Cognitive Robotics and Mathematical Engineering Yingxu Wang, Prof., PhD, PEng, FICIC, FWIF, SM.IEEE, SM.ACM President, International Institute of Cognitive Informatics and Cognitive Computing (ICIC) Director, Laboratory for Computational Intelligence and Software Science Dept. of Electrical and Computer Engineering Schulich School of Engineering and Hotchkiss Brain Institute University of Calgary 2500 University Drive, NW, Calgary, Alberta, Canada T2N 1N4 http://www.ucalgary.ca/icic/ Email:
[email protected] that is capable of perception, inference, and learning mimicking the cognitive mechanisms of the brain [22, 35, 37]. Cognitive robots emerge from basic studies in both natural intelligence in brain/cognitive sciences and artificial/abstract intelligence in computer/intelligence sciences. In cognitive robotics, intelligence is perceived as an ability that transforms information to behavior. Therefore, abstract intelligence (I) [16, 19, 35] is the kernel and formal embodiment of general intelligence shared by both humans and cognitive systems. A reference model of cognitive robots (RMCR) [22] is elaborated for how a cognitive robot is formally modeled at the imperative, autonomic, and cognitive layers from the bottom up. It will be demonstrated that cognitive robotics is a typical field of contemporary science and engineering where all fundamental theories and solutions are highly dependent on DM. The development on cognitive robots based on mathematical engineering methodologies reveals a wide range of applications of DM in complex system modeling, formal inference, big data processing, knowledge manipulation, machine learning, abstract intelligence, artificial intelligence, brain science, cognitive computers, computational linguistics, and computational intelligence.
ABSTRACT It is recognized in cognitive informatics [10, 12-14, 20, 25, 29, 30] that the core scientific knowledge of the mankind is mainly archived in mathematical forms [1, 2, 5-9, 10-39]. The entire set of fundamental and long-lasting problems in contemporary disciplines, such as, inter alia, intelligence science, robotics, knowledge science, information science, brain science, system science, software science, data science, neuroinformatics, cognitive linguistics, and computational intelligence, indicate that the aforementioned problems in nature are a hard mathematical problem where there is a lack of suitable mathematical means [3, 4, 8, 9, 12-14, 22, 25, 31, 39]. The current forms of analytic mathematics are inadequate to solve the complex problems in modern sciences and engineering when brain, mind, semantics, knowledge, intelligence, and systems become the objects, because none of them is in the domain of any type of numbers. This notion leads to the generic methodology known as mathematical engineering and the generic solution coined as denotational mathematics [15, 16, 21, 24, 25, 27, 30, 31]. Denotational mathematics (DM) is a category of novel mathematical structures as function of functions on hyperstructures () [24, 27, 31], beyond those of real numbers () and bits (), in order to formalize rigorous expressions and inferences [15, 16, 21, 24, 25, 27, 30]. In DM, the mathematical entities in hyperstructures, such as abstract objects, complex relations, neural clusters, big data, information, concepts, semantics, truth, knowledge, behavioral processes, causations, patterns, perceptions, memories, inferences, decisions, intelligence, and systems, are generally modeled as a typed n-tuple [31, 38]. The mathematical operators of DM are denoted by hyper functions, such as relational, reproductive, and compositional operators, on the hyperstructures. The framework of DM is shown in Fig. 1 where its paradigms are such as concept algebra [18], behavioral process algebra (RTPA) [11, 17], system algebra [38], semantic algebra [28], inference algebra [23], granular algebra [32], big data algebra [36], fuzzy truth algebra [37], and fuzzy probability algebra [34]. This keynote lecture presents the DM system for mathematical engineering and its applications in cognitive computing and computational intelligence particularly cognitive robotics. A cognitive robot is an autonomous robot Proc. 2015 IEEE 14th Int'l Conf. on Cognitive Informatics & Cognitive Computing (ICCI*CC’15) N. Ge, J. Lu, Y. Wang, N. Howard, P. Chen, ;7DRB. Zhang, & L.A. Zadeh (Eds.) 978-1-4673-7290-9/15/$31.00 ©2015 IEEE
Keywords: Cognitive informatics, denotational mathematics, mathematical engineering, abstract intelligence, cognitive robots, intelligence science, artificial intelligence, computational intelligence, cognitive computers, software science, knowledge science, soft computing, hyperstructures. ABOUT THE KEYNOTE SPEAKER Yingxu Wang is professor of cognitive informatics, brain science, software science, and denotational mathematics, President of International Institute of Cognitive Informatics and Cognitive Computing (ICIC, http://www.ucalgary.ca/icic/). He is a Fellow of ICIC, a Fellow of WIF (UK), a P.Eng of Canada, and a Senior Member of IEEE and ACM. He was visiting professor (on sabbatical leave) at Oxford University (1995), Stanford University (2008), UC
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Berkeley (2008), and MIT (2012), respectively. He received a PhD in Computer Science from the Nottingham Trent University in 1998 and has been a full professor science 1994. He is the founder and steering committee chair of the annual IEEE International Conference on Cognitive Informatics and Cognitive Computing (ICCI*CC) since 2002. He is founding Editor-in-Chief of Int. Journal of Cognitive Informatics & Natural Intelligence, founding Editor-in-Chief of Int. Journal of Software Science & Computational Intelligence, Associate Editor of IEEE Trans. on SMC - Systems, and Editor-in-Chief of Journal of Advanced Mathematics & Applications. Dr. Wang is the initiator of a few cutting-edge research fields such as cognitive informatics, denotational mathematics (concept algebra, process algebra, system algebra, semantic algebra, inference algebra, big data algebra, fuzzy truth algebra, and fuzzy probability algebra, visual semantic algebra, granular algebra), abstract intelligence (I),
mathematical models of the brain, cognitive computing, cognitive learning engines, cognitive knowledge base theory, and basic studies across contemporary disciplines of intelligence science, robotics, knowledge science, computer science, information science, brain science, system science, software science, data science, neuroinformatics, cognitive linguistics, and computational intelligence. He has published 400+ peer reviewed papers and 29 books in aforementioned transdisciplinary fields. He has presented 28 invited keynote speeches in international conferences. He has served as general chairs or program chairs for more than 20 international conferences. He is the recipient of dozens international awards on academic leadership, outstanding contributions, best papers, and teaching in the last three decades. He is the most popular scholar of top publications at University of Calgary in 2014 and 2015 according to RG worldwide stats.
The Theoretical Framework of Denotational Mathematics (DM)
New mathematical objects
Hyper system structures
Intelligence
New DM paradigms
New expressional needs
Concept algebra
New application fields
Intelligence science
System algebra
Concepts
Abstract system behaviors
Semantics
Knowledge manipulation
Behaviors Causations
Abstract intelligence
Neural clusters
Process algebra Semantic algebra
Efficient complexity handling
Patterns
Rigorous sys. modelling
Brain science
Inference algebra Big data algebra
Big data
Knowledge science
Fuzzy truth algebra Fuzzy probable algebra
System science Cognitive informatics Cognitive computers
Granular algebra
Systems Expressive sys. denotation
Memory
Visual semantic algebra
Software science
Figure 1. The framework of denotational mathematics
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