On abstract intelligence and its denotational mathematics foundations

Recent researches reveal that various paradigms of intelligence, such as natural, artificial, machinable, and computational intelligence, can be unified at the logical and functional levels known as abstract intelligence. This paper introduces abstract intelligence as a form of driving force that transfers information into knowledge and behaviors. An architectural framework of abstract intelligence and the generic abstract intelligence mode (GAIM) are formally developed that provide a unified theory for explaining the mechanisms of advanced intelligence. In order to deal with the highly complex and abstract objects in abstract intelligence, denotational mathematics is introduced as a category of expressive mathematical structures for modeling and manipulating high-level mathematical entities beyond numbers and sets, such as abstract objects, complex relations, behavioral information, abstract concepts, knowledge, processes, and systems. Applications of denotational mathematics in abstract intelligence, cognitive informatics, and computational intelligence are elaborated.