Cognitive robotics and mathematical engineering

It is recognized that the core problems across contemporary disciplines such as cognitive science, intelligence science, robotics, knowledge science, brain science, and computational intelligence are a fundamental mathematical problem where none of them may be simply reduced onto any type of numbers. This keynote lecture presents an emerging field known as mathematical engineering (ME) underpinning cognitive robotics. ME is a contemporary form of abstract engineering that studies formal structural models and functions of complex, abstract, and mental objects and their systematic and rigorous manipulations. ME is embodied by denotational mathematics (DM) supplement to traditional analytic mathematics. DM is a category of novel mathematical structures as function of functions on hyperstructures beyond those of real numbers and bits, in order to formalize rigorous expressions and inferences. ME powered by DMs provides a novel approach to solve complex and intelligent computing problems centric in the development of cognitive robots towards autonomous perception, inference, and learning mimicking the cognitive mechanisms of the brain.