Intelligent Mathematics (IM): Indispensable Mathematical Means for General AI, Autonomous Systems, Deep Knowledge Learning, Cognitive Robots, and Intelligence Science

It is recognized that the core knowledge of humans in natural sciences and engineering is archived in mathematical forms. Intelligent Mathematics (IM) is a category of contemporary denotational mathematics extending classic analytic mathematics as defined in real numbers (R). IM represents a collection of novel mathematical structures that formalizes rigorous expressions and manipulations on complex entities known as hyperstructures (H) beyond R. Instances of the complex entities in H include formal concepts, semantics, relations, knowledge, intelligence, behavioral processes, causality, inferences, and systems. Paradigms of IM developed in my lab include real-time process algebra (RTPA), concept algebra, semantic algebra, system algebra, inference algebra, fuzzy probability algebra, big data algebra, image frame algebra, and the causal probability theory, etc.This keynote speech presents the IM foundations of emerging intelligent science and AI paradigms. A set of novel IMs will be presented for rigorously manipulating complex cognitive entities in the brain and abstract intelligence including data, information, knowledge, and intelligence from the bottom up. IM will lead to the emergence of mathematical engineering (ME), which addresses the challenges in formal structural and functional modeling of complex mental objects and their rigorous manipulations in a wide range of applications such as cognitive robots, autonomous systems, intelligent IoT, and unmanned systems.