Definition 1:Cognitive Informatics (CI) is a transdisciplinary enquiry of computer science, information science, cognitive science, and intelligence science that investigates into the internal information processing mechanisms and processes of the brain and natural intelligence, as well as their engineering applications in cognitive computing (Wang, 2002a, 2003a, 2003b, 2004, 2005, 2007b, 2008b, 2009a; Wang & Kinsner, 2007; Wang & Wang, 2006; Wang, Kinsner, & Zhang, 2009a, 2009b; Wang et al., 2006, 2009).
The latest advances and engineering applications of CI have led to the emergence of cognitive computing and the development of cognitive computer that think and learn, as well as autonomous agent systems.
Definition 2:Cognitive Computing (CC) is an emerging paradigm of intelligent computing methodologies and systems based on cognitive informatics that implements computational intelligence by autonomous inferences and perceptions mimicking the mechanisms of the brain (Wang, 2002a, 2009b, 2009g).
CC is emerged and developed based on the transdisciplinary research in cognitive informatics, abstract intelligence, and denotational mathematics since the inauguration of the 1st IEEE International Conference on Cognitive Informatics (ICCI 2002, see Figure 1) (Wang et al., 2002, 2008).
IEEE ICCI’08 keynote speakers and co-chairs at Stanford University (from right to left: Jean-Claude Latombe, Lotfi A. Zadeh, Yingxu Wang, Witold Kinsner, and Du Zhang)
Definition 3:Abstract Intelligence (αI) is the general mathematical form of intelligence as a natural mechanism that transfers information into behaviors and knowledge (Wang, 2009a).
Typical paradigms of αI are natural intelligence, artificial intelligence, machinable intelligence, and computational intelligence, as well as their hybrid forms.
Definition 4: Denotational Mathematics (DM) is a category of expressive mathematical structures that deals with high-level mathematical entities beyond numbers and sets, such as abstract objects, complex relations, perceptual information, abstract concepts, knowledge, intelligent behaviors, behavioral processes, and systems (Wang, 2002b, 2007a, 2008a, 2008c, 2008d, 2008e, 2009d, 2009f;Wang, Zadeh & Yao, 2009).