a counterpart of bit (binary digit) for information and data.
Learning is a central ability of machine intelligence and cognitive systems for knowledge and behavior acquisition. The taxonomy of machine learning methodologies can be classified into six categories known as object identification, cluster classification, pattern recognition, functional regression, and behavior (game) generation, and knowledge acquisition. The current project focuses on the 6th category of cognitive knowledge learning. It is revealed that machine created Cognitive Knowledge Bases (CKB) may be mutually shared by both humans and systems towards knowledge learning.
Intelligence is a mental process that transfers information into behaviors and knowledge which is the top level of cognitive ability of human brains and artificial counterparts. Intelligence science (IntS) is a contemporary discipline that explores the nature of intelligence and its biological, neurological, physiological, functional, logical, mathematical foundations. Basic research in IntS studies how intelligence is aggregated among the cognitive entities of data, information, and knowledge from the bottom up. Representative theories of IntS developed in I2CICC is Abstract Intelligence (aI) theories and Intelligent Mathematics (IM) in order to rigorously explain various forms of natural, artificial, machinable, and computational intelligence.
Intelligent Mathematics (IM) for AI, Abstract Intelligence (aI), Computational Intelligence (CI), and Brain Informatics (BI)
Intelligent Mathematics (IM) is a collection of novel mathematical structures that formalize rigorous expressions and operations on complex entities known as Hyperstructures (H) beyond the traditional domain R of classic analytic and numerical mathematics. Typical complex entities in H include formal concepts, semantics, behaviors, relations, big data, knowledge, intelligence, systems, and causal probability. Paradigms of IM developed in I2CICC include Concept algebra, Semantic algebra, Real-Time Process (behavior) algebra (RTPA), System algebra, Inference algebra, Fuzzy Probability algebra, Image Frame algebra, Big Data algebra, and Causal Probability algebra. This leads to the emergence of Mathematical Engineering (ME) for solving almost all AI and ML problems that had out of the domain of R for over a half century.
A recent discovery in data science reveals that big data systems in nature are a Recursive N-dimensional Typed Hyperstructure (RNDTH). This topological property of big data indicates that the mathematical foundation of big data science is underpinned by an IM structure known as Big Data Algebra (BDA) which is an efficient mathematical means for dealing with the inherited complexities and unprecedented challenges in big data engineering.
The seminar work of Late Prof. Lotfi A. Zadeh on fuzzy sets and fuzzy logic [Zadeh, 1965, 1975, 2008, 2016] has led to a novel field of contemporary mathematics known as Fuzzy Mathematics. The project on fuzzy mathematics studies Fuzzy Arithmetic, Fuzzy Logic Algebra (FLA), Fuzzy Probability Algebra (FPA), Fuzzy Semantic Analyses (FSA), and Fuzzy Truth Algebra (FTA), towards formally manipulating the hyperstructures of fuzzy mathematical entities in AI, computational intelligence, cognitive computing, and deep machine learning.
Software science is a discipline that studies the formal properties and mathematical models of software, general methodologies for rigorous and efﬁcient software development, and coherent theories and laws underpinning software behaviors and software engineering practices. This project focuses on the general mathematical model of software and systems. It reveals that any software system is a Cartesian product between the functional behaviors and abstract data entities formally described as the sets of Process Models (PMs) and Structure Models (SMs), respectively. Recent developments in software science have paved the way to theoretical foundations and novel technologies of AI programming.
Autonomous systems (AS) are a category of advanced intelligent systems functioning without intervention of humans for implementing complex cognitive abilities aggregating from reflexive, imperative, and adaptive intelligence to autonomous and cognitive intelligence. We are addressing some of the fundamental challenges to AS such as the theoretical framework of the emerging field of AS, cognitive robots, cognitive decision making, IM for AS, unmanned systems, intelligent IoT, and trustworthy AS technologies, as well as co-organization of the inaugural IEEE International Conference on Autonomous Systems (Montreal, 2021).
The contemporary wonder of sciences and engineering has recently refocused on the starting point of them: how the brain processes internal and external information autonomously rather than imperative computers? Brain science is both a classical and contemporary discipline that studies the functional and logical model of the brain, a set of cognitive processes of the mind, internal information processing mechanisms, and their engineering applications towards Brain-Inspired Systems (BIS). An Abstract Intelligence (aI) theory is created for modeling the structures and functions of the brain across the neurological, physiological, cognitive, and logical levels. A Layered Reference Model of the Brain (LRMB) has been developed for explaining the functional mechanisms and cognitive processes of the brain. The theoretical and transdisciplinary models have led to applications in the development of highly intelligent systems such as cognitive computers, cognitive knowledge bases, autonomous learning machines, and cognitive robots.