On cognitive foundations of big data science and engineering

Big data are one of the representative phenomena of the information era of human societies. A basic study on the cognitive foundations of big data science is presented with a coherent set of general principles and analytic methodologies for big data manipulations. It leads to a set of mathematical theories that rigorously describe the general patterns of big data across pervasive domains in sciences, engineering, and societies. A significant finding towards big data science is that big data systems in nature are a recursive n-dimensional typed hyperstructure (RNTHS). The fundamental topological property of big data system enables the inherited complexities and unprecedented challenges of big data to be formally dealt with as a set of denotational mathematical operations in big data engineering. The cognitive relationship and transformability between data, information, knowledge, and intelligence are formally revealed towards big data science.

[1]  Yingxu Wang,et al.  On Abstract Intelligence: Toward a Unifying Theory of Natural, Artificial, Machinable, and Computational Intelligence , 2009, Int. J. Softw. Sci. Comput. Intell..

[2]  Adam Jacobs,et al.  The pathologies of big data , 2009, Commun. ACM.

[3]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[4]  Yingxu Wang.  On the Big-R Notation for Describing Iterative and Recursive Behaviors , 2006, 2006 5th IEEE International Conference on Cognitive Informatics.

[5]  Yingxu Wang.  Inference Algebra (IA): A Denotational Mathematics for Cognitive Computing and Machine Reasoning (I) , 2011, Int. J. Cogn. Informatics Nat. Intell..

[6]  John C. Mitchell,et al.  Type Systems for Programming Languages , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[7]  Juris Hartmanis,et al.  On computational complexity and the nature of computer science , 1995, CSUR.

[8]  John V. Guttag,et al.  Abstract data types and the development of data structures , 1977, CACM.

[9]  L. A. Zadeh,et al.  Fuzzy logic and approximate reasoning , 1975, Synthese.

[10]  Yingxu Wang,et al.  On Cognitive Foundations and Mathematical Theories of Knowledge Science , 2016, Int. J. Cogn. Informatics Nat. Intell..

[11]  Yingxu Wang.  Cognitive Informatics: A New Transdisciplinary Research Field , 2003 .

[12]  Jennifer Widom,et al.  A First Course in Database Systems , 1997 .

[13]  P. Martin-Löf.  An Intuitionistic Theory of Types: Predicative Part , 1975 .

[14]  Yingxu Wang,et al.  On the informatics laws and deductive semantics of software , 2006, IEEE Trans. Syst. Man Cybern. Syst..

[15]  Yingxu Wang,et al.  Software Science: On the General Mathematical Models and Formal Properties of Software , 2014 .

[16]  Yingxu Wang,et al.  On the Cognitive Complexity of Software and its Quantification and Formal Measurement , 2009, Int. J. Softw. Sci. Comput. Intell..

[17]  Luca Cardelli,et al.  On understanding types, data abstraction, and polymorphism , 1985, CSUR.

[18]  Yingxu Wang,et al.  On Semantic Algebra: A Denotational Mathematics for Natural Language Comprehension and Cognitive Computing , 2013 .

[19]  Yingxu Wang,et al.  In Search of Denotational Mathematics: Novel Mathematical Means for Contemporary Intelligence, Brain, and Knowledge Sciences , 2012 .

[20]  Marina Chicurel,et al.  Databasing the brain , 2000, Nature.

[21]  A. M. Turing,et al.  Computing Machinery and Intelligence , 1950, The Philosophy of Artificial Intelligence.