It is discovered in the abstract intelligence theory [Wang, 2009; Wang et al. 2017] of intelligence science that AI may merely carry out imperative, reflexive, iterative and recursive intelligence. However, more sophisticated human intelligence such as those of cognitive, causal and inductive intelligence will hardly be implemented by the traditional computational power, because none of the advanced forms of aforementioned intelligence are iterative and the sizes of recursions are normally infinitive.    

Further information may be found in:

Wang, Y. (2009), On Abstract Intelligence: Toward a Unified Theory of Natural, Artificial, Machinable, and Computational Intelligence, International Journal of Software Science and Computational Intelligence, 1(1), 1-17.

Yingxu Wang, Lotfi A. Zadeh, Bernard Widrow, Newton Howard, Françoise Beaufays, George Baciu, D. Frank Hsu, Guiming Luo, Fumio Mizoguchi, Shushma Patel, Victor Raskin, Shusaku Tsumoto, Wei Wei, and Du Zhang (2017), Abstract Intelligence: Embodying and Enabling Cognitive Systems by Mathematical Engineering, International Journal of Cognitive Informatics and Natural Intelligence, 11(1), 1-15.

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